RocketCat sez

Listen up, you newbie science fiction authors! If you don't want to embarrass yourself, you'd better get at least a vague notion of where things are in space and how far they are.

For that matter; if you don't know the difference between a planet and a star they will revoke your skiffy card. You'd better audit an Astronomy 101 course or flip through Astronomy For Dummies, for cryin' out loud.

Logarithmic scheme of the observable universe. Artwork by Pablo Carlos Budassi. Use horizontal scroll bar to pan the map.

Space is Big 1

The introduction begins like this: "Space," it says, "is big. Really big. You just won't believe how vastly hugely mindboggingly big it is. I mean you may think it's a long way down the road to the chemist, but that's just peanuts to space. Listen ..." and so on.

Space is Big 2

     "Beeblebrox," he said, sticking his hands behind his head, "have you any idea what's going to happen to you on the Frogstar?"
     "They're going to feed me?" hazarded Zaphod hopefully.
     "They're going to feed you," said Roosta, "into the Total Perspective Vortex!"
     Zaphod had never heard of this. He believed that he had heard of all the fun things in the Galaxy, so he assumed that the Total Perspective Vortex was not fun. He asked what it was.
     "Only," said Roosta, "the most savage psychic torture a sentinent being can undergo."
     Zaphod nodded a resigned nod.
     "So," he said, "no food, huh?"

     "Listen!" said Roosta urgently, "you can kill a man, destroy his body, break his spirit, but only the Total Perspective Vortex can annihilate a man's soul! The treatment lasts seconds, but the effect lasts the rest of your life!"
     "You ever had a Pan Galactic Gargle Blaster?" asked Zaphod sharply.
     "This is worse."
     "Phreeow!" admitted Zaphod, much impressed.

     The Universe, as has been observed before, is an unsettlingly big place, a fact which for the sake of a quiet life most people tend to ignore.
     Many would happily move to somewhere rather smaller of their own devising, and this is what most beings in fact do.

     For instance, in one corner of the Eastern Galactic Arm lies the large forest planet Oglaroon, the entire "intelligent" population of which lives permanently in one fairly small and crowded nut tree. In which tree they are born, live, fall in love, carve tiny speculative articles in the bark on the meaning of life, the futility of death and the importance of birth control, fight a few extremely minor wars, and eventually die strapped to the underside of some of the less accessible outer branches.
     In fact the only Oglaroonians who ever leave their tree are those who are hurled out of it for the heinous crime of wondering whether any of the other trees might be capable of supporting life at all, or indeed whether the other trees are anything other than illusions brought on by eating too many Oglanuts.

     Exotic though this behaviour may seem, there is no life form in the Galaxy which is not in some way guilty of the same thing, which is why the Total Perspective Vortex is as horrific as it is.
     For when you are put into the Vortex you are given just one momentary glimpse of the entire unimaginable infinity of creation, and somewhere in it a tiny little marker, a microscopic dot on a microscopic dot, which says "You are here."


500 Kilometer Radius

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 launching rocket's ground track to be passing over parts of Terra's surface that are uninhabited and either belong to you or to nobody (or at least belonging to nobody with enough political power to complain about toxic flaming rocket debris raining down from the sky). Over the ocean is prefered. China launch ground track passes over villagers who know better than to protest.

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.


Oceanic pole of inaccessibility

The oceanic pole of inaccessibility (48°52.6′S 123°23.6′W) is the place in the ocean that is farthest from land. It lies in the South Pacific Ocean, 2,688 km (1,670 mi) from the nearest lands: Ducie Island (part of the Pitcairn Islands) in the north, Motu Nui (part of the Easter Islands) in the northeast, and Maher Island (near the larger Siple Island, off the coast of Marie Byrd Land, Antarctica) in the south.

Known as "Point Nemo", Latin for "no one" and also a reference to Jules Verne's Captain Nemo, it lies more than 1,400 nautical miles from the nearest land. This point was featured in the short story, The Call of Cthulhu, by H. P. Lovecraft as the location of the fictional city of R'lyeh.

The area is also known as a "spacecraft cemetery" because hundreds of decommissioned satellites, space stations, and other spacecraft have been deposited there upon re-entering the atmosphere to lessen the risk of hitting any inhabited locations. Point Nemo is relatively lifeless; its location within the South Pacific Gyre blocks nutrients from reaching the area, and being so far from land it gets little nutrient run-off from coastal waters.

From the Wikipedia entry for POLE OF INACCESSIBILITY

The phrase Spacecraft Cemetery can refer to an area in the southern Pacific Ocean 3,900 kilometres (2,400 mi) southeast of Wellington, New Zealand, where spacecraft, notably the defunct Mir space station and waste-filled Progress cargo ships are and have been routinely deposited. The area corresponds with the "Point Nemo" oceanic pole of inaccessibility; the area of ocean furthest from land. It has been chosen for its remoteness, so as not to endanger or harm human and oceanic life. The nearest land is approximately 2,415 kilometres (1,501 mi) away from the cemetery.

