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.
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."
There are several ways of dealing with the lifespan issue. Go to the Tough Guide to SF and read the entry "Slowboat".
In the "Generation ship" concept, the starship is huge (typically a hollowed-out asteroid) and contains an entire community. As the ship crawls to its destination, generations of people are born, have children, and die of old age. 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, and the later generations forgetting where they came from, forgetting where they are going, and forgetting the fact that they are on a starship. An interesting incremental approach is the Cross-generation ship.
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.
A variation is the "Seed ship" concept. The starship is tiny, containing a payload of millions of frozen fertilized eggs, artificial wombs, robots, and a master computer. After traveling for thousands of years, the ship lands in a good spot for a colony. The master computer thaws out enough eggs for the available 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.
Examples include The Song of Distant Earth by Sir. Arthur C. Clarke, and "Longshot" by Vernor Vinge.
Still more extreme is the "digital crew" concept. Since every atom of mass is a penalty, the logical ship would just carry a master computer and no frozen fertilzed eggs and associated equipment. However, nobody wants wants to read about the adventures of a computer (yes, I know there have been some SF stories on this theme, but it requires extraordinary skill on the part of the author). Authors such as Sean Williams, Shane Dix, and Greg Egan have gotten around this by postulating 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. Sean Williams and Shane Dix handwave the end run around Burnside's Zeroth Law by stating that artificial intelligence proved to be an unexpectedly difficult challenge.
One could add equipmment capable of manufacturing artificial bodies for the crew from local materials. 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.
In the "Sleeper ship" concept, the crew is frozen into suspended animation, so they do not age nor require food and oxygen during the thousand year journey. 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.
A variation of this 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 1/1000th normal, and perceive things at the same rate. 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. But normal humans move so fast that S-state humans cannot see them, and normal humans will still perceive the trip taking about forty years.
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.
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.
And 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.
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 implications of relativity that we have to worry about. 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. 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 (i.e., faster than about 14% c) will age and experience time at a slower rate than people who stayed at home on Terra. 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.
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.
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.
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.
The crew of a ship moving at relativistic velocities will notice some weird effects. The view of the sky will be distorted both fore and aft by relativistic aberration. Doppler shift will make the stars ahead look more blue, and the stars behind will appear more red. Back in the 1970's it was thought that the two effects would combine to make a sort of a rainbow of stars around the ship's destination. Alas, in 1980 a study published in the Journal of the British Interplanetary Society did the math and proved that it just wasn't going to happen.
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:
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.)
Of course there are some other problems.
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.
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 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.