So you give someone an inch and they want a yard. Given them a rocket ship and suddenly they want a star ship. SF writers want to use exotic settings on alien planets, but the real estate in our solar system mostly looks like a bunch of rocks. "That's OK," the writer thinks, "There are a million-jillion other solar systems in the galaxy, surely they are not all a bunch of rocks (I know they are there, I've got a map). I know that those spoil-sports at NASA have ruined our solar system for SF writers since their nosy space probes failed to find dinosaur-infested jungles of Venus and scantily-clad Martian princesses. But they haven't sent probes to other stars yet! Why not turn my rocket ship into a star ship?"
Unfortunately it isn't that easy. The basic problem is that interstellar distances are freaking huge.
Let's make a mental model. Say the scale is such that one astronomical unit is equal to one millimeter (1/25th inch). There is a glowing dot for the Sun, and one millimeter away is a microscopic speck representing the Earth. The edge of the solar system is about at Pluto's orbit, which varies from 30 mm to 50 mm from the Sun (about 1 and 3/16 inch to almost 2 inches). Imagine this ten-centimeter model floating above your palm.
This would put Proxima Centauri, the closest star to the Sun, at about 272 meters away. That's 892 feet, the length of about two and a half football fields or four and a half New York city blocks! Glance at the ten-centimeter solar system in your hand, then contemplate the nearest solar system four and a half city blocks away.
And the center of the galaxy would be about 1600 kilometers away (about 990 miles), which is a bit more than the distance from Chicago, Illinois to Houston, Texas.
"All right, all right!" the SF author grumbles, "So the distance is outrageous. What of it?"
This of it. How long do you think it is going to take to travel such distances? As an example, the Voyager 1 space probe is currently the fastest human made object with a rest mass, zipping along at a blazing 17.46 km/s. This means that in the space of an eyeblink the little speed demon travels a whopping eleven miles! That's smokin'. What if it was aimed at Proxima Centauri (it isn't), how long would it take to reach it?
About 74,000 years! Which means that if Neanderthal men had launched something as fast as Voyager 1 to Proxima, it would just barely be arriving right now. And the joke's on them. Neanderthals are extinct so not even their descendants would reap the benefit of any scientific broadcasts from the Proxima probe. A similar argument could be used against any interstellar probes we could launch.
This leaves us with two alternatives: deal with the fact that average human lifespan is 74 years, not 74,000; or make the starship go faster.
Well, three, if you count "faster than light", but that will be covered later.
As Gordon Woodcock put it, the three methods of travelling to other stars are "go slow", "go fast", and "go tricky." This means "deal with short human lifespan", "use relativistic speeds", and "go faster than light". In other terminology:
- NAFAL: Not As Fast As Light = Go Slow
- AAFAL: Almost As Fast As Light = Go Fast
- FTL: Faster Than Light = Go Tricky
Distance between stars is huge, traveling said distance slower-than-light will take a huge amount of time, human beings have a very limited lifespan. And it is much easier to travel at 10% the speed of light than it is to travel at 99.99999% the speed of light
"Go Slow" means to focus on the limited human lifespan problem, and be content to travel slowly at 10% c or so.
There are several ways of dealing with the lifespan issue. See sub-sections below
Since every atom of mass is a penalty, the logical starship would just carry a master computer and no human crew. This avoids the payload mass of the crew, the habitat module, the life support system, food, water, and everything. The starship might be under a meter long, which would make this concept the lowest mass of all the slowboat starships.
However, nobody wants wants to read about the adventures of a computer (yes, I know there have been a couple of SF stories on this theme, but it requires extraordinary skill on the part of the author, and the stories are not wildly popular. With the exception of the Bolo stories by Keith Laumer et al.).
Enter the "digital crew" concept. You postulate technology capable of "uploading" human brain patterns into a computer. In essence, the ship's computer is running incredibly advanced simulations of the crew, creating a virtual reality much like that found in the movie The Matrix. This also allows the author to pontificate upon the nature of reality, ask if we are actually unaware virtual people in a virtual reality, and stuff like that. Authors who have used this concept include Sean Williams, Shane Dix, and Greg Egan.
The point is the author is allowed to write stories about human beings, but the digital humans and their digital environment take up zero mass.
One could add equipmment capable of manufacturing artificial bodies for the crew from local materials upon arrival at the destination. However, the advantage of a digital crew ship over a seed ship is the lower ship mass due to the absence of frozen embryos, artificial wombs, and robot mommies. Adding artifical body manufacturing facilites would reduce or remove the advantage. The only remaining advantage is that the new bodies inhabited by adults instead of babies.
You could regain the advantage if the manufacturing equipment is really tiny. Say a couple of grams worth of nanotechnology self-replicating machines, intended to work on handy asteroids or other free materials lying around the destination solar system. The nanotechnology bootstraps itself by replicating using in-situ resources as feedstocks until it has mass of a few tons, then shifts gears to start manufacturing artificial bodies.
The next higher mass class of slowboat is the Seed ship aka Embryo Space Colonization via an embryo-carrying interstellar spaceship (EIS). It will tend to have more mass than a Digital Crew ship and less than a Sleeper Ship.
The starship is tiny, containing a payload of millions of frozen fertilized eggs, artificial wombs, robot factory, and a master computer. No mass is needed for life-support, habitat modules, or any human crew.
After traveling for thousands of years, the ship lands in a good spot for a colony. The robot factory starts cranking out robots. Robots build the settlement buildings and start growing food (if the planet is really nasty they might have to spend a few centuries terraforming the planet first). Then the master computer thaws out enough eggs for the available artificial wombs, brings the babies to term, then tries to convince the babies that the robots are mommy and daddy.
I don't know about you but I suspect that the first generation is going to grow up a little bit emotionally stunted.
The most straightforward method is to cryogenically preserve human embryos. The more difficult but more flexible method is to carry frozen sperm and egg cells, and do in vitro fertilization at the destination. The most unobtanium method is to carry genetic information in computer files, then synthesize the required genetic sequences at the destination.
As with all interstellar colonization proposals, there are quite a few technological challenges to solve:
The ship robots will have to be advanced enough to raise and nurture the children, as well as building the settlement and growing crops. They could be teleoperated drones controlled by the ship's computer.
The side problem is they will have to be manufactured at the destination using in situ resources. The whole idea behind the Seed Ship is to minimize the payload mass, carrying an army of robots negates this.
Examples of Seed Ships in science fiction include The Songs of Distant Earth by Sir. Arthur C. Clarke, 2001 Nights chapter Night 4 by Yukinobu Hoshino, Long Shot by Vernor Vinge, Voyage from Yesteryear by James Hogan and the movie Interstellar.
Sleeper ship tend to have more mass than a Seed Ship and less than a Generation Ship.
The crew is frozen into suspended animation, so they do not age nor require food and oxygen during the thousand year journey. Or spacious living accomodations. The Sleeper Ship does require the mass of the crew, enough mass for a spartan habitat module, and only enough consumables for the time the crew will be awake.
Poul Anderson warned that frozen crew have a limited shelf life. Naturally-occurring radioactive atoms in the human body will cause damage. Normally the body will repair such damage, but one in suspended animation cannot. After a few hundred years, enough damage will accumulate so that a corpse instead of a living person is thawed out at journey's end. This may force one to thaw each crew member every fifty years or so to allow them to heal the damage, then freezing them again.
The highest mass type of slowboat tends to be the Generation ship. This is because it has to carry the mass of an entire community as crew, a habitat module at the minimum the size of a small town, and enough life support for the people for however many hundreds of years the journey takes. As the ship crawls to its destination, generations of people are born, have children, and die of old age.
If the generation ship is escaping from some Terra-destroying catastrophe; carrying Terra's scientific and cultural heritage, a representative sample of animal species, colony equipment and supplies, and a fertile representative sample of humanity, the craft is termed an Interstellar Ark.
Problems include the later generations refusing to cooperate with their forefather's vision, civil wars that wreck the ship, failure of the closed ecological life support system, ship arriving at the destination but the current generation does not want to colonize an icky dirty planet because they like living in their ship and the later generations forgetting where they came from, forgetting where they are going, and indeed forgetting the fact that they are in a starship. The classic "forgetting you are on a ship" stories are Robert Heinlein's Orphans of the Sky (1941) and Brian Aldiss' Non-Stop (1958).
In Larry Niven and Jerry Pournelle's FOOTFALL, the aliens deal with the "forgetful generation" problem by including a group of original crew frozen in suspended animation. Members of the original crew are periodically woken so they can ensure that the generational crew keeps the faith. The concept is sort of a combination of sleeper starship and generation starship.
The concept was sort of touched on in Don Wilcox's The Voyage that Lasted 600 Years (1940), though in that story only the captain was frozen. Since he was only a single person he had a limited influence on the generational tribes.
There are also disturbing ethical questions about the morality of condemning several generations of people to living inside a space-going rock. This can lead to political problems starting a Generation ship development project in the first place.
Noted SF author Kim Stanley Robinson apparently got very annoyed at people who dismissed the generation ship ethical questions while simultaneously being infected with a blind faith techno-utopianism over the feasibility of building a generation ship. Currently our technology has utterly failed to build a closed ecological life support system that can operate longer than a year or so, much less a couple of centuries. The same goes for spacecraft components. The second law of thermodynamics is a harsh mistress. The techno-utopians have to understand that there is no plan B.
As a sort of wakeup call, Mr. Robinson wrote the deliberately pessimistic novel Aurora about a disastrous generation ship heading for Tau Ceti and all the things that could and did go wrong. And the novel featured some techno-utopian characters in a most unfavorable light. The more optimistic members of the science fiction community have been raging at Mr. Robinson ever since.
A variation of the "Increase Lifespan" technique was in Charles Sheffield's Between The Strokes Of Night. A technique was discovered that would allow human metabolism to enter the "S-state." In this state, humans age at a rate 1/2000th normal, and perceive things at the same rate. There was also a protocol that would return an S-state person back to normal metabolism.
So with ships traveling at a slow 10% light speed, the trip to Proxima Centauri seems to take only a few weeks to an S-state person. Of course to a human in normal state, the trip will take about forty years.
As far as the S-state person is concerned, the ships are travelling faster than light. As long as they always stay in S-state.
To an S-state person, a normal state person moves so fast that they are invisible. To a normal state person, an S-state person appears to be immobile, though they are actually moving very very slowely. Of course to an S-stater all those normal state persons grow old and die 2000 times faster.
Finally there is the "Methuselah" concept. Advances in medical technology might increase human lifespan to thousands of years. So prolonged interstellar trips are more a problem of boredom instead of life-span.
The advantage is the starship does not have to carry the mass of the engine and the propellant, you leave it at home. This makes the task of designing the starship merely incredibly difficult, instead of utterly impossible.
The home system can also add to the laser batteries gradually after the starship's journey starts, as needed (the inverse-square law will weaken the beam as the range increases). You cannot do this with a self-contained starship, all of its engines have to be built before the journey starts.
And if a home system's laser battery or two break down, no problem! The resources of the home system are available to fix it. If a self-contained starship engine breaks down on the other hand, they are in trouble. They do not have the resources of the home system to help, all alone in interstellar space. They have to fix it themselves with whatever spare parts they managed to bring along. Or die all alone in the night.
The disadvantage is the starship is at the mercy of whoever is in charge of the laser station back in the Solar System. If there is a revolution back home and the Luddites seize power, the starship and crew are up doo-doo pulsar with no gravity generator. Dr. Forward came up with two clever ways of using the home system's lasers to decelerate the starship into the target solar system. In Larry Niven and Jerry Pournelle's classic The Mote In God's Eye the Motie aliens laser sail starship rather pointedly do NOT use Dr. Forwards deceleration methods, because they absolutely do not trust the laser station controllers back at their homeworld. In Dr. Forward's The Flight of the Dragonfly aka "Rocheworld" political foot-dragging and short-sighted policies almost lead to disaster for the laser station and starship. In Buzz Aldrin and John Barnes's Encounter With Tiber politics does kill the laser station and starship.
Starwisp is an ultra-low mass interstellar probe, a tiny sail driven by a beam of microwaves. The concept was invented by Dr. Robert L. Forward, and expanded upon by Dr. Geoffrey A. Landis.
Dr. Forward assumed that the microwave beam would be efficiently reflected by starwisp, so he calculated it would be a superconducting metal mesh with a sail mass of 16 grams and a payload mass of 4 grams; total mass of probe is 20 grams. Dr. Landis found this turned out not to be the case, it would absorb quite a bit of microwaves and heat up (i.e., the design is thermally limited). In Dr. Landis' design the starwisp is woven out of carbon wires with a sail mass of 1,000 grams, a payload mass of 80 grams, and a diameter of 100 meters.
Acceleration is 24 m/s2, microwave lens 560 km in diameter transmitting 56 GW of power, accelerating the probe to 10% of the speed of light.
Yes, it probably could be weaponized. See Accelerando by Charles Stross.
So your gigantic laser battery at home pushes the laser sail starship to its destination, accelerating it to about half the speed of light. Presumably you want to stop at your destination instead of streaking through it at 0.5c. But how?
If you were going about an order of magnitude slower, you might be able to use the sunlight from the destination star to put on the brakes. However that ain't gonna be enough at 0.5c. You'll just pancake into the star at a substantial fraction of the speed of light and be vaporized.
Dr. Philip Norem had a clever idea. Interstellar space has large magnetic fields. So one can use large electrical charges on the starship to make huge light-year wide sweeping turns by the Lorentz force.
Say you were going to Alpha Centauri. You aim the starship not at the destination, but instead off to one side. How far off depends upon the starship's turning radius. The laser battery back at the solar system pushed the starship up to relativistic velocities over the next 27 years or so. Then the lasers turn off.
The starship deploys one hundred metal cables, each about 50,000 kilometers long. It then charges them up to 800,000 volts and 3.7×104 coulombs. This is timed to interact with the interstellar magnetic field (as mapped) so that the starship makes a huge gradual turn, until it is approaching Alpha Centauri from the back door. That is, so that a line drawn from the starship to Alpha Centauri will pass directly through the solar system and the laser battery.
