There are certain favored locations for launch sites. Sites that launch into polar orbits have the rockets depart either north or south depending on the orbit. Sites that launch into equatorial orbits always launch east. In both cases, you want the rocket to be passing over parts of Terra's surface that are uninhabited and either belong to you or to nobody. Over the ocean is prefered. In addition, equatorial launch sites should be as close to the equator as possible (for reasons explained in the link above).
Possible equatorial launch sites:
- The North Maluku province of Indonesia has parts right on the equator. It has pretty much the entire Pacific Ocean to use as a launch corridor, except only scattered tiny islands in the launch corridor. Possible launch site.
- There is a part of the coast of Brazil that is right on the equator. It has pretty much the entire Atlantic Ocean to use as a launch corridor. Possible launch site.
- Parts of the Galápagos Islands are right on the equator. Unfortunately it only has 906 km of Pacific Ocean launch corridor before flaming rocket bits start raining down on Ecuador. Possible launch site.
- In ARTEMIS by Andy Weir the launch site is in Kenya, with parts right on the equator. It has pretty much the entire Indian Ocean to use as a launch corridor. However, the part closest to the equator that does not include Somalia in the launch corridor is located at 1.7° S latitude.
- In ISLANDS IN SPACE by Arthur C. Clarke the launch site is at New Guinea, with point closest to equator at about 2.6° S latitude. It has pretty much the entire Pacific Ocean to use as a launch corridor, except for the Solomon Islands.
- The real world Guiana Space Centre in French Guiana is at about 5° N latitude. It has pretty much the entire Atlantic Ocean to use as a launch corridor.
- Palmyra Atoll is at about 5° N latitude. It has pretty much the entire Pacific Ocean to use as a launch corridor. And it is a US unorganized incorporated territory. Drawbacks include it is pretty much on the opposite side of Terra from the continental US so that logistics is a nightmare, and the highest point is (currently) only 10 meters above sea level.
- The US Virgin Islands are at about 17.7° N latitude. It has pretty much the entire Atlantic Ocean to use as a launch corridor. Possible launch site.
- In High Justice by Jerry Pournelle the launch site is at Cabo San Lucas, Mexico. It is at an unhelpful 22.8° N latitude. And it only has 390 kilometers of launch corridor.
- The real world Kennedy Space Center Launch Complex 39 is at an ugly 28.5° N latitude. But the United States does not get that much closer to the equator. It has pretty much the entire Atlantic Ocean to use as a launch corridor.
- The real world Baikonur Cosmodrome is at an almost utterly worthless 45.6° N latitude. What's worse it it has to launch at a 51.6° inclination, since China takes a very dim view of being in the launch corridor. Sadly Baikonur is probably located at the best out of Russia's poor selection of launch sites.
If you are launching Orion nuclear pulse rockets from the surface of Terra, you'd best do so from 80° to 90° magnetic latitude (no more than 111 kilometers from the north magnetic pole). This will create an artificial radiation belt that lasts a few minutes. From 40° to 80° the belt will last for a few weeks. From the equator to 40° the belt will last for years, and will fry satellites in LEO.
Also, if you launch an Orion from near one of the magnetic poles, you will reduce the amount of fallout landing on the surface by a factor of ten.
Terran Orbital Space
An orbit is a clever way to constantly fall towards a planet but never hit the ground. Rick Robinson defines "orbital space" as "a planet's orbital space is the region dominated by its gravity." The Hill Sphere is where the central body dominates the attraction of satellites and moons, usually the sphere fitting between Lagrangian points L1 and L2.
Many, but not all, space stations are in orbit around a planet.
There are certain preferred orbits.
An equatorial orbit is a non-inclined orbit with respect to Terra's equator (i.e., the orbit has zero inclination to the equator, 180° inclination if retrograde). Most civilian satellites use such orbits. The United States uses Cape Canaveral Air Force Station and the Kennedy Space Center to launch into equatorial orbits.
An ecliptic orbit is a non-inclined orbit with respect to the solar system ecliptic.
An inclined orbit is any orbit that does not have zero inclination to the plane or reference (usually the equator).
A polar orbit is a special inclined orbit that goes over each pole of the planet in turn, as the planet spins below (i.e., the orbit is inclined 90° to the equator). Heinlein calls it a "ball of twine" orbit since the path of the station resembles winding string around a string ball. The advantage is that the orbit will eventually pass over every part of the planet, unlike other orbits. Such an orbit is generally used for military spy satellites, weather satellites, orbital bombardment weapons, and Google Earth. The United States uses Vandenberg Air Force Base to launch into polar orbits. Google Earth uses data from the Landsat program, whose satellites are launched from Vandenberg.
(the section about launch site inclinations has been moved here)
Orbits around Terra (geocentric) are sometimes classified by altitude above Terra's surface:
- Low Earth Orbit (LEO): 160 kilometers to 2,000 kilometers. At 160 km one revolution takes about 90 minutes and circular orbital speed is 8 km/s. Affected by inner Van Allen radiation belt.
- Medium Earth Orbit (MEO): 2,000 kilometers to 35,786 kilometers. Also known as "intermediate circular orbit." Commonly used by satellites that are for navigation (such as Global Positioning System aka GPS), communication, and geodetic/space environment science. The most common altitude is 20,200 km which gives an orbital period of 12 hours.
- Geosynchronous Orbit (GEO): exactly 35,786 kilometers from surface of Terra (42,164 km from center of Terra). One revolution takes one sidereal day, coinciding with the rotational period of Terra. Circular orbital speed is about 3 km/s. It is jam-packed with communication satellites like sardines in a can. This orbit is affected by the outer Van Allen radiation belt.
- High Earth Orbit (HEO): anything with an apogee higher than 35,786 kilometers. If the perigee is less than 2,000 km it is called a "highly elliptical orbit."