Other spacecraft types that routinely use the South Pacific re-entry location include several other unmanned resupply spacecraft to the ISS: the Japanese H-II Transfer Vehicle, and the European Space Agency Automated Transfer Vehicle (ATV). A total of more than 263 spacecraft were disposed of in this area between 1971 and 2016.

From the Wikipedia entry for SPACECRAFT CEMETERY

The South Atlantic Anomaly (SAA) is an area where the Earth's inner Van Allen radiation belt comes closest to the Earth's surface, dipping down to an altitude of 200 kilometres (120 mi). This leads to an increased flux of energetic particles in this region and exposes orbiting satellites to higher-than-usual levels of radiation.

The effect is caused by the non-concentricity of the Earth and its magnetic dipole. The SAA is the near-Earth region where the Earth's magnetic field is weakest relative to an idealized Earth-centered dipole field.


The area of the SAA is confined by the intensity of Earth's magnetic field at less than 32,000 nanotesla at sea level, which corresponds to the dipolar magnetic field at ionospheric altitudes. However, the field itself varies in intensity as a gradient.

Position and shape

The Van Allen radiation belts are symmetrical about the Earth's magnetic axis, which is tilted with respect to the Earth's rotational axis by an angle of approximately 11 degrees. The intersection between the magnetic and rotation axes of the Earth is located not at the Earth's "middle", but some 450 to 500 km (280 to 310 mi) further north. Because of this asymmetry, the inner Van Allen belt is closest to the Earth's surface over the south Atlantic Ocean where it dips down to 200 km (120 mi) in altitude, and farthest from the Earth's surface over the north Pacific Ocean.

If Earth's magnetism is represented by a bar magnet of small size but strong intensity ("magnetic dipole"), the SAA variation can be illustrated by placing the magnet not at the Equator, but some distance away from it, more or less over Singapore. As a result, over northern South America and the south Atlantic, near Singapore's antipodal point, the magnetic field is relatively weak, resulting in a lower repulsion to trapped particles of the radiation belts there, and as a result these particles reach deeper into the upper atmosphere than they otherwise would.

The shape of the SAA changes over time. Since its initial discovery in 1958, the southern limits of the SAA have remained roughly constant while a long-term expansion has been measured to the northwest, the north, the northeast, and the east. Additionally, the shape and particle density of the SAA varies on a diurnal basis, with greatest particle density corresponding roughly to local noon. At an altitude of approximately 500 km (310 mi), the SAA spans from −50° to 0° geographic latitude and from −90° to +40° longitude. The highest intensity portion of the SAA drifts to the west at a speed of about 0.3 degrees per year, and is noticeable in the references listed below. The drift rate of the SAA is very close to the rotation differential between the Earth's core and its surface, estimated to be between 0.3 and 0.5 degrees per year.

Current literature suggests that a slow weakening of the geomagnetic field is one of several causes for the changes in the borders of the SAA since its discovery. As the geomagnetic field continues to weaken, the inner Van Allen belt gets closer to the Earth, with a commensurate enlargement of the SAA at given altitudes.


The South Atlantic Anomaly is of great significance to astronomical satellites and other spacecraft that orbit the Earth at several hundred kilometers altitude; these orbits take satellites through the anomaly periodically, exposing them to several minutes of strong radiation, caused by the trapped protons in the inner Van Allen belt. The International Space Station, orbiting with an inclination of 51.6°, requires extra shielding to deal with this problem. The Hubble Space Telescope does not take observations while passing through the SAA. Astronauts are also affected by this region, which is said to be the cause of peculiar "shooting stars" (phosphenes) seen in the visual field of astronauts, an effect termed the cosmic ray visual phenomena. Passing through the South Atlantic Anomaly is thought to be the reason for the early failures of the Globalstar network's satellites.

The PAMELA experiment, while passing through the SAA, detected antiproton levels that were orders of magnitude higher than expected. This suggests the Van Allen belt confines antiparticles produced by the interaction of the Earth's upper atmosphere with cosmic rays.

NASA has reported that modern laptops have crashed when Space Shuttle flights passed through the anomaly.

In October 2012, the SpaceX CRS-1 Dragon spacecraft attached to the International Space Station experienced a transient problem as it passed through the anomaly.

The SAA is believed to have started a series of events leading to the destruction of the Hitomi, Japan's most powerful X-ray observatory. The anomaly transiently disabled a direction-finding mechanism, causing the satellite to rely solely on gyroscopes that were not working properly, after which it spun itself apart.