Meanwhile, the solar system laser battery starts up its barrage long enough in advance so that the leading edge of the laser wavefront will reach the starship just as it is aligned properly. It then continues the barrage for the years required to bring the starship to a halt exactly at Alpha Centauri.
In Mallove and Matloff's The Starflight Handbook, they note that if the interstellar magnetic fields have not been well mapped, this scheme could potentially doom the starship to a lonely death. If the starship misses the beam, it just goes sailing off into the Big Dark. The Starflight Handbook has the equations for a starship using the Lorentz force, if you are interested.
A related issue is mechanical reliability. Currently the best space probe NASA can build cannot be guaranteed to properly function past about forty years. The starship will need an extensive self-repair capability or have some way of having humans periodically available to fix things.
A common science fiction gag is the "jumping the gun" plot. A slower than light ship departs on a 500 year journey to Alpha Centauri. About 100 years after launch, some joker on Terra invents a faster-than-light starship. Fleets of FTL ships fly to Alpha Centauri and colonize the place. The slower than light ship arrives to find not the virgin planets they were expecting, but instead 400 year old colonies. Har, har, silly slowboat.
The earliest example of this trope that I could find was A. E. van Vogt's "Far Centaurus" (1944)
In 2006, scientist Andrew Kennedy actually studied the problem. He published his analysis in a paper called Interstellar Travel: The Wait Calculation and the Incentive Trap of Progress. In it, he introduced his solution: the Wait Calculation.
The Wait Calculation allows future space explorers to avoid the "jumping the gun" problem (and also avoid being paralyzed with indecision by terror of jumping the gun). The equation shows that, assuming technology develops in such a way that there is exponential growth in the velocity of travel, there is an optimal departure time for arriving earliest. Kennedy states that the equation applies even if somebody invents faster-than-light travel.
You see, there comes a time when although technological advances continues to produce higher speeds, the waiting time for that advance is too long to make up the velocity difference. If you wait too long for a higher speed, a slower ship launched sooner will have enough of a head start to beat you.
Distance between stars is huge, traveling said distance slower-than-light will take a huge amount of time, human beings have a very limited lifespan. And it is much easier to travel at 10% the speed of light than it is to travel at 99.99999% the speed of light
"Go Fast" means to focus on traveling near the speed of light so that relativity will partially fix things. Time dialiation will allow the crew to experience only a few months passing while traveling to a star 50 light years away. Travleing back home to Terra will add a few more months to the crew's experience. Unfortunately they will discover that 50+50 = 100 years have passed n Terra during their round trip. But you can't have everything.
Naturally to the SF author, the more attractive option is to increase the speed of the starship. But this too has several serious problems.
First off, the equation for deltaV coupled with the huge velocities required imply some truly ugly mass ratios. We are talking about a crew cabin the size of a coffin strapped to the nose of a rocket ten times the size of the Empire State building. Or worse.
And thirdly is the fact that space is not 100% empty. Remember Rick Robinson's First Law of Space Combat. At near light speeds hitting a dust speck will be like a contact explosion from a thermonuclear bomb. Indeed, individual protons will be transformed into deadly cosmic rays.
Einstein's theory of Special Relativity is an incredibly complicated topic, and I don't pretend to understand it all. Certainly I don't understand it enough to try and teach it. I'd advise you to go study the Wikipedia Special relativity for beginners or Jason Hinson's tutorial. If you want an intuitive feel for this: run, don't walk and get a copy of Poul Anderson's classic novel TAU ZERO.
But there are only a few specific implications of relativity that we have to worry about. Unless you are writing Gregory Benford style novels, in which case you know about the extra implications already.
First is of course the well-known fact that Special Relativity forbids any object possessing a rest mass from traveling at the speed of light in a vacuum (Which boils down to no FTL travel for you. Not yours. Science fiction authors have been cursing Einstein for decades over that one).
The second concern is "time dilation", crew members on a starship moving relativistically will age and experience time at a slower rate compared to people who stayed at home on Terra. The crew won't notice anything odd, until they return home to the Rip Van Winkle Experience. As a general rule, you can figure the start of "moving relativistically" is arbitrarily when the the dilation effect gets bigger than 1/100th. This is when γ equals 1.01, which happens at about 14% c.
Thirdly it makes calculating transit times and mass ratios much more difficult.
In relativistic equations, a common factor called gamma (γ) appears often. Its value depends on the velocity of the starship.
γ = 1 / Sqrt[ 1 - (v2 / c2) ]
- γ = gamma, the time dilation factor (dimensionless number)
- Sqrt[x] = square root of x
- v = current ship's velocity as measured in Terra's frame of reference (m/s)
- c = speed of light in a vacuum = 3e8 m/s
Or more conveniently, you can make c = 1.0 and v the percentage of c, e.g., a starship moving at three-quarters light-speed would have v = 0.75. The ship's γ would be about 1.51. In other words
γ = 1 / Sqrt[ 1 - (vpercent2) ]
vpercent = Sqrt[ 1 - (1 / γ)2 ]
- vpercent = current ship's velocity as measured in Terra's frame of reference (percentage of c)
How do you use gamma?
- Time : A viewer on Terra will observe the crew of a starship moving relativistically relative to Terra living in slow motion. One unit of crew time will pass during one unit times gamma of Terra time
- Mass : A viewer on Terra will observe a starship moving relativistically relative to Terra having an increased mass. The mass will be multiplied by gamma.
- Length : A viewer on Terra will observe a starship moving relativistically relative to Terra having its length in the direction of motion shortened. The width and height will be the same, but the length will appear flattened. The length will be divided by gamma.
If a starship is moving at 0.99c relative to Terra, it's γ = 7.09. When the crew mark off one day passing inside the ship (the so-called "proper time"), 1 day * 7.09 = 7.09 days will pass on Terra. From the view point of people on Terra, the starship crew will be living and moving in slow motion, experiencing time at about 1/7th the rate on Terra (Due to the weird non-intuitive implications of relativity, from the viewpoint of the crew it will be the inhabitants of Terra who are moving in slow motion, but if you are not going to take the time to learn more about relativity you'd best ignore this).
With respects to a viewer on Terra, the starship's mass will increase by a factor of γ (which makes relativistic kinetic weapons quite deadly). The ship's length in the direction of travel will decreased by a factor of 1/γ, but nobody cares since this has little practical effect other than making the ship look funny.
As a side note, at around 0.7 c the starship will be at Functional Lightspeed. This is because 0.7 c has a gamma of 1.4, and 1/1.4 is about 0.7 (unlike all the other values on the table). Well, actually after playing around on a spreadsheet it looks like it is closer to 0.707 c with a gamma of 1.414. But anyway:
What does this mean?
Say the good starship Breakaway is traveling to Alpha Centauri (distance 4.4 light-years) and is cruising at the Functional Lightspeed velocity of 0.7 c. The gamma is 1.4 and 1/γ = 0.7. From the viewpoint of the crew, the 4.4 light year distance appears to be only 3.1 light years (4.4×0.7=3.1 where 0.7 is 1/γ). The speed is still 0.7 c.
So for the crew, the trip will appear to take 4.4 years (3.1/0.7 where 0.7 is percent of lightspeed), where 4.4 is the quote "real" unquote distance to Alpha C in light-years. The crew will conclude they are traveling at one light-year per year, the speed of light, even though they are not. "Functional Lightspeed."
As another side note, the equation for gamma demonstrates how things go haywire when you calculate speed faster than light. Look at the formula for gamma above. If c = 1.0 and v = 2.0 (that is, a velocity of twice light speed), what is gamma?
Well, there is a problem there:
γ = 1 / Sqrt[1 - (v2 / c2)]
γ = 1 / Sqrt[1 - (2.02 / 1.02)]
γ = 1 / Sqrt[1 - (4 / 1)]
γ = 1 / Sqrt[1 - 4]
γ = 1 / Sqrt[-3]
The problem is when you try to take the square root of -3. If you try it on your calculator it will flash you INVALID INPUT! This is because there ain't no number you can multiply by itself to get a negative number (because a positive times a postive is a positive number, and a negative times a negative is also a positive). The only way you can get a negative number is by multiplying a negative by a postive, but by definition squaring a number means multiplying the same number together.
So if you try to calculate the gamma of a velocity faster than light, the equation blows up in your face.
Mathematicians have constructed towers of bizarre theories by saying "let's wave our hands and say there is weird number called i, such that i2 = -1." These are called, appropriately enough, imaginary numbers. The practical point is these numbers have been around since the 17th century, but they haven't helped much making a faster than light starship.
About now somebody has a question about adding velocity. If a starship is moving at half lightspeed, and somebody shoots their laser laser pistol in the direction of starship motion, how fast does the laser beam travel? Since the beam travels at 100% lightspeed and the starship is moving at 50% lightspeed, then the combined velocity should be 100 + 50 = 150% the speed of light, right?
Not so fast, it don't work like that, nohow. As it turns out, velocities do not add. Instead rapidities add. You have to use the relativistic velocity addition formula. Which is so constructed that no matter what the two velocities are or in which direction, adding them will never ever make a velocity faster than lightspeed. That noise you hear is the shade of Albert Einstein, snickering in the background. Curse you, Albert!
As a third side note, a kinetic energy weapon whose projectiles travel at 0.866 c the amount of kinetic energy is equal to the rest mass. Which means the projectiles contain the same amount of energy as if they were made out of pure antimatter.
γ = Cosh[a*T/c] (given acceleration and proper time)
γ = Cosh[(Ve / c) * ln(R)] (given exhaust velocity and mass ratio)
γ = Sqrt[1 + (a*t/c)2] (given acceleration and Terra time)
γ = a*d/(c2) + 1 (given acceleration and distance)
- a = acceleration (m/s2) remember that 1 g = 9.81 m/s2
- T = Proper Time, the slowed down time experienced by the crew of the rocket (s)
- t = time experienced non-accelerating frame of reference in which they started (e.g., Terra) (s)
- d = distance covered as measured in Terra's frame of reference (m)
- v = final speed as measured in Terra's frame of reference (m/s)
- c = speed of light in a vacuum = 3e8 m/s
- Δv = rocket's total deltaV (m/s)
- Ve = propulsion system's exhaust velocity (m/s)
- R = rocket's mass ratio (dimensionless number)
- γ = gamma, the time dilation factor (dimensionless number)
- Sqrt[x] = square root of x
- ln[x] = natural logarithm of x
- Sinh[x] = hyperbolic Sine of x
- Cosh[x] = hyperbolic Cosine of x
- Tanh[x] = hyperbolic Tangent of x
The hyperbolic trigonometric functions should be present on a scientific calculator and available as functions in a spreadsheet.
In many cases it will be more convenient to have T and t in years, distance in light-years, c = 1 lyr/yr, and 1 g = 1.03 lyr/yr2.
Here are some typical results with a starship accelerating at one gravity.
T Proper time elapsed t Terra time elapsed d Distance v Final velocity γ Gamma 1 year 1.19 years 0.56 lyrs 0.77c 1.58 2 3.75 2.90 0.97 3.99 5 83.7 82.7 0.99993 86.2 8 1,840 1,839 0.9999998 1,895 12 113,243 113,242 0.99999999996 116,641
Of course, as a general rule starships want to slow down and stop at their destinations, not zip past them at 0.9999 of the speed of light. You need a standard torchship brachistochrone flight plan: accelerate to halfway, skew flip, then decelerate to the destination (which makes sense, since such starships will have to be torchships). To use the above equations, instead of using the full distance for d, divide the distance in half and use that instead. Run that through the equations, then take the resulting T or t and double it.
But if you have more mathematical skills than I have, you could easily derive this short cut:
Tt = 1.94 * ArcCosh[dly/1.94 + 1]
- Tt = Proper Time experienced during a brachistochrone flight (years)
- dly = total distance to destination(light-years)
Remember this equation assumes a constant 1 g acceleration.
In plain English, it means you cannot figure out which of two objects are moving. For example: according to the equivalence principle, you cannot tell if you are standing stationary while a .22 caliber bullet travels at 340 meter per second and embeds itself in your ass OR if the .22 caliber bullet is hovering stationary while your ass travels backwards at 340 m/s and impales itself on the bullet. Well, ignoring things like the entire world and the atmosphere traveling backward along with you, but you see the principle.
"Who gives a rat's heinie?", I hear you exclaim. "What of it?"
This of it: there is no difference between a starship traveling at 0.01 c plowing through a stationary cloud of protons AND a stationary starship being hit by a lethal solar proton storm with radiation particles moving at 3,000 kilometers per second..
For all intents and purposes: a starship moving relativistically will find that the interstellar medium has been transformed into deadly radiation. Curse you, Einstein!
Oh, it gets worse. If you had ever studied kinetic energy weapons, you'd be aware that their destructive energy is equal to ½v2m, that is, 0.5 times the square of the velocity v times the mass m. This means if you get hit in the head by a 1 kilogram brick traveling at 1 meter per second; if the brick was reduced to 0.1 kilograms, to get the same sized headache you'd only have to increase the velocity to 3 m/s. Not to 10 m/s like you'd expect, because just a little bit of velocity increase makes a big difference in the destructive energy. You might have noticed in the equation that while the mass is just in there plain, the velocity is squared.
Getting back to starships: first off if the starship is moving at relativistic velocities (above 0.1 c), squaring that velocity is going to make a huge number. And secondly, space ain't 100% empty. Yes, the interstellar medium is pretty darn close to being a perfect vacuum, but that is not the same as zero atoms. When you are multiplying this by a relativistic velocity squared, every atom counts.
In other words, a starship traveling relativistically will suffer as if it was under bombardment by a particle beam weapon. Over every square centimeter of frontal surface area. For decades.
And if you hit something larger than an atom, like for instance a microscopic grain of interstellar dust, it will be like a shell from a naval 16-inch gun.
Within about 200 light-years of Sol the density is around 7×10-2 atoms/cm3, because Sol in inside a bubble. Elsewhere it varies from 10-4 to 106 atoms/cm3 depending upon what sort of space you are in.