- Lunar Orbit: Luna's orbit around Terra has a pericenter of 363,300 kilometers and a apocenter of 405,500 kilometers.
Geosynchronous Orbits (aka "Clarke orbits", named after Sir Arthur C. Clarke) are desirable orbits for communication and spy satellites because they return to the same position over the planet after a period of one sidereal day (for Terra that is about four minutes short of one ordinary day).
A Geostationary Orbit is a special kind of geosynchronous orbit that is even more desirable for such satellites. In those orbits, the satellite always stays put over one spot on Terra like it was atop a 35,786 kilometer pole. For complicated reasons all geostationary orbits have to be over the equator of the planet. In theory only three communication satellites in geostationary orbit and separated by 120° can provide coverage over all of Terra.
All telecommunication companies want their satellites in geostationary orbit, but there are a limited number of "slots" available do to radio frequency interference. Things get ugly when you have, for instance, two nations at the same longitude but at different latitudes: both want the same slot. the International Telecommunication Union does its best to fairly divide up the slots.
The collection of artificial satellites in geostationary orbit is called the Clarke Belt.
Note that geostationary communication satellites are marvelous for talking to positions on Terra at latitude zero (equator) to latitude plus or minus 70°. For latitudes from ±70° to ±90° (north and south pole) you will need a communication satellite in a polar orbit, a highly elliptical orbit , or a statite. Russia uses highly eccentric orbits since those latitudes more or less define Russia. Russian communication satellites commonly use Molniya orbits and Tundra orbits.
About 300 kilometers above geosynchronous orbit is the "graveyard orbit" (aka "disposal orbit" and "junk orbit"). This is where geosynchronous satellites are moved at the end of their operational life, in order to free up a slot. It would take about 1,500 m/s of delta V to de-orbit an old satellite, but only 11 m/s to move it into graveyard orbit. Most satellites have nowhere near enough propellant to deorbit.
Lagrangian points are special points were a space station can sit in a sort-of orbit. Lagrange point 1, 2, and 3 are sort of worthless, since objects there are only in a semi-stable position. The ones you always hear about are L4 and L5, because they have been popularized as the ideal spots to locate giant space colonies. Especially since the plan was to construct such colonies from Lunar materials to save on boost delta V costs. The important thing to remember is that the distance between L4 — Terra, L4 — Luna, and Terra — Luna are all the same (about 384,400 kilometers). Meaning it will take just as long to travel from Terra to L4 as to travel from Terra to Luna.
For a more exhaustive list of possible Terran orbits refer to NASA.
It is also possible for a satellite to stay in a place where gravity will not allow it. All it needs is to be under thrust. Which is rather expensive in terms of propellant. Dr. Robert L. Forward noted that solar sails use no propellant, so they can hold a satellite in place forever (or at least as long as the sun shines and the sail is undamaged). This is called a Statite.
If the planet has an atmosphere and the station orbits too low, it will gradually slow down due to atmospheric drag. "Gradually" up to a point, past the tipping point it will rapidly start slowing down, then burn up in re-entry. Some fragments might survive to hit the ground.
The "safe" altitude varies, depending upon the solar sunspot cycle. When the solar activity is high, the Earth's atmosphere expands, so what was a safe altitude is suddenly not so safe anymore.
NASA found this out the hard way with the Skylab mission. In 1974 it was parked at an altitude of 433 km pericenter by 455 km apocenter. This should have been high enough to be safe until the early 1980's. Unfortunately "should" meant "according to the estimates of the 11-year sunspot cycle that began in 1976". Alas, the solar activity turned out to be greater than usual, so Skylab made an uncontrolled reentry in July 1979. NASA had plans to upgrade and expand Skylab, but those plans died in a smoking crater in Western Australia. And a NOAA scientist gave NASA a savage I Told You So.
The International Space Station (ISS) orbited at an even lower at 330 km by 410 km during the Space Shuttle era, but the orbit was carefully monitored and given a reboost with each Shuttle resupply mission. The low orbit was due to the Shuttle carrying up massive components to the station.
After the Shuttle was retired and no more massive components were scheduled to be delivered, the ISS was given a big boost into a much higher 381 km by 384 km orbit. This means the resupply rockets can carry less station reboost propellant and more cargo payload.
If the planet the station orbits has a magnetic field, it probably has a radiation belt. Needless to say this is a very bad place to have your orbit located, unless you don't mind little things like a radiation dosage of 25 Severts per year. And that is for Terra, Jupiter's radiation belts are a thousand times worse. In 1973 Pioneer 11 was surprised by radiation levels around Jupiter ten times greater than NASA had predicted. This is why Pioneer did not send back photos of the moon Io since the radiation belt had fried its imaging photo polarimeter. Work on the Voyager space probe came to a screeching halt as they frantically redesigned it to cope with the radiation, but still be assembled in time for the launch window.
Terra's zone of glowing blue death is called the Van Allen radiation belts.
The Inner Belt starts at an altitude from 400 km to 1,200 km, depending on latitude, and ends at an altitude of about 6,000 km, with its most lethal area 3,500 km out. The South Atlantic Anomaly can potentially disrupt satellites in polar orbits, but usually does not pose a problem for manned spaceflights. Except for the ISS. The radiation is high-energy protons (400 MeV).
The Outer Belt ranges from 13,000 km to 60,000 km, with its most lethal area 27,000 km out. The Outer Belt is affected by solar winds, and is thus flattened to 59,500 km in the area directly between the Earth and the Sun, and extends to its maximum distance in the shadow of the Earth. The radiation is high-energy electrons (7 MeV).
A safe channel exists between the belts from 9,000 km to 11,000 km.
The Apollo missions had trajectories designed to shoot through the belts at high speed to minimize radiation exposure.