Remember, this was one of the problems a Bussard Ramjet was designed to solve.
While the bombardment will erode away the solid metal of the leading edge of the starship, the main threat is the radiation. The bombardment will be functional equivalent of you basking your unprotected body in the radioactive glow of twenty unshielded nuclear reactors. According to Dr. Oleg Semyonov, the estimated radiation dose is about:
D = 1.67×10-8 × Q × n × S × β × c × H(β) × d(β) / M
D = radiation dose (rem/s)
Q = radiation quality factor (for protons Q = 10)
n = concentration of interstellar gas (cm-3) varies from 104 cm-3 om galactic clouds to less than 1 cm-3 between clouds. Around Sol 0.2 cm-3
S = cross-section of a human body (cm2) ≈ 104 was used in the paper
H = stopping power of particles in human tissue (MeV cm2/g)
d = EITHER penetration depth of particles in human tissue OR thickness of human body in direction of motion (35 cm), whatever is less (g/cm2)
M = mass of individual (g)
c = speed of light in a vacuum (cm/s) = 29,979,245,800 cm/s
β = percentage of the speed of light, v/c
Paper says The data for H and d as functions of energies of nucleons are taken from the NIST (National Institute of Standards and Technology) online database.
A safe dose is about 3×10-7 rem/s or about 10 rems/year.
The paper estimates that up to 0.3 c the radiation can be controlled with a titanium radiation shield about 2 cm thick. Above 0.3 c the thickness increases "dramatically". Around 0.8 c the titanium shield will have to be several meters thick.
You can find details and other equations in Radiation Hazard of Relativistic Interstellar Flight by Oleg Semyonov. Also fun reading is The Interaction Of Relativistic Spacecrafts With The Interstellar Medium.
As you may expect, the mass ratio for such rockets are generally absolutely outrageous. The "Relativistic Rocket" website made some estimates on the best possible mass ratios, assuming a 100% efficient photon rocket using constant acceleration.
R = (Mpt / Me) + 1, (1)
Mpt/Me = e(aT/c) - 1, (2)
Substituting (2) into (1):
R = e(a * T / c)
- R = mass ratio (dimensionless number)
- Mpt = Spacecraft's total propellant mass(kg)
- Me = Spacecraft's empty (dry) mass (kg)
- e = base of natural logarithms = 2.71828...(most calculators have an ex key, and spreadsheets have the exp() function)
Why are these mass ratios absolutely outrageous? Because it is probably impossible to make a single-stage spacecraft with a mass ratio over about 20. And because the mass ratios that come out of the equation are the theoretical maximums of a 100% efficient photon drive. Since a real rocket is not going to be 100% efficient, and may not be a photon drive, the mass ratio will probably be much worse than what the equation suggests. It is also important to keep in mind that one g of constant acceleration is pretty huge. If the Peek-A-Boo only does 1/10th g, it will take 30 years of proper time to get to Vega, but it will only need a mass ratio of 21.
A common feature of fantasy tales about the mystical land of Fairie is that time is weird there. Typically the protagonists will stumble into the Fairy Dimension, stay for what seems to be a few days, return to our mundane reality, and be shocked to discover that while they were in Fairie a century or two elapsed at home. Nobody recognizes the protagonist, any of their small children have since died of old age, that sort of thing. TV Tropes calls it Year Outside, Hour Inside. Older readers will recognize the concept from Brigadoon. Slightly less older readers read about this in Andre Norton's Dread Companion and Here Abide Monsters.
Science fiction authors writing about relativistic starships take great delight in transposing this concept into a future key. Starship crews leave Terra on a relativistic round-trip that takes a few months subjective time, then the author can write chapters and chapters about the bizarre Terran cultural changes and the cultural shock experienced by the "Rip Van Winkle" starship travelers. James Nicoll calls it the The Urashima effect of NAFAL travel. One-way time travel into the future, yes-siree-bob!
Science fiction that uses this theme include The Forever War by Joe Haldeman, Time For The Stars by Robert Heinlein, A World Out Of Time by Larry Niven, The Pusher by John Varley and the movie Interstellar.
Note that in The Forever War, Joe Haldeman cleverly uses the cultural shock experienced by the relativistic army troops as a metaphor for the cultural shock experienced by the US soldiers returning from Vietnam. As a side note: yes, the troops in The Forever War travel faster-than-light by collapsar jump. But to safely enter a collapsar the starship must move at relativistic speeds.
The crew and passengers on a relativistic starship will notice a peculiar optical illusion. The view of the sky will be distorted both fore and aft by relativistic aberration.
The starship at rest will see all the stars in the galaxy in their normal positions. The yellow lines show where stars located 90° from the ship's nose (pointed straight up). The green lines are for stars at 60°, the blue for 120° and so on.
But once the starship reaches a velocity larger than about 25% the speed of light in a vacuum (v/c = 0.25), the stars in the ship's "sky" won't be in their proper positions. The sky will warp so the stars will start to crowd towards that point where the ship's nose is pointing.
The stars with real positions closest to 90° are distorted the most, the stars fore and aft are distorted to a lesser degree. The stars at angle yellow should appear at 90°, but they have been distorted so they look like they are 75° away from the nose. The blue angle stars should be at 120°, but they appear at 105°. The red and light blue angle stars are at slightly different positions.
At 50% lightspeed (v/c = 0.50), yellow angle stars that should be 120° away from the nose point will have their positions distorted so they will appear to be at 90° i.e., around the ship's equator.
At 99.99% lightspeed (v/c = 0.9999), violet angle stars that should be 175° from the nose (i.e., 5° away from the stern) are distorted so much they look like they are only 15° from the nose. Only the stars that are almost exactly aft will appear there, almost all the other stars will be crammed straight ahead.
This will make navigation a bit of a challenge.
Doppler shift will make the stars ahead look more blue, and the stars behind will appear more red. The effect isn't really noticeable until the starship gets above 10% c or so. The effect is strongest directly ahead and behind, fading in strength the closer you get to the starship's "celestial equator" (i.e., at 90° to the ship's line of flight).
In 1961 Ing E. Sänger did some calculations that he published in a paper entitled "Some Optical and Kinematical Effects in Interstellar Astronautics", which appeared in the Journal of the British Interplanetary Society. He was trying to figure out what the sky would actually look like to a traveler in a starship moving at relativistic velocities.
He did make a simplifying assumption: all stars are monochromatic yellow.
Relativistic doppler shift would make most of the stars ahead invisible because their yellow light had been doppler blue-shifted into ultraviolet and x-rays. Most of the stars to the rear are invisible because they had been doppler red-shifted into infrared and microwaves.
Around the celestial equator the stars would still be yellow, shading to violet toward the zenith (in the direction of flight) and shading to red toward nadir. A rainbow in other words.
He calculated the addition of aberration would cram the rainbow ring toward zenith, while simultaneously making it narrower. The starship would appear to be flying in the direction of a rainbow ring.
Sänger called it a Starbow.
In 1972 noted science fiction author Frederik Pohl was reading a current issue of Spaceflight (published by the British Interplanetary Society) and came across a popularization of Sänger starbow concept. Mr. Pohl was thunderstruck at what a fantastically vivid metaphor the starbow was. He simply had to use it in his next science fiction story.
Said story was started almost as soon has he had finished the article. Do you know how large crystals are grown? You start with a jar filled with a supersaturated solution of whatever chemical the crystal is made of. Then you drop in a tiny seed crystal. In the solution the seed crystal rapidly grows into a larger one, incorporating the chemical molecules floating in the solution.
In this case, Mr. Pohl mind was full of random facts and half-baked ideas that could be used in future stories (I am given to understand this is common among many authors). That was the functional equivalent of a supersaturated solution. And the starbow concept was the seed crystal. A couple of his more interesting random facts suddenly attached themselves to the seed crystal and the story rapidly grew. It was called The Gold at the Starbow's End.
The story was well received, but more importantly it popularized the starbow concept. It became a standard part of any science fiction story featuring relativistic starships. It even made an appearance in Star Trek: The Motion Picture in 1979.
Unfortunately in 1979 the story caught the attention of two science fiction fans named John M. McKinley and Paul Doherty. "Unfortunate" because they were also physicists at Oakland University in Rochester, Michigan. They were inspired to examine the starbow concept more closely, and even do some computer simulations.
And they killed it. According to their simulations the starbow does not exist.
They reported their party-pooping results in a paper called “In search of the 'starbow': The appearance of the starfield from a relativistic spaceship.” (behind a paywall). As it turns out, stars do not emit only yellow monochromatic light. Instead they emit blackbody-like spectra and a distribution of temperatures. They integrated the transformed spectrum of a star, over the response function of the human eye. They also took into account relativistic beaming.
The computer simulations showed no starbow. You can see their disappointing images here.
McKinley and Doherty were apologetic about it, they didn't want to destroy such a memorable image. But physicists have to deal with reality, not fantasy.
Be that as it may there are still science fiction stories using the starbow because the word has not gotten around everywhere yet.
So, there is the obscenely-huge-mass-ratio problem, and the deadly-space-junk problem. SF authors were depressed. Then in 1960, a brilliant physicist named Robert W. Bussard proposed to use these two problems to solve each other.
If your starship is moving fast enough, the widely scattered hydrogen atoms will hit your hull like cosmic rays, and damage both the ship and the crew. One can theoretically use magnetic or electrostatic fields to sweep the hydrogen atoms out of the way so the ship doesn't hit them.
But wait a minute. Hydrogen is propellant, and could also be fusion fuel. Instead of sweeping it away, how about gathering it?
And if you are gathering your propellant instead of carrying it along with you, your mass ratio becomes infinity. This means you could theoretically accelerate forever.
This is the legendary "Bussard Interstellar Ramjet." No mass ratio problems, and no space junk problems. Pretty slick, eh? Accelerating at 1 g a Bussard ramjet could reach the center of the galaxy in a mere twenty years of proper time, and could theoretically circumnavigate the entire visible universe in less than a hundred years.
(Keep in mind that twenty years to the galactic core is in terms of "proper time", that is, the time as experienced by the crew. The people who stay at home on Earth will still see the Bussard ramjet taking the better part of 25,000 years to make the trip.)
The density of the vacuum of space is about 10e-21 kg/m3. This means you have to scoop a gargantuan 10e18 cubic meters in order to harvest a single gram of hydrogen. Bussard, working with an estimate of one hydrogen atom per cubic centimeter, and desiring a 1,000-ton spacecraft with an acceleration of 1 g, figured that the scoop mouth will need a frontal collecting area of nearly 10,000 km2. Assuming the scoop mouth is circular, I figure the mouth will have to be about 56 kilometers radius or 112 kilometers diameter. Other estimates have the scoop orders of magnitude larger. It is probably out of the question to build a physical scoop of such size, so it will have to be an immaterial scoop composed of magnetic or electrostatic fields.
Hydrogen ignores magnetic and electrostatic fields unless it is ionized. This means you will need a powerful ultraviolet beam or strong laser to ionize the hydrogen heading for the scoop.
A Bussard ramjet has to be boosted to a certain minimum speed before the scoop can operate. Estimates range from 1% to 6% of c, which is pretty awful. There is an equation here but it depends upon other assumptions about the minimum mass-collection rate.
The Sun has the misfortune to be located near the center of a huge region about 330 to 490 light-years in diameter called "The Local Bubble". The interstellar medium within the Local Bubble has a density of about 0.07 atoms/cm3, which is about ten times lower than in the rest of the galaxy. This makes a thin fuel source for a Bussard ramjet. The Local Bubble is thought to have been caused when the star Geminga went supernova about 300,000 years ago.
And to top it off, trying to use hydrogen in a fusion reactor would require mastery of proton-proton fusion, which is so much more difficult than deuterium fusion that some scientist doubt that we will ever learn how to do it.
But none of these were show-stoppers. There was a Renaissance of science fiction novels written using Bussard ramjets. Arguably the best is the classic Tau Zero by Poul Anderson, which you absolutely must read if you haven't already. Other include Larry Niven's Protector and short stories set in his "Known Space" series, Footfall by Larry Niven and Jerry Pournelle, A Deepness in the Sky by Vernor Vinge, and The Outcasts of Heaven's Belt by Joan Vinge.
Things started to unravel in 1978. T. A. Heppenheimer wrote an article in Journal of the British Interplanetary Society entitled "On the Infeasibility of Interstellar Ramjets." Heppenheimer applies radiative gas dynamics to ramjet design and proves that radiative losses (via bremsstrahlung and other similar synchrotron radiation-type mechanisms) from attempting to compress the ram flow for a fusion burn would exceed the fusion energy generated by nine orders of magnitude, that is, one billion times. The energy losses will probably show up as drag. This was confirmed by Dana Andrews and Robert Zubrin in 1989.
The effect of drag? What it boiled down to was that the ramjet had a maximum speed, where the relative velocity of the incoming hydrogen equaled the drive's exhaust velocity. It has a "terminal velocity", in other words.
A proton-proton fusion drive has an exhaust velocity of 12% c, so a proton-proton fusion Bussard Ramjet would have a maximum speed of 12% c. You may remember that a spacecraft with a mass ratio that equals e (that is, 2.71828...) will have a total deltaV is exactly equal to the exhaust velocity. So if a conventional fusion rocket with a mass ratio of 3 or more has a better deltaV than a Bussard Ramjet, what's the point of using a ramjet?
Things look bleak for the Bussard Ramjet, but it isn't quite dead yet. First off, Dr. Andrews and Dr. Zubrin's analysis depends upon certain assumptions. But even if the drag problem is as severe as calculated, there may be ways to avoid it.
The drag is caused by bremstrahlung and synchrotron radiation produced by the motion of the charged particles as they spiral through your collector fields and into your fusion chamber. It is theoretically possible to recover energy instead of it being wasted as drag. Then the energy could be added to the fusion energy and used to accelerate the exhaust stream, thus defeating the drag.
It would be a Bussard Scramjet, in other words.
But only theoretically. It is incredibly difficult, as in "we might not manage to do it with five hundred years of research" level of difficult.
The information here is mostly from Deep Space Probes: To the Outer Solar System and Beyond by Dr. Gregory Matloff.
The good news is that he managed to drastically reduce the drag.
The bad news is it uses an array of flimsy superconducting wires in front of the spacecraft. Which means only accelerations on the order of 0.04g are possible. That is about 50 snails worth of acceleration, which is pathetic.
Earlier attempts to stop drag used electrostatic fields for the scoop. But the Debye-Hückel screening effect raised its ugly head. The interstellar ions are charged (otherwise they wouldn't be ions), so are attracted to the electrostatic scoop. The trouble is the charge on the ions is also an electrostatic field. The huge cloud of attracted ions that gather in front of the scoop make a huge electrostatic field of their own (of opposite polarity), perfectly positioned to totally mask the scoop field. This screening ensures that ions further away do not even see the scoop field, forget about them actually being scooped up.
Others tried to eliminate the drag with standard Bussard electromagnetic fields by playing around with the geometry. Alas, most of the designs were better at reflecting away the ions instead of gathering them. Talk about counter-productive.
Cassenti's design was electromagnetic not electrostatic. Thus avoiding the heartbreak of Debye-Hückel screening.
And Cassenti's design did not affect the ions until they are actually inside the scoop, so there would be little or no ion reflection.
The scoop is a torus (donut shape) with a superconducting wire wound around the circumference. Depending upon the current direction and ion charge, an ion entering the torus will either be deflected to the center or the circumference. The idea is to deflect to center, so eventually they will enter the engine intake. Deflect to the cirumference would also be counter-productive.
So an ion in the interstellar media is just sitting around, minding its own business. Here comes the ramjet starship traveling at a sizable fraction of c. As the ion passes through the torus, it gets an electromagnetic shove to the center. As the ion passes further on, it gets closer and closer to the thrust axis. Using this information one can calculate the point where the ion hits the axis. This is where you put the engine fuel intake.
Cassenti analyzed a sample design of a ramjet with a scoop radius of 400 kilometers (800 km diameter), a supercurrent of 3×105 amps, twelve wire turns, traveling through the interstellar medium at 0.1 c. Using some hideous equations that I won't scare you with, Cassenti calculated that an ion entering the torus 200 kilometers from torus center would travel about 170 kilometers parallel to the thrust axis before it moved laterally enough to hit it.
Translation: the scoop torus will have to be held 170 kilometers in front of the engine fuel intake or the ions will miss the intake.
Since every gram counts and the freaking scoop is too huge to fit between New York and Cleveland the wire structure will have to be dangerously flimsy. Cassenti's design uses rotation produced centripetal force and minimal supporting structure, but still would collapse if the acceleration got above a measly 0.04 g.
His design had a featherweight mass of a few hundred thousand kilograms, making it very un-dense. This is about the mass of the International Space Station. But the scoop is more than seven thousand times as wide. Same mass but bigger means the torus is less dense than the ISS. And the station wasn't that dense to start with. Unfortunately very low density usually means flimsy, weak, and vulnerable to strong acceleration.
Cassenti looked into supporting the scoop with ion drive thrusters and/or laser beam radiation pressure (where part of the support structure is composed of beams of radiation with zero or almost zero mass), but one rapidly gets to the point of diminishing returns with that sort of thing.
A helpful reader named Yoel Mizrahi (יואל מזרחי) contacted me explaining that I had the design incorrect. Not surprising considering the sparse details I had. Mr. Mizrahi said Dr. Cassenti's design did not use fusion for propulsion. Instead it utilized beamed power. A large power plant back home at Sol energized a free-electron x-ray laser whose beam was sent to the light-years distant toroidal-field ramscoop. But instead of the laser beam pushing a laser sail, it is turned into electricity and used to accelerate the hydrogen scooped up.
So it is like a beam-powered RAIR with a no-drag scoop. The advantage of the toroidal scoop is that a conventional RAIR requires mass for fusion fuel and mass for the fusion reactor. In addition the conventional RAIR scoop suffers from drag. Beamed power is a good way to drastically reduced the mass of the propulsion system. The main drawback is that the starship is at the mercy of whoever back home controls the x-ray laser.
Advantages of toroidal scoop: does not waste mass on carrying propellant or energy. And the scoop is drag free.
Disadvantage: the acceleration of a toroidal scoop will be limited to about 0.4 m/s2 (0.04 g). The scoop does not gather a lot of hydrogen propellant due to the thinness of the interstellar medium, and due to the relatively small scoop radius. The exhaust consists of only light ions. More importantly, if the acceleration climbs above 0.4 m/s2 the flimsy scoop will buckle and collapse.
Technical challenges: designing a high-efficiency low mass x-ray power system. Figuring out how to use electricity to efficiently accelerate the scooped propellant.
Dr. Cassenti is going to send a copy of the scientific paper to Mr. Mizrahi, so stay tuned for more details. In the meanwhile, Mr. Mizrahi gave me these images:
I made some quick images with Blender 3D to figure out how the rigging worked:
The lure of infinite fuel is too big a prize to let go without a fight. The Bussard ramjet concept has gotten a lot of scrutiny, trying to derive a spin-off concept without the crippling flaws but with most of the benefits.
Basically, a RAIR carries its own fuel, but does not carry its own reaction mass.
Remember that fuel and reaction mass are generally not the same thing (unless you are dealing with a chemical rocket). For instance, in a nuclear thermal rocket, the fuel is the uranium or plutonium rods, and the reaction mass is the hydrogen propellant.
So the RAIR carries fusion fuel, feeding it to a fusion reactor in order to generate energy used to accelerate hydrogen gathered by the scoopfield. Since the RAIR carries its own fuel, it is not required to do proton-proton fusion, it is free to use whatever fusion fuel it wants.
The drag problem does not go away, but it is reduced. In a pure Bussard ramjet, the hydrogen scooped up has to be braked to a stop, creating drag (unless you can manage to make the hydrogen fuse while it is still travelling at whatever percentage of lightspeed the starship is travelling, which is pretty darn close to being impossible). In a RAIR, you do not have to slow the propellant down. You are left with the lesser problem of dealing with the braking effect of bremstrahlung and synchrotron radiation.
A related concept is the "Catalyzed RAIR." You still use a fusion rocket with internal fuel to get up to speed. But instead of heating the gathered hydrogen with the internal fusion reactor, you get it to do a low-grade reaction by itself.
You stick a target made of lithium or boron into the scooped hydrogen stream, as if it were the beam from a particle reactor. This will initiate a low-level lithium-hydrogen fusion reaction which will heat up and accelerate the rest of the stream. Lithium or boron fusion has the advantage of being almost totally without pesky neutron radiation.
Or if you want the ultimate Catalyzed RAIR, you just inject a steady flow of antimatter into the hydrogen stream. That will heat it up without requiring it to be braked to a stop first.
The draw-back to the RAIR is the fact that while the supply of propellant is infinite, the supply of fuel is not.
Thanks to Evan Rinehart for reminding me about this. It is from Are Black Hole Starships Possible. The basic idea is to see if the laws of physics will allow a practical starship using Hawking radiation of an artificial black hole as a power source.
The study authors saw the obvious fact that slower-than-light starships are going to need outrageous amounts of energy, and the two major theoretical possibilities were [a] antimatter and [b] primordial black holes.
They were looking into black holes because antimatter has lots of problems: manufacturing antimatter is outrageously inefficient, and if any of the fuel touches the fuel tank the entire starship blows up. Tiny black holes touching the fuel tank will just gobble big holes in the tank, and manufacturing black holes is mostly a matter of shoveling in enough matter into its bottomless gullet until it is the size you want (meaning it will require about a million times less energy than making antimatter).
However, astronomers have not noticed any of these primordial black holes lurking in our solar system. Believe me, they would have quickly spotted anything that gave off energy like detonating one W87 thermonuclear warhead every second. Which is most inconvenient, meaning if there are no primordial black holes nearby to scoop up and use, we'll have to manufacture one.
To simplify the math the study authors decided to just deal with Schwarzschild type black holes (with no spin or charge). Other people suggest that Kerr-Newman black holes give you more control, but I digress.
In 1975 legendary physicist Stephen Hawking discovered the shocking truth that black holes are not black (well, actually the initial suggestion was from Dr. Jacob Bekenstein). They emit Hawking radiation, for complicated reasons that are so complicated I'm not going to even try and explain them to you (go ask Google). The bottom line is that the smaller the mass of the black hole, the more energy and deadly radiation it emits.
Black holes with a mass of your average star or larger emit practically no energy. But you will get plenty of energy from naturally occurring small black holes are called "Primordial black holes."
The radiation will be the same as a "black body" with a temperature of:
6 × 10-8 / M kelvins
where "M" is the mass of the black hole where the mass of the Sun equals one. The Sun has a mass of about 1.9891 × 1030 kilograms or .
Jim Wisniewski created an online Hawking Radiation Calculator to do the math for you.
In the table:
- R is the black hole's radius in attometers (units of one-quintillionth or 10-18 of a meter). A proton has a diameter of 1000 attometers.
- M is the mass in millions of metric tons. One million metric tons is about the mass of three Empire State buildings.
- kT is the Hawking temperature in GeV (units of one-billion Electron Volts).
- P is the estimated total radiation output power in petawatts (units of one-quadrillion watts). 1—100 petawatts is the estimated total power output of a Kardashev type 1 civilization.
- P/c2 is the estimated mass-leakage rate in grams per second.
- L is the estimated life expectancy of the black hole in years. 0.04 years is about 15 days. 0.12 years is about 44 days.
"Lifespan?" I hear you ask. "What do you mean by Lifespan?". Well, as the small black holes emit energy, their mass also grows smaller. They gradually move up the table until their mass becomes zero. According to semi-classic physics, when the mass becomes zero the black hole explodes. So the ship will have to jettison the hole before that happens.
The black hole can be fed more mass, in theory, but that has problems. Trying to shove multiple kilograms of mass per second down a black hole with a mouth only a couple of attometers wide is almost impossible. Besides, the entire point of using a black hole was to avoid the entire mass-ratio problem. Feeding the hole with matter you carry along just puts you back at square one. The study authors assumed that the hole would not be fed during the journey.
Black Hole Generator
The black hole is artificially created by firing a huge number of gamma rays from a spherically converging laser. The principle is to pack enough energy into a small enough space to create the conditions of a black hole. Photons instead of particles are used to avoid the inconvenient Pauli exclusion principle.
The report talks vaguely about using "nuclear lasers" mentioned also vaguely in this report. They estimate that the laser and the lasing mass will have to be about 1010 tonnes, the size of a small asteroid.
Black Hole Drive
Proper Black Hole Size?
Now, the study authors figured that a black hole suitable to power an STL starship need the following:
- has a long enough lifespan to be useful
- is powerful enough to accelerate itself up to a reasonable fraction of the speed of light in a reasonable amount of time
- is small enough that we can access the energy to make it
- is large enough that we can focus the energy to make it
- has mass comparable to a starship
Luckily, it turns out that there are some sizes of black holes which fit all the parameters. It was not impossible that there existed no size that would fit them all simultaneously.
Long enough lifespan to be useful and powerful enough to accelerate itself up to a reasonable fraction of the speed of light in a reasonable amount of time?
For an upper limit on the most energy intensive trip, the authors used a starship on a one-way trip from Terra to Alpha Centauri with a 1 g acceleration/deceleration Brachistochrone trajectory. Proper time duration of the trip will be 3.5 years, so that sets the minimum black hole lifespan to 3.5 years, which corresponds to a minimum radius of 0.9 attometers.
A black hole with a radius of 0.9 attometers will have a mass of 606,000 metric tons and a power output of 160 petawatts. 20 days worth of output is enough energy to delta-V the 606,000 tonne black hole up to about 10% the speed of light, assuming 100% efficiency converting emitted energy to kinetic energy (the mass of the starship is probably negligible compared to the black hole). Increase the time to make up for the inefficiency, e.g., if the efficiency is only 10% then the output time becomes 200 days.
A trip proper time of 100 years requires a black hole with a radius over 2.7 attometers. This has a mass of 1,820,000 metric tons and radiates 17 petawatts. 1.5 years to delta-V up to 10% c at 100% efficiency.
The report makes a wild guess that an upper limit on starship trip proper time would be 1,000 years. This requires a black hole with a radius over 5.9 attometers. A black hole with a radius of 10 attometers has a lifespan of 5,000-odd years, mass of about 6,730,000 tonnes, and the radiated power drops to 1 petawatt. But there is a problem. At 100% efficiency this would take one hundred freaking years to delta-V up to 10% c.
Bottom line: a black hole with a long enough lifespan to be useful and is powerful enough to accelerate itself up to a reasonable fraction of the speed of light in a reasonable amount of time will have a radius between 1 and 6 attometers.
Small enough that we can access the energy to make it?
The Sun has a luminosity of about 3.8427×1026 W. This boils down to the equivalent of two million tonnes of energy in less than half a second. A square solar cell array with 100% efficiency and an edge length of 370 kilometers, in circular orbit around the sun at a distance of 1,000,000 kilometer, would in one year accumulate enough energy to make a black hole with a radius of 2.2 attometers.
Even with much less efficiency in the moving parts, this seems reasonable. No show stoppers here.
Large enough that we can focus the energy to make it?
The proposed black hole generator makes the initial hole using gamma ray laser beams (see above). Then it is installed in the starship.
The spherically converging gamma ray laser beams will need to focus in a region with a radius between 1 and 6 attometers. This will require gamma ray photons with an energy between 210 and 1,240 GeV. These will be very difficult to make. But we might be able to get away with using gamma ray photons with energies roughly matching the Hawking temperature of the black hole to be synthesized. This would be gamma ray photons with a more modest energy of 3 to 16 GeV. These are comparable to wavelengths within the Compton radii of nucleii, so are technically possible.
Mass comparable to a starship?
Black holes with radii between 1 and 6 attometers have mass ranging from 673,000 to 4,040,000 tonnes. Starships of equal mass would be quite large. And if need be several black hole engines can be used if you wanted a larger starship.