Since Terra's rotational and magnetic axes do not intersect at Terra's Center, there is a deadly spot in the inner belt called the South Atlantic Anomaly. The inner edge of the belt proper is usually 1,000 kilometers from Terra's surface, but the anomaly gets as close as 200 kilometers. Satellites and space stations need extra radiation shielding for when they periodically pass through the anomaly. The ISS has extra shielding for that reason. Astronauts have seen phosphene shooting lights in their eyeballs, laptops have crashed, control computers experience transient problems as they pass through the anomaly.
Since the Van Allen Belts will destroy expensive satellites as well, there have been proposals to drain the radiation out of the belt.
Depending on your opinion on the subject of Pluto, there are four tiny rocky planets and four huge gas giants. Or as Arthur C. Clarke said, the Solar System consists of four planets, plus debris.
Heinlein said "Mother very thoughtfully made a jelly sandwich under no protest" but I learned it as "My very educated mother just served us nine pumpkins."
Solar System Mother MERCURY $.39 Very VENUS $.72 Thoughtfully TERRA $1.00 Made MARS $1.50 A ASTEROIDS (around $2.77) Jelly JUPITER $5.20 Sandwich SATURN $9.50 Under URANUS $19.00 No NEPTUNE $30.00 Protest PLUTO $39.50
Heinlein used dollar amounts to show the distance of each from Sol (the Sun to you) in Astromical Units. He used dollars since his mind tends to pay attention to money. One AU is the distance between Terra and Sol, about 150 million kilometers.
The big thing to notice is that the planet distances tend to double. Say you are traveling from Sol to Saturn, a distance of 9.5 AU. When you get to the orbit of Jupiter (the orbit just before Saturn) you have only traveled 5.2 AU. In other words, when you have reached the orbit of Jupiter you are only half-way to Saturn!
Planetary Fact Sheets! All hail Planetary Facts Sheets! These are handy sheets from Dr. David Williams of NASA containing vital statistics of various solar system planets. Also useful is Wikipedia's List of gravitationally rounded objects of the Solar System (i.e., Sol and the planets)
|Surface Gravity||0.003 m/s|
|Escape velocity||5.556 m/s|
|LEO to Deimos||1.8 km/s delta-V|
270 days transit
|Deimos to LEO||5.6 km/s delta-V|
270 days transit
Deimos is the smaller of the two moons of Mars. In terms of delta-V cost, Deimos is the closest hydrated body to LEO. Since water is one of the most valuable in situ resources, this makes Deimos valuable. There is water ice on Phobos as well, but it is buried more deeply. On Deimos the ice is within 100 meters of the surface at the equator, and within 20 metrers at the poles.
Rob Davidoff and I worked up an entire future history centered around Deimos, called Cape Dread
Jupiter is closer to Terra and has 3He as well. But Jupiter's gravity is fierce! If the scoopships used solid core nuclear thermal rockets they'd need a whopping mass ration of 20 to escape back to orbit (43 km/s delta V). They wouldn't be able to carry enough 3He to be economical. Saturn on the other hand has a much lower gravity. NTR scoopships could manage with a mass ratio of 4 (26 km/s delta V), which is much more reasonable.
Tanker ships would need only 18 km/s delta V to travel from Saturn to Terra.
I worked up a sketchy future history centered around Saturn, called Ring Raiders.
The focal point for the Solar Gravitational Lens is about 542 astronomical units from Sol. Theoretically it can map the continents on extrasolar planets. However, each star will require its own telescope eyepiece, or it will have to be mounted on a torchship. Moving the eyepiece to look at a different star means moving it hundreds of astronomical units.
These are "maps" of the delta-V cost to move from one "location" to another (instead of maps of the distance from one location to another). A spacecraft with propellant in the tanks has a delta-V reserve (NASA calls it the delta-V "budget"). Spacecraft "spend" delta-V from their budget to "pay" for the cost of moving from one location to another (what they actually do is burn their rocket engine to expend propellant and thus perform a maneuver). The unit of currency in the delta-V budget is the meter per second of velocity change (abbreviated as "m/s"). If you'd rather use larger denominations then 1,000 m/s of delta-V is equal to 1 kilometer per second of delta-V ("km/s").
Keep in mind that some of the locations are actually orbits. And keep in mind that the "locations" are just useful waypoints spacecraft use to get from one interesting planet/moon/whatever to another. Meaning that there are actually infinitely many "locations", but most of them do not lead to anywhere except a one-way trip into the inky depths of space. We didn't bother to put such worthless locations on the map because what's the point?
If there is a planet with an atmosphere involved and your spacecraft has an aeroshell, then "aerobraking" may be used (i.e., diving through the planet's atmosphere to use friction to burn off delta-V for free in lieu of expending expensive propellant). There is a limit to how much delta-V can be gotten rid of by aerobraking. The general rule is that aerobraking can kill a velocity approximately equal to the escape velocity of the planet where the aerobraking is performed (10 km/s for Venus, 11 km/s for Terra, 5 km/s for Mars, 60 km/s for Jupiter, etc.).
Finally, all these maps show the minimum delta-V cost for travel. This is because for most near-future spacecraft their delta-V budgets are quite tiny. In other words the spacecraft are poor and can only afford to purchase shoddy items from the dollar store. In this case, "shoddy items" means Hohmann Transfer orbits. They are shoddy because they take a long time to travel (e.g., about nine months to travel from Terra to Mars) and because you can only use it when the launch window opens (e.g., every 26 months for Terra to Mars). Transit time and launch windows to a few major destinations can be found here.
The flip side is if you have a far-future spacecraft with an outrageously huge delta-V budget (a "torchship"), you do not need any of these maps. You just point your ship at the destination and ignite the engines. To find the delta-V cost and transit time refer to the Mission Tables under the columns labeled "Brachistochrone".
- LEO: Low Earth Orbit. Earth orbit from 160 kilometers to 2,000 kilometers from the Earth's surface (below 200 kilometers Earth's atmosphere will cause the orbit to decay). The International Space Station is in an orbit that varies from 320 km to 400 km.
- GEO: Geosynchronous Earth Orbit. Earth orbit at 42,164 km from the Earth's center (35,786 kilometres from Earth's surface). Where the orbital period is one sidereal day. A satellite in GEO where the orbit is over the Earth's equator is in geostationary orbit. Such a satellite as viewed from Earth is in a fixed location in the sky, which is intensely desirable real-estate for telecommunications satellites. These are called "Clarke orbits" after Sir. Arthur C. Clarke. Competition is fierce for slots in geostationary orbit, slots are allocation by the International Telecommunication Union.
- EML1: Earth-Moon Lagrangian point 1. On the line connecting the centers of the Earth and the Moon, the L1 point is where the gravity of the two bodies cancels out. It allows easy access to both Earth and Lunar orbits, and would be a good place for an orbital propellant depot and/or space station. It has many other uses. It is about 344,000 km from Earth's center.
Rocket Flight Delta-V Map
In the also regrettably out of print game Rocket Flight the map is ruled off in hexagons of delta V instead of hexagons of distance (wargames use hexagons instead of squares so that diagonal movement is the same distance as orthogonal). Moving from one hex to an adjacent hex represents a delta V of 3 kilometers per second. This also means that in this map each hexagon represents an entire orbit (instead of a location), due to "rotating frames of reference" (no, I do not quite understand that either; but people I know who are more mathematically knowledgable than I have assured me that it is a brilliant idea).
In order to move to an adjacent hexagon in one turn, the spacecraft has to expend propellant mass points. To discover how much, refer to the table and cross reference the spacecraft propulsion's specific impulse with the spacecraft's dry mass points:
0 to 5
6 to 10
11 to 20
21 to 30
31 to 99
If you want to move two hexes in one turn, you have to burn four times the specified number of propellant points. You can move three hexes for eight times the propellant, four hexes for 16 times the propellant, and 5 hexes for 32 times the propellant. Which is why most people opt to just move one hex per turn unless it is an emergency.
However, the various propulsion systems have a maximum mass flow rate, which is the maximum number of propellant points it can expend in one turn. This corresponds to the spacecraft's acceleration rate.
High Frontier Delta-V Map
The black hexagons are sites, which are planets, moons, and asteroid spacecraft can land on. some planets are composed of several sites, e.g., the planet Mars is composed of three sites: North Pole, Hellas Basin Buried Glaciers, and Arsia Mons Caves.
Sites are connected by lines called routes which are paths that spacecraft can move along. During the turn, a spacecraft can move as far as it wants along a path, until it encounters a pink circle. In order to enter a pink circle it has to expend one "burn" (paying the 2.5 km/sec delta V cost and also expending a unit of propellant). At the beginning of each turn, a spacecraft is given an allotment of "burns" equal to its acceleration rating. These burns can be used during its turn, unused burns are lost. Remember in order to use a burn the spacecraft must pay a point of propellant.
When a spacecraft runs out of burns, it can no longer enter pink circles during this turn. It has to stop on any "Intersections" on its current path prior to the pink circle. And when a spacecraft runs out of propellant, it can no longer make burns at all until it is refueled no matter what turn it is.
The number of propellant units and the acceleration rating of a spacecraft depends upon its propulsion system and mass ratio.
Different routes cross each other. If one of the routes has a gap (so it appears that one route goes "over" and the other goes "under", see "No Intersection" in the diagram) the two routes are not connected. If both routes have no gaps they are connected, this is called a "Hohmann Intersection". If the place the two routes cross is marked with a circle they are connected, this is called a "Lagrange Intersection." At the end of a turn all spacecraft must be occupying either an Intersection or a Site.
A spacecraft can turn at an Interstection to switch from the route it is on to the route it was crossing (otherwise it has to stay on its current route). It costs one burn to turn at a Hohmann intersection, turning at a Lagrange intersection is free (due to gravity being negated by a nearby planet).
Some Lagrange intersections are marked with symbols:
- Skull and Crossed Bones: a Crash Hazard. Spacecraft has to roll a die to see if it crashes and is destroyed.
- Parachute: an Aerobrake Hazard. Spacecraft has to roll a die. If it rolls 2 to 6, it successfully areobrakes, and can now move to land on a Site with no cost in propellant. If it rolls a 1, it burns up in reentry and is destroyed. Spacecraft with Atmospheric ISRU Scoops are immune to Aerobrake Hazards, they are automatically successful. In addition such spacecraft can refuel if they ends their move there. A spacecraft using one of the three kinds of lightpressure sail propulsion is automatically destroyed if it enters an Aerobrake Hazard.
- Number: Gravitational Slingshot. Spacecraft obtains that number of extra burns which do not require propellant to be expended. These burns can be used in the remainder of the game turn. NASA loves gravitational slingshots and use them at every opportunity.
- Lunar Crescent: Moon Boost. As per Gravitational Slingshot, except it only gives +1 extra propellant-free burn.
- Nuclear Trefoil: Radiation Belt. Spacecraft entering this suffer a radiation attack. Roll one die and subtract the spacecraft's modified thrust to find the radiation level (the faster you can fly the lower the radiation dose). All spacecraft systems with a radiation hardness lower than the radiation level are destroyed. If sunspots are active add 2 to the die roll. The UN Cycler is immune to the Earth radiation belt. Spacecraft with a sail propulsion system are immune to radiation belts. Spacecraft with Magnetic Sails are immune and in addition get a Moon Boost.
High Trader Delta-V Map
A pity this game never saw the light of day.