So the answer to the four questions are all "Yes."
A Quark Nugget is a chunk of "strange matter", which is composed of "strangelets", which are composed of roughly equal numbers of up, down, and strange quarks. In technical science speak it is described as Compact Composite Objects (CCOs) nuggets of dense Color-Flavor-Locked Superconducting quark matter created before or during the Quantum ChromoDynamics phase transition in the early universe. Now you know as much as I do.
Suffice to say that it is weird stuff.
Some scientist have become fascinated by the concept because:
- It can explain Dark Matter (or why is there over five times as much gravity in the universe than can be accounted for with observed matter?)
- It can explain the observed cosmological baryon asymmetry (that is, why isn't the universe half matter and half antimatter and thus suffering cosmic explosions every ten seconds?)
- It can explain both of the above within exisiting physics, you do not need to postulate some bizarre new particle.
Thomas Marshall Eubanks examined the concept and wrote a scientific paper about them. You can tell it is relevant to our interests by the title: Powering Starships with Compact Condensed Quark Matter.
He calculates that this stuff is everywhere, left over from the Big Bang. There must be tons and tons of it, because it causes Dark Matter gravity. The point being it should be readily available in our own solar system. Now due to the incredible density of quark nuggets, it is all going to be at the core of various solar system objects. We won't be able to mine any at the core of Sol, the planets, or the moons, but asteroids are a different mattter. Eubanks notes there do exist so-called Very Fast Rotating asteroids, the little whirling dervishes have rotation periods measured in tens of seconds. This is consistent with strange matter asteroids with core masses between 1010 and 1011 kilograms (50 million metric tons). The cores can be extracted and used (but alas cannot be subdivided, the mutual attraction is too strong). The cores will typically be about one millimeter in radius.
Why do we care?
Because such quark nuggets can be used as SUPER-EFFICIENT ANTIMATTER FACTORIES, that's why.
Using Andreev reflection you could create about 109 kilograms (1 million metric tons) of antimatter before the nugget wore out. You bombard the nugget with a 100 MeV particle stream and some of the particles will transform into their antiparticle (it is actually more complicated than that, but who cares?). Each 1010 kg of quark nugget can produce 109 kg of antimatter.
One the one hand it is far easier to generate antimatter as you need it, instead of trying to carry a million tons of touchy antimatter. Especially since an antimatter containment failure would make an explosion big enough to obliterate an entire solar system.
On the other hand it will be a major engineering feat to drag along a quark nugget with a mass that is a substantial fraction of the weight of Mount Everest. That's why I filed this here in the "Starship" page instead of the "Engines You Can Use Within The Solar System" page.
The URSS Alabama is a fictional Bussard Ramjet starship from Alan Steele's novel Coyote (2002). It was the first starship, build by the authoritarian conservative regime which took over after the fall of the United States. At its dedication ceremony, it is hijacked by the captain, and escapes the regime by travelling to 47 Ursae Majoris. The 46 light-year journey takes 230 years cruising at 0.2c, with the crew and colonists in biostasis.
The good starship ISV Venture Star from the movie Avatar is one of the most scientifically accurate movie spaceships it has ever been my pleasure to see. When I read the description of the ship, I got a nagging feeling that something was familiar. A ship with the engines on the nose, towing the rest of the ship like a water-skier? Wait a minute, that sounds like Charles Pellegrino and Jim Powell's Valkyrie starship.
Well, as it turns out, there was a good reason for that. James Cameron likes scientific accuracy in his movies. So he looked for a scientist who had experience with designing starships. Cameron didn't have to look far. As it turns out he already knew Dr. Pellegrino. This is because Dr. Pellegrino had worked with Cameron on a prior movie, since Dr. Pellegrino is one of the worlds greatest living experts on the Titanic.
In the upper diagram is a green arrow at the ship's nose, indicating the direction of flight. The ship is 1.5 kilometers long. In the Sol departure phase, a battery of orbital lasers illuminates a 16 kilometer diameter photon sail attached to the ship's nose (sail not shown). A mirror shield on the ship's rear prevents the laser beams from damaging the ship. The lasers accelerate the ship at 1.5 g for 0.46 year. At the end of this the ship is moving at 70% the speed of light (210,000 kilometers per second).
Keep in mind that battery of orbital lasers is going to have to be absolutely huge if it is going to push a lightsail at 1.5 g. This is not going to be a tiny satellite in LEO.
I cannot calculate the exact power rating since figures on the mass of the ISV Venture Star are conspicuous by their absence. The equation is Vs = (2 * Ev) / (Ms * c) where Vs is the starship acceleration, Eb is the energy of the beam, Ms is the mass of the starship, and c is the speed of light in a vacuum. Dr. Geoffrey Landis says is boils down to 6.7 newtons per gigawatt.
In Dr. Robert Forward's The Flight of the Dragonfly (aka Rocheworld), his starship's light sail is illuminated by a composite laser beam with a strength of 1500 terawatts. This pushes the starship with an acceleration of 0.01g (about 150 times as weak as the acceleration on the Venture Star). The beam is produced by one thousand laser stations in orbit around Mercury (where solar power is readily available in titanic amounts). Each station can produce a 1.5 terawatt beam, 1500 terawatts total. By way of comparison, in the year 2008, the entire Earth consumed electricity at a rate of about 15 terawatts. Since the Venture Star appears to be more massive than Forward's starship, and is accelerating 150 times as fast, presumably its battery of laser cannons is orders of magnitude larger.
As a side note, it is good to remember Jon's Law for SF authors. and The Kzinti Lesson. While technically this laser array is a component of a propulsion system, not a weapon; in practice it will have little difficulty vaporizing an invading alien battlefleet. Or hostile human battlefleet, for that matter (with the definition of "hostile" depending upon who actually controls the laser array). As Commander Susan Ivanova said in the Babylon 5 episode Deathwalker: "Our gun arrays are locked on to your ship, and will fire the instant you come into range. You will find their firepower most impressive ... for a few seconds."
Anyway, after the laser boost period is over, the sail is then collapsed along molecular fold lines by service bots, and stowed in the cargo area. The ship then coasts for the next 5.83 years to Alpha Centauri.
There are no batteries of laser cannon at Alpha Centauri so the lightsail cannot be used to brake to a halt. Instead, the twin hybrid fusion/matter-antimatter engines are used. These engines are not used for the Sol departure phase because that would increase the propellant requirement by about four times with a corresponding decrease in cargo capacity. The engines burn for 0.46 year, producing 1.5 g of thrust, thus braking the ship from a velocity of 70% c to zero.
Matter and antimatter is annihilated, and the energy release is used both in the form of photons and to heat up hydrogen propellant for thrust. A series of thermal shields near the engines protect the ship's structure from the exhaust heat. The engines are angled outwards a few degrees so that the exhaust does not torch the rest of the ship (exhaust path indicated in diagram by red arrows). This does reduce the effective thrust by an amount proportional to the cosine of the angle but is acceptable.
Why is most of the ship behind the engine exhaust? Because this reduces the mass of the ship. And when you are delta-Ving a ship up to and down from 70% c, every single gram counts. Conventional spacecraft have the engines on the bottom and the rest of the ship build on top like a sky scraper. This design has the engines on the top and the rest of the ship is dragged behind on a long tether (the "tensile truss" on the diagram). The result is a massive reduction in structural mass.
The engines are topped by monumental heat radiators used to get rid of waste heat from the matter-antimatter reaction. According to the description, after the burn is finished, the radiators will glow dull red for a full two weeks.
Immediately stern ward of the engines is the cargo section. It is arranged in four ranks of four modules each. Each module contains 6 cargo pods. A mobile transporter with a long arm moves within the cargo section in order to load and unload the shuttles.
Next comes Two Valkyrie trans-atmospheric vehicles, aka "surface to orbit shuttles." They are docked to pressurized tunnels connected to the habitation section. Each is capable of transporting either:
- the contents of two cargo pods and 100 passengers OR
- the contents of six cargo pods and no passengers
Next come the habitation module. This holds the passengers in suspended animation for the duration of the trip. This is constructed almost totally from non-metallic materials, to prevent secondary radiation from galactic cosmic radiation.
The habitation module's life support system can only support all the passengers being awake for a limited time. There is no problem for the short period when the passengers are woken up and shuttled to the planet's surface. However, if the suspended animation system malfunctioned half-way through the multi-year voyage, life support could not handle it. In theis case, the passengers would be "euthanized" instead of being awakened.
Next is the two on-duty crew modules. These are spun on the ends of arms to provide artificial gravity. When the ship is under thrust, the spin is taken off, and the arms are folded down along their hinges so that the direction of gravity is in the proper direction.
Finally comes the shield. While the ship is being boosted by the laser batteries, the shield protect the ship (but not the sail) from the laser beams. After boost, while the ship is coasting at 70% c, the ship is rotated so that the shield is in the direction of travel. The shield is constructed as a Whipple shield, and protects the ship from being damage by grains of dust.
At 70% c relative, each dust grain would have 4,900,000,000 freaking Ricks of damage. This means a typical interstellar dust grain with a mass of 4 x 10-6 grams will hit with the force of 20 kilograms of TNT, or about the force of four anti-tank mines.
When the ship wants to depart Alpha Centauri and return to Sol, it re-fills its antimatter and propellant tanks from the local fueling stations, uses the matter-antimatter engines to boost up to 70% c again, coasts for five-odd years, and is decelerated to a halt by the laser batteries at Sol.
This is from Colonized Interstellar Vessel: Conceptual Master Planning by Steve Summerford (2012)
The focus of the report is on the habitable space of the starship. It is assumed that any suitable interstellar propulsion system can be attached, so that is outside the scope of the report. Some sort of fusion power generation is assumed, since the inverse-square law will solar photovoltaic panels worthless long before the edge of the solar system is reached.
Mr. Summerford notes that all those images of generational starships built inside hollow asteroids are very pretty, but it will be centuries before our technology is up to actually building one. Let alone paying for it. Yes, it would be real nice to have a starship environment that looks like Terra. But in the spirit of learning how to walk before you run, perhaps it would be best to design a more modest starship. True, the enviroment will probably look more urban and less like rural. However it will be pleasant to have a design we can actually build. And pay for.
The drawback is that while the other methods only have to worry about breakdowns of the ship's technology, generational ships have to also worry about social breakdowns of generations of inhabitants. So attention must be paid to preservation of the physical, spatial, and psychological needs of the colony. It wouldn't do for the starship to fail because the fifth generation snapped psychologically due to living for 125 years inside miserable little steel boxes. These design problems are just as important as matters of radiation shielding, fuel suppply, and food production.
Therefore the report does devote some space to issues such as architecture, healthy community living, privacy needs, and other "soft" problems. Many of the principles come from basic urban planning.
To expand a Standford Torus, the logical method would be to stack several toruses. But this would be an engineering nightmare, and a wasteful increase of mass. Instead, a banded cylinder design is used. Flat-bottomed faceted cylinders called "bays" are used. This allows sufficient colonial living space while maintaining a compact vehicle design.
Each bay contains dwellings, agicultural areas, civic structures, open spaces, an places of work and research.
To avoid spin nausea, the spin rate should be no more than about 2 rpm. The design goes with 1.5 rpm, spin radius of 400, meters, and an artificial gravity of 1.0 g. A rate of 2.0 rpm was looked at to reduce the spin radius, but the increase in the coriolis effect was considered unacceptable.
For urban planning, they use a metric called "floor-to-area ratio" or FAR. In a site, you take all the buildings therein, and add up the surface area of all the floors in all the buildings. This is the "floor". Divide by the surface area of the site and you have the FAR. Example: if a site with a surface area of 10,000 m2 had a single bulding, and it was a four story building with each floor containing 2,500 m2, then the FAR would be 1.0. The FAR of the generation ship was set to from 1.25 to 1.75 in an attempt to enforce some park like open areas with no buildings.
There is not one, not two, but three different slower-than-light starships in Encounter With Tiber by Buzz Aldrin and John Barnes.
9,000 years ago, the aliens ("Tiberans") living around Alpha Centauri A become aware of a rogue planet that is going to drastically lower the property values of their home planet. They need to migrate their civilization to another planet, and their is not any suitable candidates in the Alpha Centauri star system. So they take a look at our Solar System.
In the 73rd century BCE they mount an interstellar scouting mission to Terra, using the starship Wahkopem Zomos. The mission mysteriously fails. In the 72nd century BCE a follow-up mission is sent, using the starship Egalitarian Republic. It fails as well.
Around 2030 we humans discover artifacts from the two alien mission on Luna's south pole and on Mars. In 2069 a mission is sent to Alpha Centauri to make first contact, using the starship Tenacity.
A plasma-core antimatter booster section sends the starship Wahkopen Zomos into a close perihelion approach to the primary star (Alpha Centauri A). A 1000 kilometer diameter solar sail is unfurled. This accelerates the ship to a close approach to Alpha Centauri B for a second perihelion manoeuvre. It is then further accelerated by lasers until it reaches a velocity of 0.4c. It then cruises to Sol for about 18 (alien) years.
Approaching Sol, it deploys a "brakeloop" of superconducting wire 100 kilometers in diameter. This converts the ship's kinetic energy into heat in the interstellar medium. Two years of braking is enough to slow the starship into the solar system.
The plan was for the homeworld to launch a 5000 kilometer laser sail and guide it into the solar system. Then it could reflect laser beams on to the Wahkopen Zomos' sail and return it to Alpha Centauri A. Unfortunately politics at home led to abandoning this plan, thus stranding the Wahkopen Zomos. This is an occupational hazard for laser lightsail starships. The advantage is you leave at home your engine and its inconvenient mass. The disadvantage is you are at the mercy of the people at home (and their political parties) who control the engine.
During acceleration the ship emits a spray of antiprotons as a starship bumper to ward off relativistic dust particles in the interstellar medium. Since the antiproton energy release will be on the side of the dust particle facing the ship, the energy will propel the dust out of the ship's path. This does cause a bath of gamma rays over the ship's nose so there is extra shielding there.
During deceleration the fury of the photon drive will vaporize and ionize any dust particles that get in the way.
The ship can hover in a pseudo-orbit over a given spot on a planet, boosted by the photon drive. However if the spot was on dry land, it would rapidly turn into a gigantic volcano.
The Tenacity gets its initial impetus from a ring of antimatter-powered booster rockets around its tail. The main propulsion is a battery of Casimir-effect lasers, thirty zero-point-energy lasers (photon drive). The acceleration is 0.06 g. On the trip to Alpha Centauri it will accelerate for several years to a speed of 0.75 c. Once the ship enters the Alpha C system and comes within 35 AU of the primary star, it will deploy a magnetic loop brake to decelerate. That will take about two years.
The Enzmann starship is a concept for a manned interstellar spacecraft proposed in 1964 (date is disputed) by Dr. Robert Enzmann. Over the years the basic design has evolved, and there were several types in the initial design. It was quite popular in the science fiction community. An analysis of the Enzmann starship can be found here.
In 1972 space artists Don Davis and Rick Sternbach worked with Dr. Enzmann to develop the idea. This refined the "lollypop" look of the ship. For some odd reason most paintings of the Enzmann starship show two of them in formation. The original design had a naked sphere of frozen deuterium as fuel. Calculations with Sternbach and Davis revealed that the deuterium could not be kept frozen and was too structurally weak to be accelerated. So the redesign encased the deuterium in a huge tank.
The Enzmann exploded into the science fiction community with the October 1973 issue of Analog magazine. G. Harry Stine wrote an extensive article about the concept, accompanied by a stunning piece of cover art by Rick Sternbach. Stine said the ships were 12 million tonnes, could reach 0.30 c (highly unlikely), had 8 engines, and used spinning habitats for artificial gravity.
- Command center 30 meters in diameter
- Central core load bearing struture 15 meters diameter
- Frozen deuterium 300 meters diameter
- Living modules 90 meters diameter × 90 meters long
- Engineering compartments 70 meters diameter
In Science Digest, Rick Sternbach's 1972 piece depicts a pair of Enzmanns departing from an asteroid factory. The number of engines was increased from 8 in the original design to 24. Modular sections were created that can separate from the starship. Height of starship was 690 meters. 3 million tonnes of deuterium, with metal shell (doubling as a radiation shield). Magnetic confined fusion propulsion. 20 decks per habitat, 100 rooms per deck. Cruising speed 0.09c.
Thomas Schroeder wrote an article entitled "Slow Boat to Centauri" in Astronomy Magazine. Claimed a cruising speed of 0.1c, and an advanced design might reach 0.3c. 12 million tonnes deuterium. The outer layers of the habitats were composed of bulk material as radiation shielding for the inner layers. Bulk means nuclear reactor, store rooms, heat exchangers, airlocks, landing craft, observation areas, communication equipment. Eight Project Orion nuclear pulse units.
- Frozen deuterium 305 meters diameter
- Height 609.6 meters
- Living modules 91.5 meters diameter × 91.5 meters long
- From bottom of fuel sphere to top of Orion engines 305 meters
In the 1980's Dr. Enzmann started designing variants.
In 2011, K. F. Long, A. Crowl, and R. Obousy did a study on the Enzmann starship, and tried to rationalize it with recent developments in astronautics. First they took the historical concepts:
|Sphere Diameter||305 m||same||same|
|Total Habitat Length||273 m||same||same|
|Individual Habitat length||91 m||same||same|
|Habitat Diameter||91 m||same||same|
|Core Diameter||15 m||same||same|
|Propellant Mass||3×106 metric tons||12×106 metric tons||3×106 metric tons|
|Cruise Speed||27,000 km/s|
Long et al created three variants. The primary difference is the size of the population carried. The rest of the design was re-sized to handled the population. As near as I can calculate, the cruise and mission times for all three are for a mission to Alpha Centauri.
|Specific Power||11.5 MW/kg|
|Thrust Power||344 terawatts|
|Length||620 m||979 m||1752 m|
|Dry Mass||30,000 MT||300,000 MT||3,000,000 MT|
|Propellant Mass||3 × 106 MT||3 × 106 MT||3 × 106 MT|
|Exhaust Velocity||11,700 km/s||11,260 km/s||12,119 km/s|
|Cruise Velocity||27,000 km/s|
|18.95 yrs||98.67 yrs||84.9 yrs|
|41.05 yrs||51.33 yrs||265.1 yrs|
|60 yrs||150 yrs||350 yrs|
|Mass Flow Rate||5.02 kg/s||0.96 kg/s||1.12 kg/s|
|Thrust||58,730 kN||10,810 kN||13,573 kN|
|Exhaust Velocity||9.99×107 m/s|
|Thrust Power||587.4 TW|
|Average Accel||0.098 m/s|
|Gamma radiation||996.3 TW|
|Dust Shield||6,530 MT|
|Power Systems||1,064.6 MT|
|Payload Rad Shield|
|Radiator Rad Shield||6.4 MT|
|Magnet Rad Shield||103.3 MT|
|R. R. + |
|Total Dry Mass||70,940.6 MT|
|Engine Magnet Radiation Shield|
|cross-section area||0.088 m2|
to ignition point
to ignition point
|fraction of gamma|
|Radiator Radiation Shield|
|cross-section area||2.488 m2|
to ignition point
to ignition point
|fraction of gamma|
|System & Payload|
|cross-section area||311.026 m2|
to ignition point
|fraction of gamma|
|2-sided area||1.025×107 m2|
This is from AIAA 2003-4676 How To Build an Antimatter Rocket For Interstellar Missions by Robert H. Frisbee. The basic spacecraft has a delta V of one-quarter the speed of light and an acceleration of 0.01 g. The freaking thing is about 700 kilometers long (about the distance between Washington DC and Montpelier Vermont), due to the off-the-chart levels of gamma radiation and the 500 kilometers of heat radiators required to keep the ship from vaporizing.
Most of the 500 km of heat radiators is to reject the gamma-ray heat absorbed by the radiation shields.
The superconducting magnet in the engine proper is kept cool to 100 Kelvin, the liquid hydrogen is cooled to 20 K, and the solid anti-hydrogen pellets are cooled to 1 K.
On the nose is the dust impact shield, which protects against interstellar dust impacts. Because at 0.25 c even a speck of dust is going to hurt.
Everything you hit will have about 625 mega-Ricks worth of damage. This means if you hit a grain of sand that had a mass of one milligram (10-3 kg), it would explode with about the force of 625 metric tons of TNT. Now your average interstellar dust grain has only a mass of 10-17 kg which makes the boom much smaller. Unfortunately the interstellar medium has a dust density of 10−6 × dust grain/m3, and there are a lot of meters in a light year.
My slide rule says a cylinder with a diameter of 19.9 meters and a length of one light-year will contain about 2.94×1018 m3. This is the volume the nose of the starship will plow through per one light-year of travel. At a dust density of 10−6 grain/m3 means the nose will hit 2.94×1012 dust grains. 10-17 kg per grain means total mass impacting the shield per light year is 2.94×10-5 kg. At 625 mega-Ricks this means it will only subject the dust shield to the equvalent of an explosion of 18.4 metric tons of TNT. Per light year.
The design specs called for a cruising velocity of 0.5 c, which means you'd need four stages, that is, a stack of four of these monsters. One stage to boost up to the coasting speed of 0.5 c, second stage to brake from 0.5 c to halt at the destination, third stage to boost to 0.5 c for the trip home, and 0.5 c to brake to a halt at Terra. The four stage vehicle will have a length between 1,900 and 7400 kilometers, depending upon the technology assumptions. Egads.
As it turns out the starship needs a minimum acceleration or it will take a century to get up to speed. Dr. Frisbee drew up the above chart and figured if you wanted to maximize the mission time spent at peak velocity the starship would have to be capable of accelerating and decelerating at about 0.01 gee minimum. The trouble is that beam core antimatter drives are classic high specific impulse/low thrust rockets. This means you have to really crank up the propellant mass flow if you want to get 0.01 g. Which means the engine mass will skyrocket.
Another problem with using proton-antiproton antimatter rockets is that only 22% of the propellant mass actually propels the starship. The rest is wasted. This means that the standard delta V equation has to be modified to take this into account. It needs to be modified further for relativity if the delta V is substantial fractions of the speed of light. The equation was use to draw the graph above. The equation itself is below.
So a normal rocket that does not annihilate its reaction mass so that 100% of it propels the starship uses the standard delta V equation. This says if the specific impulse is 0.33 c and the delta V is 0.25 c, the mass ratio would be a modest 2.15. But for this antimatter rocket with only 22% of the propellant working (a=0.22), the mass ratio climbs to 5.45. By doing some estimates on the minimum tankage masses, Dr. Frisbee concludes that 0.25 c is the maximum delta V per stage of the starship. You can read his reasoning in the report.
It is bad that only 22% of the propellant is doing its job. What is worse, 38% of the propellant mass is turned into deadly gamma rays that will fry anything unprotected from their deadly shine. This means heavy radiation shields, which need 500 kilometers of heat radiators to keep the gamma-ray heat from vaporizing them. This also forces the vehicle to be long and narrow to minimize the solid angle of intercepted gamma radiation from the engine.
|Mission Duration||48 years|
|Cruise Phase||44 years|
|Boost Phase||2.05y (stage 1)|
+ 1.78y (stage 2)
|Wet Mass||5.4×107 kg|
|Propellant Mass||5.0×107 kg|
|Dry Mass||4×106 kg|
|Payload Mass||450,000 kg|
|Min Kinetic Energy to cruise speed||3.5×1022 J|
|Min Power to cruise speed||291TW|
|Pellet pulse freq||250Hz|
|Stage Dry Mass||1.69×106 kg|
|Num Propellant Tanks||x6|
|Propellant Tank Mass||7.666×106 kg|
|Total Propellant Tank||4.5996×107 kg|
|Stage Wet Mass||4.7686×107 kg|
|Accel (1st stage ignition)||0.14 m/s2|
|ICF capsule Q||63|
|Exhaust Velocity||1.06×107 m/s|
|Specific Impulse||1.08×106 sec|
|Stage Dry Mass||9.8×105 kg|
|Num Propellant Tanks||x4|
|Propellant Tank Mass||1.0×106 kg|
|Total Propellant Tank||4.0×106 kg|
|Stage Wet Mass||4.98×106 kg|
|Accel (2nd stage ignition)||0.13 m/s2|
|Accel (2nd stage burnout)||0.676 m/s2|
|ICF capsule Q||35|
|Exhaust Velocity||9.21×106 m/s|
|Specific Impulse||9.39×105 sec|
This was a study conducted between 1973 and 1978 by the British Interplanetary Society to design a plausible uncrewed interstellar spacecraft. Yes, it is naught but a mere space probe, but it is a starship.
Given the mission parameters and state-of-the-art of various propulsion designs, the study chose an inertial-confinement fusion engine. In an effort to cut down on radiation shield mass, they selected the close-to-aneutronic deuterium—helium-3 fuel. A neutron radiation shield protecting a starship 190 freaking meters long will savagely cut into the payload mass. Since there isn't enough helium-3 in the entire world, the study proposed a titanic mining operation to gather the stuff from Jupiter's atmosphere. The study details about 3He skimming is why the Traveller role-playing-game allows "Wilderness Refueling". But I digress.
Even using a two stage fusion propulsion system, Daedalus could only get up to 12% the speed of light, and could not slow down. The good news is it only takes 48 years to reach Barnard's Star (so some of the scientists who sent it might actually live long enough to see the data). The bad news is since it cannot slow down, it will streak through the Barnard's system at 12% c and have only a couple of days to frantically take pictures and do all the science it possibly can. Basically if Daedalus was designed so it could come to a halt at the Barnard system, the trip time would double to about 96 years. This would guarantee that all the scientists who sent the blasted ship would be long dead of old age, which makes it hard to work up any enthusiasm to work on the project. Or to convince the public to fund it.
|Inertial Confinement Fusion|
|1||Pellet Injection Gun|
|2||Superconducting field coils (4)|
|3||Electron beam generators|
|4||Plasma exhaust jet|
|6||Energy extraction coils|
|7||Frozen nuclear pellet|
Project Icarus is a design study to create an unmanned probe starship to investigate a nearby star. It was inspired by the old Project Daedalus study. In 2013 they had a "contest" for research groups to submit proposed designs given some pre-defined limitations.
|Wet Mass||17,800 metric tons|
|Dry Mass||2,365 metric tons|
|Payload||150 metric tons|
|Propulsion||Z-Pinch DD Fusion|
|Exhaust Velocity||1.289×107 m/s|
|Accel time||4 years|
|Coast time||93 years|
|Decel time||1 years|
|Wet Mass||45,000 metric tons|
|Dry Mass||3,000 metric tons|
|Payload||150 metric tons|
|Propulsion||Z-Pinch DD Fusion|
|Specific Impulse||one million seconds|
|Accel time||25 years|
|Coast time||70 years|
|Decel time||5 years|
Most of the other Icarus fusion designs use inertial confinement fusion. That's because IC fusion is easier to get halfway worthwhile power levels. Magnetic confinement fusion would be nicer but once you get enough nuclear fusion going to to be worthwhile, the magnetic bubble pops like a cheap balloon.
The drawback to IC fusion is that the confinement time is pathetic. The longer you confine the fusion reaction, the more of the fusion fuel actually burns and generates energy. But in IC fusion the first bit of fusion acts to blast the pellet apart, scattering the un-burnt fuel to the four winds.
Back in the olden days of fusion research, the darling was Z-Pinch fusion. You send a bolt of electricity (about 5 mega-amps) down the center of a long tube full of ionized plasma, creating magnetic field which compresses the plasma enough to ignite nuclear fusion. One of the big advantages with Z-Pinch was that the confinement time (and net energy output from the burn) can be increased by simply making the reaction chamber longer.
Unfortunatley, the disadvantage is that Z-Pinch fusion suffers from several hydrodynamic instabilities which disrupt the plasma. So researchers stopped working on it in.