Each triangle or diamond shape is an Orbital. Spacecraft in orbitals must always be facing one of the sides of the orbital. Turning to face an adjacent side requires one burn of 2.5 km/s delta V. Spacecraft can move from the orbital they are in, jumping over the face they are pointing at, and enter the next orbital. There is no cost to do so unless the face has a Burn Dot on it. In that case the spacecraft must expend one burn of 2.5 km/s delta V. If the spacecraft does not have that much delta V left it is forbidden to cross the Burn Dot.
Each new orbital entered adds 2 months to the spacecraft's travel time.
Starting at Neptune's orbit (30 AU) and extended a bit beyond Pluto's orbit (50 AU) is the Kuiper belt. It is like the asteroid belt except it has about 20 to 200 times as much asteroid mass as does the conventional asteroid belt. And it probably has far more frozen volatiles, aka in situ resource opportunities.
The Oort cloud is about a thousand times more distant than the Kuiper belt, and is spherical instead of being a belt. It is where the comets come from. Its inner edge is at about 20,000 AU and the outer edge is at about 50,000 AU (about 0.8 light-years or about 1/5th the distance to Proxima Centauri).
There are some short period comets with aphelions in the zone from Jupiter's orbit (about 5 AU) out to about 500 AU. There are some longer period comets with aphelions in the zone from 500 AU to the inner edge of the Oort cloud (20,000 AU).
Oddly enough there are no comets with aphelions in the zone from 1000 AU to 5000 AU. Presumably there is some as-yet undiscovered body there which gravitationally perturbs any comet's aphelion out of the forbidden zone.
Pretty much nothing until you reach the fringe of Alpha Centauri's Oort cloud. Maybe a rogue planet or two.
Interstellar space is pretty empty. 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.
For specific advice about laying out star maps of interstellar empires, the main article is here.
Maps usually have distance and coordinates in light-years. Occasionally you will find them using parsecs, since that the measurement of choice of astronomers. No Han Solo jokes, please. 3.26 light-years equals 1 parsec. So if you are dealing with a nasty parsec map, multiply all distances and coords by 3.26 to convert to light-years.
Yes, parsecs is the scientifically accurate choice, but science fiction readers hate it with a passion. Since such fans vote with their wallet, wise science fiction writers use light-years.
Traditionally at this point science commentators insert Douglas Adams' "Space is Big" quote here.
The surface of Terra is close enough to being flat that one can get away with using a two-dimensional map printed on a flat piece of paper.
The planets of the solar system can still be managed on a flat map, though not as easily. The planets are all pretty close to the plane of the ecliptic, except for that pesky Pluto. But comets do not map well at all.
On a broad scale, you can sort of manage to map the entire galaxy as a whole. It is about 100,000 light years in diameter, but only about 1,000 light years thick. A 100:1 ratio is close to a plane. Except for that pesky bulbous core. But the globular cluster do not map well at all.
Unfortunately, interstellar map of individual stars pretty much demand three-dimensional maps. As do maps of clusters of galaxies.
This wouldn't be a problem except for the tragic lack of 3-D holographic projectors on the consumer market. Paper maps and flat images on computer screens are so much more available. The most afordable solution I've found to date is the Windows software AstroSynthesis. It allows one to dynamically rotate the map with your computer mouse, zoom in, and make short video clips. If you do purchase it, be sure to download the free HIP and Kepner star catalogs of nearby stars.
So what you are reduced to is taking a 3D map and turning it into a 2D map so it can be printed on a flat piece of paper. You plot each star on the paper using only two of the three coordinates, then print next to each star the third coordinate. That tells you how far above or below the surface of the paper you have to imagine the star being actually located.
Such maps are confusing since two stars can look very close on the map, but actually be quite distant from each other due to the z coordinate. Not good, but its all we got until reasonably priced holographic displays re commonplace.
These maps may be created in equatorial coordinates (where the X-Y plane is parallel to Terra's equator) which is old and busted, or in galactic coordinates (where the X-Y plane is parallel to the planet of the galaxy) which is the new hotness. Inferior equatorial coordinate maps can usually be identifed by the fact that Barnard's Star is dead on the -Y axis (XYZ 0,-6,0 in light-years).
To find the actual distance between two stars, given their xyz coordinates, one has to use the True Distance Formula.
To actually calculate the distance between two given stars:
- DIST = SQRT[ (X1-X2)^2 + (Y1-Y2)^2 + (Z1-Z2)^2 ]
where SQRT[x] means "take the square root of x", and (x)^2 means "square x".
Three dimensional maps flatted into two dimensional maps quickly reach their limits. They are confusion, it is hard to tell which stars are actually closet to each other, and the more stars you add to the map the more stars start printing on top of each other. Here is a horrible example.
Node maps (or 2-1/2 dimensional maps) are an attempt to fix the problem.
The idea is instead of being able to see the distance between a star and every single one of the zillions of other stars on the map, perhaps it might be good enough to see the distance between a star and only its two or three closest neightbors. If you can live with that, you can make a map that looks more like a subway map, with all the stars flat on the paper and not overlapping. The important part is the distances between a star and its neighbors, shown as path lines thoughtfully labeled with the distance the line represents.
Imagine a planet inhabited by imperialistic little opportunistic aliens, just like us, whose star is in a galaxy totally uninhabited by any other intelligent creatures (or at least uninhabited by creatures who can defend themselves). Once our imperialists discover interstellar travel, they will spread to the surrounding stars in a manner similar to a watermelon hitting the sidewalk. Their empire will approximate an expanding sphere, with their homeworld at the center.
It is useful to be able to calculate a bit of geography for your interstellar empires. The control radius between the Imperial (or Sector) Capital and the Rim give you the size of your empire. It would be nice to be able to figure out how many stars are inside the empire, especially if you want to ensure that the Imperial Bureaucracy can actually handle it.
In order to expand the size of an empire, they will sometimes delegate authority to imperial governors who rule imperial sectors. These sectors are traditionally named after the brightest star within the sector limits.