But in 1998 Dr. Uri Shumlak discovered you could eliminate the instabilities if you made the plasma move at high velocities. Based on this work, Z-Pinch was selected for the Icarus design.
The Firefly's long thin tail is the Z-Pinch tube, frantically fusing and radiating x-rays like a supernova. So the starship was given its name for similar reasons as the one on the TV show: it is a flying thing whose tail lights up.
The spacecraft profile is long and skinny, for two reasons:
- Its cruise velocity is a substantial fraction of the speed of light (4.5% c for the 2013 version). This make interstellar dust grains impact with about 9.1×10-4 joules worth of damage, the equivalent of 46,000 cosmic ray photons. You want to reduce the ship's cross section as much as possible to minimize the number of grain impact events.
- The longer the ship is, the farther the payload can be placed from the deadly radioactive Z-Pinch drive, taking advantage of distance shielding.
Many other starship designs use 3He-D fusion, because all the reaction products are charged particles that can be easily shieldied. The drawback is that 3He is rare, you'd have to harvest the atmosphere of Jupiter for twenty years in order to get enough.
Instead, Firefly uses D-D fusion, since deuterium can be easily found in common seawater. Of course then you have to deal with all the nasty neutrons and x-rays produced by that reaction. Firefly's approach is to forgo the use of massive radiation shields, and instead try to let as much of the radiation escape into space. The Z-Pinch core is almost totally open to space with only a triad of support rails connecting the aft electrode and magnetic nozzle to the rest of the vessel.
Even with that, the waste heat is going to be titanic. That's where the heat radiators come in. Notice how they are the bulk of the ship. Makes the thing look like a garantuan lawn-dart. The radiators use beryllium phase-change technology, and are positioned as close as possible to the heat loads on the tail.
A long conical shield forwards of the reactor core deflects x-rays away from the payload using shallow-angle effects. The electrodes, rails, and other structure near the core are constructed of zirconium carbide (which is capable of surviving the intensely radioactive environment.
The 2014 design had a total length of just under one kilometer, half of which is the fuel tanks. The forward part of the ship uses the old fuel tank in lieu of spine trick in an effort to save on ship mass.
A fission reactor provides secondary power.
|Pellet Mass||2 grams @|
|Ignition Rate||150 Hz|
|Specific Impulse||540,240 s|
|Exhaust Velocity||5,299,750 m/s|
|Dry Mass||7,444,000 kg|
|Propellant Mass||247,100,000 kg|
|Wet Mass||263,991,000 kg|
|Mission Duration||118.5 years|
|TOTAL TANK||927,000 kg|
|TOTAL PAYLOAD||150,000 kg|
|TOTAL SUBSYSTEM||4,670,000 kg|
|Magnetic Sail||1,780,000 kg|
|Dust Shield||15,000 kg|
|Tritium Prod (decel)||95,000 kg|
|D/T tanks, pellet manufacture||20,000 kg|
|TOTAL FUSION ENGINE||11,144,000 kg|
|Laser system||1,000,000 kg|
|Neutron Shield||82,000 kg|
|TOTAL DRY MASS||7,444,000 kg|
|TOTAL PROPELLANT||247,100,000 kg|
|TOTAL WET MASS||263,991,000 kg|
This was the winner in Project Icarus' 2013 contest to design an interstellar starship using current technology. The entry was created by the Munich Ghost Team headed up by Andreas Hein. The basic rules were to design a spacecraft which was mainly fusion powered and on a mission to Alpha Centauri carrying a 100 to 150 tonnes payload and reaching the destination in no more than 100 years.
The design uses Deuterium-Deuterium fuel, even though it has only half the exhaust velocity of Deuterium-Tritium and Deuterium-Helium3, and about 38% of the energy expresses itself as nasty neutron radiation. They rejected D-T because blasted Tritium has a freaking half-life of only 12 years so most of it would decay away during the 15.6 year acceleration phase and the 54 year coast phase. You'd have to carry a huge excess penalty mass of extra Tritium to allow for decay. They also rejected D-He3 because there probably isn't enough He3 on all of Luna, and harvesting it from a gas giant's atmosphere would require a huge space infrastructure.
Forced to use D-D, the designers looked for ways to turn that pesky neutron flux from a liability into an asset.
Standard inertial-confinement fusion engines use a circular firing squad of lasers to implode the fuel pellet. The compression ignites the fusion fuel. The designers note this is a bit inefficient. By analogy, it is possible to detonate a stick of TNT by squeezing it but you have to squeeze real hard. It takes a lot less energy to use a match to light the fuse on the TNT.
So the designers used a so-called "fast ignition scheme". The circular firing squad just has enough laser power to confine the fusion fuel, but not the extra energy needed to compress it to ignition. A secondary high-powered laser acts as the fuse, piercing the pellet and igniting it. You get the same energy from the pellet, but you need a whole lot less input laser energy.
Alas, a "whole lot less" is still freaking huge. Lasers are power hogs.
The standard method is to harvest some of the fusion energy and convert it into electricity. This is stored in huge banks of heavy capacitors, to be used for the next laser pulse. The initial capacitor charge comes from a nuclear reactor or something which trickle charges the capacitor banks. The problem is the mass of all those capacitors is a punishing amount of penalty-weight.
That's when the designers turned the D-D waste neutron flux into an asset. Have you ever heard of Nuclear-pumped lasers?
All lasers consist of a lasing medium which emits laser light when it is pumped. Conventional lasers pump the medium with electricity or light. Nuclear lasers on the other hand pump with the awesome might of nuclear fission. Uranium-235 is exposed to neutrons, undergoes fission, the energy pumps the lasing medium, and a rather powerful laser beam emerges.
The main draw-back of nuclear-pumped lasers is the lack of convenient sources of high neutron flux. A nuclear reactor can provide a bit of neutrons, and in theory a fission warhead detonation can provide lottsa neutrons (see Bomb-Pumped Lasers). The light-bulb went off over most of your heads while you were reading the previous paragraph. Yes, the neutron flux from the detonating D-D fuel pellets would work splendidly.
The designers used a solid-core nuclear laser instead of liquid-core, since solid-core is more suitable for generating extremely short high-powered pulses. A ring-shaped chamber circles the thrust chamber, centered on the fusion pellet detonation point. The chamber is filled with a uranium dioxide aerosol and a fluorescent gas acting as the lasing medium. Some of the neutrons from the fusion detonation enter the chamber, causing fission reaction with the uranium 235 atoms, the fissile products then excite the fluorescent gas thus pumping it. The light flash from the fluorescent gas is transmitted through a light pipe into the laser amplifier. This creates the laser beam.
This system is about 8% efficient, which is pathetic for a general device but actually fantastic for a laser. And it is using all those otherwise worthless neutrons. The drawback is the uranium dioxide aerosol and fluorescent gas are expended with each laser bolt, that is, they are consumables. Which adds to the mass load.
However, even with the consumables the total mass of the ignition system is less than 1,000,000 kilograms, which is far less than all those banks of capacitors.
The report states an exhaust velocity of 0.018 c, which is considerably smaller than the theoretical maximum of D-D fusion (0.043 c). Which is probably very realistic.
As with all high-energy propulsion there is huge amounts of waste heat to get rid of, and this system does not lend itself to open-cycle cooling (not enough mass in the exhaust to carry off enough heat). Meaning you actually need plenty of heat radiators. The design use liquid-droplet radiators with a total area of 7.6 square kilometers. It has a very high heat rejection rate of 500 kW/kg by using liquid aluminum as the heat-conducting liquid.
The spine of the ship is a cylindrical truss structure composed of carbon nanotubes. This material has an exceptionally high tensile strength at a very low density, prime spacecraft building material. And you are going to need it. An engine thrust of 1.6 megaNewtons is 160 metric tons of compressive force which the spine has to endure for a bit more than 15 years. Thin spines tend to buckle so the design has a spine with a fat diameter of 100 meters. I did some analysis of the above image, if the spine is 100m in diameter, the pictured ship is about 1.1 kilometers long.
Starting wet mass is 153,940,000 kg, of which 150,000,000 kg is propellant. Outrageous mass ratio of freaking 45.9!
It accelerates for 25.63 years, reaching a velocity of 0.05c. It then coasts for 56.43 years.
Upon approaching Alpha Centauri, it deploys a magnetic sail. This drags on the interstellar medium, decelerating the spacecraft for 36 years. Once the velocity is down to 0.01c the fusion engine is used to finish the job of bringing the ship to a halt. The ship is now totally out of fuel. It then deploys lots of scientific probes and drones to gather as much scientific information as it possibly can, and transmits it back to Terra.
|Distance||0.37 ly||3 ly||0.02 ly||0.0024 ly|
|End Velocity||5% c||-||3,470 km/s|
|Duration||25.63 yrs||56.43 yrs||36 yrs||0.229 yrs|
|Num Propellant Tanks|
|Num Propellant Tanks|
|Bombardment Shield||53,650 kg|
|Bombardment Shield Thickness||9.01 mm|
|Engine Mass||318,000 kg|
|Fusion Pellet||0.000288 kg|
9.97 mm dia
|Pulse Rate||150 Hz|
|Exhaust Velocity||9,210,000 m/s|
|Mass Flow||0.0432 kg/sec|
|Jet Power||1.832 TW|
|Boost Phase||15.184 yrs|
0.274 ly from Sol
|Dist Boost Burn||0.274 ly|
|Cruise Phase||81.475 yrs|
3.936 ly from Sol
|Deburn Phase||2.861 yrs|
4.4 ly from Sol
|Dist Deburn||0.189 ly|
|Total Duration||99.519 yrs|
|Cruise Velocity||14,481,476 m/s|
|Excess Velocity at Dest||1,280 m/s|
The original Project Daedalus starship was a two-stage rocket with each stage having an inertial confinement fusion rocket. Starship Resolution is a conservative extrapolation. Instead of two engines each in a stage, it has a single engine fed by lots of drop-off tanks.
If for some obsessive-compulsive reason you need to know how many fuel pellets each stage has, simply divide the propellant mass in a stage by 0.000288.
|Specific Impulse||550,000 s|
|Exhaust Velocity||5,400,000 m/s|
|Propellant Mass||75,000,000 kg|
|Cruising Velocity||15,000,000 m/s|
This was the fourth entry in Project Icarus' 2013 contest to design an interstellar starship using current technology (it didn't win, the Ghost ship did). The basic rules were to design a spacecraft which was mainly fusion powered and on a mission to Alpha Centauri carrying a 100 to 150 tonnes payload and reaching the destination in no more than 100 years.
For reasons similar to those raised by the Ghost ship, this design also uses the relatively feeble Deuterium-Deuterium fusion reaction. Both designs use laser ignited inertial confinement fusion engines.
The main drawback to IC fusion engines is since beams of light do not push very hard, you need metric-assloads of laser energy to crush the fuel pellet to fusion ignition. Which requires lots of heavy lasers, savagely cutting into your payload mass budget. Since the laser pulse has to be microscopically short, the lasers have to be powered by huge banks of weighty capacitors, further slashing your payload budget.
The Ghost ship gets around this by replacing the capacitor banks with nuclear-pumped lasers, using the waste neutrons from the prior detonation.
The Ultra-Dense Deuterium starship gets around this with something even more tricky. It uses a weird fuel called, you guessed it, ultra-dense deuterium.
Ultra-dense deuterium (UDD) is an exotic form of metallic hydrogen called Rydberg matter. As you can probably figure out from the name the stuff is dense. Real dense. As in 1028 to 1029 grams per cubic centimeter dense. About a million times denser than frozen deuterium.
For our purposes the interesting point is it is about 150 times as dense as your average pellet of fusion fuel when laser-compressed to peak compression. Yes, this means do you not need metric-assloads of laser energy to crush the fuel pellet, a pellet just sitting on the table is already at 150 times the needed compression. It is pre-compressed. All you need is a miniscule 3 kilojoules worth of laser energy to ignite the stuff. That is pocket-change compared to what 200-odd compression lasers require. In fact it is so little that a single laser can handle the job. This results in a vast savings on laser mass and capacitor mass.
The laser pulse has to be quick, so the power rating is a scary 1 petawatt. But by the same token since the pulse is quick, it only require the aforesaid 3 kilojoules of energy.
Since you do not have to compress the fuel you can avoid all sorts of inconvienient hydrodynamic instabilities and plasma-laser interation problems.
You also have virtually unlimited "fusion gain". Meaning that with a conventional IC fusion engine there is a maximum fuel pellet size due to the hydrodynamic instabilities and the geometric increase in compression laser power. With UDD you can make the fuel pellet as large as you want (well, as large as the engine can handle without blowing up at any rate). With other laser intertial confinement fusion, if you make the pellets larger, you have to make the laser array larger as well. Not so with the UDD drive. The fusion gain depends solely on the size of the pellet, you do not have to make the lasers bigger.
An important safety tip: since UDD has such absurdly low ignition energy, there is a statistical change a large number of UDD atoms would undergo fusion spontaneously. This dangerous instability means the spacecraft will carry ordinary deuterium fuel and only convert it into UDD immediatly before use.
The cherry on top of the sundae is UDD fusion does not produce deadly neutron radiation. Instead it produces charged muons, which are not only easier to deal with, but also can be directly converted into electricity. Left alone, the muons quickly decay into ordinary electrons and similar particles.
And since deuterium is plentiful in ordinary seawater, you do not have to go strip mining Lunar Regiolith or set up atmospheric scoop operations around Jupiter were you to use a fusion reaction requiring Helium-3.
Sounds too good to be true, I hear you say. Well, there are a couple of drawbacks.
The minor drawback is that D-D fusion has a specific impulse (and exhaust velocity) which is about half of what you can get out of D-T fusion or D-He3 fusion. This drastically increases the mass ratio required for a given mission delta-V. Having said that it is still much better than what you'll get out of chemical or fission engines.
But the major drawback is UDD might not even have that magic ultra-density.