Warning, the galactic plane in the neighborhood of Sol is only about 1,000 light-years thick. If the radius is over 500 light-years the equations will calculate give an incorrect result (too many stars).
Given the empire radius in light-years, the number of stars and habitable stars inside the borders is:
Nstars = Rly3 * StarDfactor
NhStars = Rly3 * HStarDfactor
- Nstars = number of stars
- NhStars = number of stars with habitable planets
- StarDfactor = star density factor, use 0.017 or see below
- HStarDfactor = habitable star density factor, use 0.002 or see below
- Rly = empire radius in light-years
- x3 = cube of x, i.e., = x * x * x
Given the number of stars or habitable stars inside the imperial borders, the empire radius is:
Rly = cubeRoot(Nstars * StarRfactor)
Rly = cubeRoot(NhStars * HStarRfactor)
- Rly = empire radius in light-years
- Nstars = number of stars
- NhStars = number of stars with habitable planets
- StarRfactor = star radius factor, use 59.68 or see below
- HStarRfactor = habitable star radius factor, use 464.46 or see below
StarDfactor, HStarDfactor, StarRfactor, HStarRfactor: all depend upon the stellar density, that is, how many stars per cubic light year. Currently the best estimate I could find for stellar density in Sol's neighborhood is Erik Gregersen's 4.0×10-3 stars per cubic light year. The density of stars with human habitable planets I calculated by using Tarter and Turnbull's Habcat dataset. Simplistic math on my part gave a value of 5.14×10-4 habitable stars per cubic light year. But keep in mind that the HabCat dataset came out in 2003.
StarRfactor = StellarDensity / ( (4/3) * π )
StarDfactor = 1 / StarRfactor
HStarRfactor = HStellarDensity / ( (4/3) * π )
HStarDfactor = 1 / HStarRfactor
- StellarDensity = stars per cubic light-year
- HStellarDensity = habitable stars per cubic light-year
You can find how I derived this equation here.
|Erik Gregersen||4.0×10-3 s/ly3||59.68||0.017|
|Globular Cluster||2.02×100 s/ly3||0.118||8.461|
|Galactic Core||2.88×100 s/ly3||0.083||12.064|
|Galactic Center||8.5×101 s/ly3||0.003||356.047|
Now, let us start with two empires. Assuming that they have a rough technological parity, the two spheres will expand until the boarders make contact. Then it will resemble two soap bubbles stuck together, with a flat "neutral zone" populated by spies, smugglers, covert battlefleets intent on causing boarder incidents, and planets named "Casablanca".
In reality, the "neutral zone" will be the less like a plane and more like the intersection of the two spheres. It will be like a lop-sided lens shape. The equation for calculating the volume of the neutral zone can be found here
Sol's Interstellar Neighborhood
This is a three dimensional star map I made back in 2008 of the closest 100 stars according to the RECONS star catalog. As a shameless plug, I sell this map in poster form, where you can actually read the numbers without straining your eyes.
The map is a three dimensional XYZ cartesian graph with the grid and each star's coordinate is printed.
The map is in Galactic coordinates. The x-y plane is the plane of the galaxy. The +X axis points at the galactic core ("Coreward"), the -X axis points away from the core ("Rimward"), the +Y axis is the direction the galaxy's spiral arms move ("Spinward") and the -Y axis is the opposite direction ("Trailing"). Sol, our Sun is in the center at 0,0,0. Pretty much all 100 stars are within 20 light-years of Sol.
If using the True Distance Formula makes your head hurt, just look at the map's violet and green lines.
The stars are the colored star symbols. Each star has violet line drawn to its two closest stellar neighbors (two is an arbitrary number of neighbors, with three or more the map becomes a tangled mess of lines). The midpoint of each line is labeled with the distance between the two stars in light-years. So to get an idea of where the stars are without using mathematics, just look at the violet lines to see how they are connected.
Stars that are in the HabCat star catalog have a high probability of having quote "habitable" unqote planets. Note that "habitable" does NOT mean "planet that humans can live on in their shirt-sleeves." Also note that since the HabCat catalog was compiled, astronomers have learned that spectral class M red stars have more habitable planets than previously thought.
Anyway, each HabCat star has green lines drawn between it and its two closest HabCat star neighbors. HabCat stars have gold rings drawn around their star icons. The important point to remember is for your interstellar colonies and initial empires you should probably focus on the green lines.
Back in the early 2000s, I did some star map work for Ken Burnside's Attack Vector: Tactical "Ten Worlds universe."
Mr. Burnside was doing his worldbuilding right, by using real star data along with a specification for his universe's faster-than-light drive. So he would have that determine the strategy, tactics, and other constraints for his game universe.
The wrong way is to first decide upon the desired constraints, then desperately try to retrofit the map and FTL details so the desired constraints occur as emergent behavior. We call this the "wrong way" because it is almost impossible to plug up all the loop holes to prevent unintended consequences.
Mr. Burnside started by constraining the universe to stars within 10 parsecs (32.6 light-years) of Sol, since 10 was a nice round number. We would nudge the boarder in specific spots out further if need be, or if we found anything interesting. I took my best star catalog and trimmed it down to just stars at the specified distance.
Among the data in the star catalog was certain stars were flagged as having a high probablility of hosting a human-habitable planet. This was the short list of candidates for the worlds which would become the Ten Worlds.
Mr. Burnside specified that starships could only use their FTL drive to travel between stars connected by "jump routes". There were several classes of routes, Alpha type route, Beta type route, Gamma type route, etc. Two stars were connected by a given type of jump route if the distance between was greater than the minimum route length but less than the maximum route length.
For instance: the distance between Sol and Sirius is 2.64 parsecs. Delta type routes have a minimum distance of 2.4 pc and a maximum distance of 2.7 pc, therefore Sol and Sirius are connected by a Delta jump route since 2.64 is greater than 2.4 and less than 2.7. Gamma type routes have a minimum distance of 3.9 pc and a maximum of 4.4 pc so Sol and Sirius are not connected by a Gamma jump route.
A starship's jump drive is rated according to the maximum jump level it can handle. So a Gamma drive can use Alpha, Beta, or Gamma jump routes. Naturally the higher the drive rating, the more massive and more expensive it is.
Where did the minimum and maximum distances come from? Mr. Burnside had an amusing harmonic equation which he used, just because he arbitrarily liked the spacing of the intervals.
My next task was to write a quick Python script which took the trimmed star catalog as input, and figured out which stars were connected to which other stars, and by what types of jump links. You can see a graphic representation of this in the node map below.
From a wargame standpoint, the map of jump links revealed militarily interesting locations: choke points and grand central stations. Mr. Burnside used this as one of the decision factors for figuring out which of the worlds were the Ten Worlds. He wanted star colonies that were in thought-provoking locations from a interstellar trade and combat viewpoint.
Ken specified an average rate of interstellar exploration, that is, how many years per link. This is a measure of the speed of the exploration wave. I wrote another Python script that modeled the wave. Little virtual scout starships would jump to an unexplored star, add to the master list the year that star was explored, then it would spawn new virtual scout starships that would all wait for the "years per link" period to pass then jump to all unexplored stars linked to the current star. The result was a list of the year each star was explored.
The important point was when each of the star colonies were explored, since that was the earliest year each colony could be established. This also gave a value for the relative age of each colony, which relates to their levels of industrialization.
From a gameplay standpoint, there was one fly in the ointment. Sol and Terra had the overwhelming advantage. It would be centuries before any of the colonies could come anywhere near Terra's level of industrialization. And since Sol was the start of the exploration, it had the strategic advantage of a central location. The colonies didn't stand a chance. Which would make for a very boring game.
Which is why in the Ten Worlds universe came an event called the "Whatever." For reasons only known to Ken and a few Ten Worlds game designers sworn to secrecy (not including me), on a certain day the three jump links connecting to Sol abruptly vanished. And in the decades to come there has been nary a peep out of Terra.
Armed with the node map, list of colonies, and their relative levels of industrialization, Ken could now generate the future history by using the Great Game technique.
The end result is that Ken Burnside's Ten Worlds universe is solid enough to walk on.
Interstellar colonists hungry for the "light of home" will be out of luck if the colony is farther than 55.7 light years away from Sol. Beyond that distance, Sol will be dimmer than apparent magnitude 6.0, too dim to see with the naked eye. Colonists who want to see Sol will need a telescope.
This is a project I am working on. 13 interstellar empires contained within a 100 light-year radius sphere.
You can download the AstroSynthesis file here and the readme file here. Warning: you need to purchase the AstroSynthesis software to display the map, it is Windows only, the file is a work in progress and contains mistakes, and the blasted thing is 3.5 megabytes.
AstroSynthesis will allow you to rotate and pan the map manually, with is surprisingly helpful to see the relationship of all the stars.
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 0.05 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.
Here's the result of my experimental Interstellar Empire Framework project.
I started with one empire centered on Sol. For the dreaded center of the evil Zork Empire, I looked at the HabCat database and arbitrarily picked a star that was 150 light-years away from Sol: BD-09°431. The locations of the two empire centers was averaged to locate the point exactly midway between.
The map is going to encompass a capsule shaped volume, that is, a cylinder with both ends capped by hemispheres. This will represent two 60 light-year diameter spheres (30 light-year radius), one centered on Sol, the other on Zork Prime. The rest will be in a cylinder 30 light-years in radius connecting the two spheres.
The 60 light-year diameter spheres will be the "spheres of influence" of Sol and Zork. Another 60 ly diameter sphere centered on the midpoint will be the Neutral Zone. The idea is that the intrepid empire builder will decide which stars have been explored, which have mining colonies, which are colonized, and which are officially part of the empire. Once the enemy has been discovered, the neutral zone will alternate between being a demilitarized zone and the main battle line. As previously mentioned, this will be populated by spies, smugglers, covert battlefleets intent on causing boarder incidents, and planets named "Casablanca".
So I wrote a quick Python program and fed it a subset of the HabHYG database. It filtered out all the stars outside of the capsule volume and generated lines between each star and its closest two neighbors. Stars inside the two spheres of influence and the neutral zone were color coded. The program outputted this data as a GML format node map.
I then opened the file in yEd, autoformatted it, then laboriously tweeked it until it was compact. I saved it as a GIF file, and as a WMF file. I then used Adobe Illustrator to tranform the WMF file into a PDF file.
Have fun with it. Distances on the map are in parsecs, sorry about that.
For interstellar colonists, "the light of home" is the star Sol in the night sky. It is too dim to be seen by the naked eye if the colony is further than 55.7 light years away.
However, the brilliant star Sirius is a mere 8.6 light-years away from Sol. If the colony is no further than 271 light-years away from Sirius, it will have an apparent magnitude of 6.0, just barely visible to the naked eye. The colonists cannot see Sol, but they will know it is right next to Sirius.
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 0.05 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.
Fig. 1. Local cavity and LB in the plane of the Galactic equator. The filled contours show the Na i distribution (Sfeir et al. 1999), with white used for low-density regions and dark gray for high-density ones. The black contour shows the present size of the LB as determined from X-ray data (Snowden et al. 1998), with the dashed lines indicating contaminated areas where the limits of the LB cannot be accurately determined. The hatched ellipse shows the approximate position of the Ophiuchus molecular cloud (de Geus et al. 1989; Loren 1989a, 1989b). The present and past x- and y-coordinates of the center of the three subgroups of the Sco-Cen association are shown. For LCC and UCL, the past positions shown are those of 5 and 10 Myr ago, while for US only the position of 5 Myr ago is shown. The dimensions of the filled ellipses indicate the uncertainties in the past positions. Coordinates are expressed in units of parsecs.