You see, the vast majority of the UDD-related papers has been published by a single scientific group at University of Gothenburg, Sweden, led by Dr. L. Holmlid. Currently there are no third-party confirmations about UDD observations and generally very few discussions about it in the scientific community. Until the density figure is confirmed, it might be all a pipe-dream.
The spacecraft has two stages, kinda-sorta.
It accelerates for ten years using Stage One, reaching a velocity of 0.04c. Stage One is then jettisioned.
It accelerates for an additional two years using Stage Two, reaching a velocity of 0.04c. Stage Two stops burning, it still has fuel left. It jettisons about 68% of its heat radiator mass which is no longer needed.
The spacecraft proceeds to coast for the next seventy-five years.
At the end of the coast phase, the spacecraft is 0.378 light-years (0.368 + 0.010) away from the destination (Alpha Centauri). About 24,000 astronomical units. It then deploys a Magsail drag (with a mass of 238,000 kg). Over the next twelve years it decelerates the spacecraft to a velocity of 0.012c.
The spacecraft is now 0.01 light-years from destination. It jettisions the Magsail, bringing the spacecraft mass down to 612,000 kg. Stage Two's engine starts burning (in the diagram this is marked as "3rd Stage"). It burns for the next two years, bringing the spacecraft to halt at the destination. The spacecraft mass is now 320,000 kg, of which 150,000 kg is scientific payload.
The paper started when Dr. Semyonov read about the Frisbee Antimatter Starship and noticed how certain technical difficulties were being ignored or glossed over. Such as the miniscule cross-sections of electron–positron and proton–antiproton annihilation. Meaning if you crossed a stream of anti-protons with a stream of protons, a dissapointingly low number of particles would actually hit each other and react. This creates the requirement for lengthy “annihilation zones” to make sure every last particle of expensive antimatter reacts and contributes thrust. While it is relatively easy to get two hydrogen atoms to collide, a proton or an anti-proton is 60,000 times smaller.
And, as a consequence, creates poor alignment of the propulsion jet. Meaning that since the annihilation zone is a long cylinder instead of a small sphere, the propulsion jet is going to be an unfocused cone instead of a laser-like focused line. Thrust will be wasted.
So Dr. Semyonov did an analysis to design an antimatter drive starship with a more efficient engine.
The paper agrees that if a multi-ton starship carries its energy source and propellant onboard, you are going to have to use antimatter if you want to get a relativistic speed above 0.1c. Chemical, fission, or fusion are nowhere near powerful enough. The alternative is to make the energy source and propellant external, like a laser sail or something like that.
|Fuel||Energy Density MJ/kg|
|H chemical burning||140|
|Rocket chemical fuels||50|
The two traditional antimatter rocket engines are lepton antimatter and baryon antimatter.
Lepton antimatter is when you annihilate positrons with electrons, and somehow direct the all-destroying gamma-ray flux into a beam to make a photon drive. Usually directing the beam means putting the annihilation point at the focal spot of a gamma-ray parabolic mirror.
The first problem is there ain't no such thing as a gamma-ray mirror, not with anywhere near 100% efficiency at any rate. This means the bulk of the reaction energy is not going to provide thrust, it will instead heat up the mirror with the hideous fury of burning antimatter. The fraction of a second the mirror will last before vaporizing into ionized plasma will have to be written in scientific notation with a huge negative exponent.
Second problem is the abysmally tiny cross section of the annihilation reaction. Only a fraction of the positrons are going to react, the rest will travel past the focal point. Then they will either:
- Impact the mirror, destroying it in an antimatter explosion
- Fly into the depths of intergalactic space, wasting all that expensive and vitally needed antimatter
- Be forced to react by making the reaction zone hundreds of meters long, with the problem of re-directing the gamma rays not at the focal point left as an exercise for the reader
- Somehow be caught with magnetic scoops and sent back into the focal point, increasing the chance of an antimatter accident with each catch and recycle.
Baryon antimatter is when you annihilate protons with anti-protons. Unlike lepton antimatter the reaction does not produce just gamma rays. Instead it creates an assortment of pions plus gamma rays. Beam-core antimatter rockets like the Frisbee Starship use the reaction products as propellant. Plasma-core antimatter rockets use the annihilation energy to heat up propellant, which increases thrust at the expense of specific impulse. Still others use baryon antimatter annihilation to catalyze fission or fusion reactions, but the resulting specific impulse is so low that it ain't worth it. Not for a starship, it is good enough for an interplanetary ship.
- The "prompt" gamma-rays contribute nothing to the thrust, they just damage the engine and any other part of the starship that is too close
- The neutral pions decay almost instantly (90 attoseconds) into "delayed" gamma-rays which do the same thing as the prompt gamma rays.
- The abysmally tiny cross section of the annihilation reaction
Naturally with both lepton and baryon antimatter, the elephant in the room is how do you carry antimatter fuel when the stuff blows up like a supernova if it touches the matter walls of the fuel tanks? The answer is very carefully, using electromagnetic or electrostatic fields.
The report figures that neither Lepton or Baryon antimatter drive starships are efficient enough. It will be far more efficient to use antimatter in some sort of annihilation electrical power generator, and using that to run some sort of super-duper ion drive. Such a generator will be using the ultimate in concentrated fuel, and the generator will have a much lower mass than a fission or fusion reactor. Ion drives are notorious power hogs, but with antimatter power who cares?
- 1: Ion accelerators: arrays of linear accelerators of high-energy ions
- 2: Propellant tanks, and store of matter to annihilate with antihydrogen
- 3: Refrigerators for antihydrogen tank and magnetic shield
- 4: Heat insulators
- 5: Turbines and electrical power generators to energize ion accelerators, life support et al
- 6: Annihilation reactor
- 7: Control bridge
- 8: Crew quarters or AI module
- 9: Magnetic shield to protect ship from interstellar medium relativistically transformed into particle radiation. A starship bumper in other words.
- 10: Electron stripper: antidust shielding system. Second part of the starship bumper.
- 11: Heat radiator
- 12: Antihydrogen tank
Two heat radiators (11) are shown but four could be used without them thermally interfering with each other (much).
The report has the pious hope that the annihilation reactor will have a much lower mass than a fission reactor with the same power output. They figure that the lion's share of the mass goes to the radiation shielding, but since the antimatter reaction produces zero neutrons it can get by with just gamma-ray shielding. Offhand I'd say the mass reduction is not quite as much as they would hope. Looking at a sample shield it appears that for every kilogram of neutron shielding you need 33 kilograms of gamma-ray shielding. So removing the neutron shield will reduce the shield mass by only 3%.
On the other hand the annihilation reactor will not need things like uranium-235 fuel slugs, which also have lots of penalty mass. Stuff is more dense than lead, which is why the military replaced the lead in their artillery shells with depleted uranium.
Thin radial wings protruding from magnetic shield (9) and electron stripper (10) is to shield the leading edges of heat radiators (11).
You may have noticed a new problem.
From the point of view of the starship, the relativistic "radiation" is coming from the opposite direction (blue arrows) that the ship is traveling in (red arrows).
 Rocket Engine 101: you point your rocket exhaust (red flames) in the exact opposite direction your ship is traveling (red arrows) in order to speed up (accelerate). You point the exhaust in the exact same direction as the ship's vector in order to slow down (decelerate). This means in the first half of the trip the ship's nose is pointing at the destination. Then the ship rotates to point the ship's tail at the destination. Heinlein calls this a "skew flip", The Expanse calls it a "flip-and-burn". The tail stays pointed at the destination for the second half of the trip.
 Rockets Are Not Arrows: starships do not necessarily travel in the direction their nose is pointing. During deceleration the ship's vector is pointed at the destination, but the nose is pointed away from the destination.
You see the problem? If your starship is traveling to Tau Ceti, you accelerate by pointing your rocket exhaust in the opposite direction (red flames) and burn until you are up to relativistic velocity. Relativistic radiation will appear to be coming from the direction of Tau Ceti (blue arrows), and will be warded off by the starship bumper on the ship's nose.
But when you want to decelerate so as to come to a stop at Tau Ceti, you have to skew flip. This means turning the ship so that the exhaust is pointed at Tau Ceti and burning until you come to a stop. Oh calamity and woe! Because rockets are not arrows, the relativistic radiation is still coming from the direction of Tau Ceti, but the starship bumper is no longer in position to ward off the deadly radiation! The radiation quickly kills the crew.
And no, the report did the math and apparently the rocket exhaust is not powerful enough to disperse the radiation.
According to the report, the recommended solution is to design the ion accellerators so they can rotate and point ahead while the rest of the starship does not change its orientation. This way the ion accellerators can decelerate the starship while allowing the starship bumper to keep facing the radiation. Now, understand that the ion accelerators cannot face directly ahead or they will torch the ship with the exhaust. They will have to be angled slightly off-center so that the exhaust misses the ship. This will mean the thrust is subject to cosine losses, but that can be managed.
This is from the paper Interstellar Flight JBIS Vol. 11 (1952) by the legendary Les Shepherd The Journal of the British Interplanetary Society (JBIS) proudly proclaims this to be the first technical paper on interstellar flight.
Lamentably I am still trying to obtain a copy. In the meantime I will make do with Mr. Shepherd's popularization of his paper which appeared in Science-Fiction Plus April 1953.
Mr. Shepherd points out that when it comes to interstellar colonization, the problem is not transporting a man across stellar distances, it is more a problem of transporting an adequate community. If the transport is not moving at relativistic velocities you are probably talking about a generation ship (I suspect the sleeper ship concept had not been conceived of as early as 1952). Shepherd opines that interstellar explorers or colonists, faced with the knowledge that they will not only never see Terra again but also never see their destination, should adopt a similar philosophy to that of a soldier setting out on a suicide raid. There will be no personal gain, but instead the dying knowledge that some will survive to benefit from their action. This is calling for the sacrifice of entire generations in the depths of space, which admittedly will require a revolution in society. But Shepherd says this may be necessary if we are ever to become a galactic people.
Shepherd does not mention the problem of generation born en route being angry at their forebearers presumptuously committing them to this role. He does point out that the society will have to be a bit regimented. There will be specific population goals (overpopulation or underpopulation is a problem) so procreation is strictly regulated. Civilization has to be preserved, knowledge and culture will have to be carefully handed from generation to generation. New developments in science and art will be needed since Shepherd is of the opinion that "stagnation is the first step to degradation."
Shepherd figures that generation ships should not be used until the state-of-the-art allows transit times less than one thousand years. However he apparently didn't think of the "jumping the gun" problem.
For the journey to Alpha Centauri Shepherd figures that a fission-powered generation ship with an amount of fission fuel equal to 2.4 times the ship's dry mass, plus enough hydrogen propellant to rase the total mass ratio to 5.0 would have an exhaust velocity of 6,000 km/s and a deltaV of 10,000 km/s (about 0.03c). It accelerates to 5,000 km/s, cruises, then brakes down to zero at Alpha C. The transit time should be about 250 years.
If the transit time was lengthened to 350 years, the acceleration and deceleration phases could be increased to 50 years each, with 250 years of coasting in the middle. This would reduce the required acceleration to 0.00327 m/s2 (about 1/3000 g). Which would reduce the required engine power output per short ton of wet mass (specific exhaust power) to "only" 10 megawatts. E.g., if the wet mass was 10,000 short tons the engine power would be 100,000 megawatts (100 gigawatts). Shepherd admits that designing engines which can crank out 100 gigawatts for fifty years will be a bit of a challenge.
Shepherd says the transit time can be cut to 140 years if "lithium-hydrogen" fusion is used, but I think Mr. Shepherd was unaware that there are much better fusion reactions that can be used. I'd be more sure if I could read his actual paper.
Shepherd tries to put a spin on matters, pointing out that while a thousand years sounds like a long time to us, it is actually a small interval in terms of geological time. Which will fool nobody with an I.Q. higher than room temperature. He also mentioned that it would be a real good idea if astronomers made quite sure that the target star indeed had a habitable planet. Otherwise it would be a most tragically ironic ending to a very long mission.
Shepherd also acknowledges that the biological problem of maintaining a life support system for thirty generations is a major engineering challenge, but that isn't his department. Conservation of resources is important since losses can really add up over a thousand years. E.g., a million ton vessel losing 100 milligrams of air per second doesn't sound too serious, but over a 1,000 years that adds up to about three thousand tons of atmosphere loss.
The ship should also transport an entire ecosystem to be transplanted to the new world. This would turn the ship into a veritable Noah's Ark, and might force the ship to be a hollowed-out asteroid in order to carry everything. An asteroid has such a large radius that it could be spun up for artificial gravity at a low enough rate to prevent spin nausea.
Noted polymath Charles Pellegrino and Brookhaven physicist Jim Powell have an innovative antimatter powered starship design called a Valkyrie. They say that current designs are guilty of "putting the cart before the horse", which create ships that are much more massive than they need be. Their "spaceship-on-a-string" starship is capable of accelerating up to ninety-two percent the speed of light and decelerating back down to stationary. At this velocity, relativity mandates that time on board the ship will travel at one-third the rate of the stay at home people on Terra (actually it's closer to 1/2.55). They figure this will be adequate for visiting stars up to about twelve light-years from Terra, without using up excessive amounts of the crew's lifespan.
Dr. Pellegrino served as a scientific consultant on James Cameron's Avatar movie. The interstellar vehicles seen in the film are based on the designs of Pellegrino and Powell's Valkyrie rockets, fused with Robert L. Forward's designs. I figured this out when I noticed that the Avatar starship had the engine in the front, which is a unique feature of the Valkyrie.
If I am reading this correctly, this is a mass ratio of 1.5, which I find a little difficult to believe. The equations above seem to say that accelerating up to 92%c and back down to zero will require a mass ratio around 22.
Adam Crowl got in touch with Mr. Pellegrino on this matter. As it turns out, the mass ratio of 1.5 only applies to a Valkyrie capable of approaching ten percent lightspeed.
Mr. Pellegrino's response to Adam Crowl:
Anyway, back to the main description:
The third of Gordon Woodcock's methods of interstellar travel is "go tricky".
This means to cheat and find a way to travel to the stars faster than light.
This is such can of worms that it has an entire page to itself.