Translation into English:
View is looking down on the galactic plane. Sol is dot in the center. Coreward is to the right (labeled "To the GC"), Spinward is to the top (labeled "Rotation Direction"). Scale on the edges are in parsecs, map is area plus or minus 200 parsecs (652 light-years).
The black dotted line is the boarder of the Local Bubble. As near as I can tell the black square icon tracked with arrows (the Sco-Cen OB association UCL subgroup) is the same as the Pleiades subgroup B1 mentioned below.
Fig. 2. Sketch of the solar neighborhood seen from above the galactic plane. The center of mass position of Pleiades subgroup B1 is labeled with “B1”. The solid line, ending at the actual position of B1, provides the trajectory of the moving group during the past 30 Myrs in the epicyclic approximation (see Sect. 3); center of mass positions 13, 20, and 30 Myrs ago are labeled with -13, -20, and -30. Approximately 13 Myrs ago the most massive B1 star(s) (M ≈ 20 M⊙) must have exploded. The local cavity contours as derived from Nai absorption line studies by Sfeir et al. (1999) are shown as thick solid lines (dashed lines denote directions of uncertain local cavity borders). As can be seen, existing B1 member stars (or at least some of them, given their spatial spread) should have crossed the region, which now forms the Local Bubble.
Translation into English:
View is looking down on the galactic plane. Sol is dot in the center. Coreward is to the right (labeled "GC"), Spinward is to the top. Scale on the axes are in parsecs, map is area plus or minus 200 parsecs (652 light-years).
The large gray disc is the Local Bubble. B1 is the Pleiades subgroup B1. It trails an arc showing its path through the galaxy, labeled with marks for -13, -20, and -30 million years ago. α Per (Alpha Persei Cluster), Pleiades cluster, Praesepe (Beehive) cluster, NGC 2451 cluster, IC 2391 (Omicron Velorum) cluster, and IC 2602 ( Theta Carinae or Southern Pleiades) cluster are marked.
Half The Galaxy
These terms were probably coined by Marc Miller for the Traveller RPG.
- Coreward: towards the center of the galaxy (alternate: "hubward")
- Rimward: opposite the direction to the center of the galaxy
- Spinward: towards the direction of galactic spin (alternates: "turnward", "down-spin" or "deosil")
- Trailing: opposite the direction of galactic spin (alternates: "anti-spinward", "up-spin" or "widdershins")
- Zenith: along the galactic spin axis, in the "northward" direction as per the right-hand rule (alternate: "acme")
- Nadir: along the galactic spin axis, in the "southward" direction as per the right-hand rule
In spherical coordinate systems, they often choose a direction to be "up" or "north". For rotating objects like Terra, they use the "right-hand rule". You curl your hand in the direction of rotation (for Terra, west to east), and the direction your thumb points is "north." If you are in the northward direction and you look "down" at the object, it will appear to be spinning counter-clockwise.
However, if you examine at the galactic maps below, which are done from the northward perspective, you will see they are rotating in the wrong direction, clockwise. This is because in galactic coordinates, astronomers picked the wrong direction to be north.
Why? Because back in the dawn of astronomical science when galactic coordinates were invented, astronomers had no way of telling which way the galaxy rotated. So they somewhat arbitrarily chose as "north" the galactic pole which was in the same hemisphere as Terra's north pole. Unfortunately Terra's axis of rotation has nothing to do with the galactic axis.
CfA2 Great Wall
The CfA2 Great Wall is giant wall composed of galaxies about 500 million light-years long, 300 million light-years wide, and 16 million light-years thick. It is about 200 million light-years away from Terra. It includes the Hercules Supercluster, the Coma Supercluster, and the Leo Cluster.
Sloan Great Wall
The Sloan Great Wall is giant wall composed of galaxies about 1.38 billion light-years in length (about 1/60th of the diameter of the observable universe) and 1 billion light-years away from Terra.
Hercules–Corona Borealis Great Wall
The Hercules–Corona Borealis Great Wall is a giant wall composed of galaxies. It is currently the largest and most massive structure known in the observable universe. It is about 10 billion light-years across and 9.612 to 10.538 billion light-years from Terra.
Most Distant Objects
The current most distant candidate astronomical object is a galaxy called UDFj-39546284 with a redshift z=11.9 (though some astronomers suspect it is a nearby object with a peculiar spectrum). This would give it a light-travel distance of 13.37 billion light-years.
The current most distant "proven" astronomical object is some as-yet unseen galaxy or something that emitted Gamma Ray Burst 090423. it has a redshift z=8.2. When the GRB occured, the universe was only 630 million years old.
The universe is only 13.798±0.037 billion years old, which is quite a bit less than 46.6 billion. However, due to the expansion of space astronomers are observing objects that were originally much closer but are "now" considerably farther away. That explains the discrepancy.
Astronomers technically make a distinction between the visible universe and the observable universe. When the Big Bang occured, the universe was wall-to-wall plasma that was opaque to light and other electromagnetic radiation. About 377,000 years after the Big Bang the universe had expanded to a point where all the electrons and protons in the plasma suddenly combined into hydrogen atoms (called the Recombination). No more plasma meant the universe was abruptly transparent to light.
So the visible universe only has a radius of 45.7 billion light-years (starting at recombination) while the observable universe has a radius of 46.6 billion light-years (starting at the Big Bang). To be vislbe means you need light, and there ain't none available before recombination. However, the observable universe could theoretically be observed even before recombination using gravitational waves, neutrinos, or something like that. Yes, I know, it is really nit-picky but scientists have to be precise or major break-throughs are overlooked.