From the Wikipedia entry for SOUTH ATLANTIC ANOMALY

400,000 Kilometer Radius

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.

"Okay, T.K., look at it this way. Those three hundred people in LEO Base can get back to Earth in less than an hour if necessary; we'll have lifeboats, so to speak, in case of an emergency. But out there at GEO Base, it's a long way home. Takes eight hours or more just to get back to LEO, where you have to transfer from the deep-space passenger ship to a StarPacket that can enter the atmosphere and land. It takes maybe as long as a day to get back to Earth from GEO Base— and there's a lot of stress involved in the trip."

Hocksmith paused, and seeing no response from the doctor, added gently, "We can get by with a simple first-aid dispensary at LEO Base, T.K., but not at GEO Base. I'm required by my license from the Department of Energy as well as by the regulations of the Industrial Safety and Health Administration, ISHA, to set up a hospital at GEO Base."

He finished off his drink and set the glass down. "If building this powersat and the system of powersats that follow is the biggest engineering job of this century, T.K., then the GEO Base hospital's going to be the biggest medical challenge of our time. It'll be in weightlessness; it'll have to handle construction accidents of an entirely new type; it'll have to handle emergencies resulting from a totally alien environment; it'll require the development of a totally new area of medicine— true space medicine. The job requires a doctor who's worked with people in isolated places—like the Southwest or aboard a tramp steamer. It's the sort of medicine you've specialized in. In short, T.K., you're the only man I know who could do the job . . . and I need you."

Stan and Fred discovered that it took almost nineteen minutes just to get to Charlie Victor, Mod Four Seven. There were a lot of hatches to go through and a lot of modules to traverse. "Fred, if we don't find some faster way to move around this rabbit warren, a lot of people are going to be dead before we reach them," Stan pointed out, finally opening the hatch to Mod Four Seven.

Fred was right behind him through the hatch. "I'll ask Doc to see Pratt about getting us an Eff-Mu."

"What's that?"

"Extra Facility Maneuvering Unit. A scooter to anybody but these acronym-happy engineers."

Transporting was easy in zero-g, but getting through all the hatches while continuing to monitor his condition and maintain the positive-displacement IVs was difficult. It required almost a half hour to bring the man back to the med module.

From Space Doctor by Lee Correy (G. Harry Stine) 1981


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. It is possible to put an object into an orbit around the L1, 2, and 3 points. These are called halo orbits. They are not stable, but more stable than just parking a station in the point and hoping for the best.

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.

Important but commonly little-known facts about Lagrange points:

  • L4 and L5 points are only stable if the primary mass is 24.96 times as large as the secondary mass, or larger. If it is smaller than 24.96, objects parked in those points will dift away. Example: Terra has a mass of 5.97×1024 kg and Luna has a mass of 7.34×1022 kg. So Terra is 81 times as massive as Luna, therefore the Earth-Moon L4 and L5 points are stable.

  • The distance between the primary and L4, the primary and L5, the secondary and L4, the secondary and L5, the primary and the secondary are all the exact same distance. In other words: primary, secondary, and L4 make an equilateral triangle. So does primary, secondary, and L5. Example: the distance between Terra and EML4, Luna and ML5, and Terra and Luna are all 384,399 kilometers. Keep that in mind when planning travel time or communication time-lag between them.
Terra - Lagrange distances
Distance from
L13.264×108 m0.85
L24.489×108 m1.17
L33.817×108 m0.99
L43.844×108 m1.0
L53.844×108 m1.0
Luna3.844×108 m1.0

(ed note: the protagonist La Roque is a con artist, who has just perpetrated a major swindle. So major that he thinks the entire solar system is too hot for him to hide in, the cops really want to get their hands on him. Lucky for La Roque the civilization has casual FTL travel and he can easily afford to purchase a little runabout subcompact starship which can do 400c. Unluckily for La Roque he knows diddly-squat about orbital mechanics. He figures he has a month before the cops will start looking him in a League cruiser, which is ten times faster. In a month La Roque can travel 33 light-years, a League cruiser can travel 33 light-years in about 3 days flat.)

Therefore, it was essential that a hiding place be found. A planet, where the ship could be buried or otherwise concealed, would present an impossible search problem to a hundred League ships—if there were no inhabitants to hold inconvenient memories of his landing. He might find such a world by random search, but the distance he could travel in his month of grace was limited; and, he realized, very few suns lay within that distance. He got out a set of heliocentric charts and began his search on paper.

There is no excuse for him. His destination should have been planned before he left the ground—planned not only as to planet, but to location on the planet. He had always planned his “deals” with meticulous care; and had sneered at less careful colleagues whose failure to do so had resulted in more or less lengthy retirement to League reform institutions. It is impossible to say why he didn’t see that the same principle might apply to interstellar flight. But he didn’t.

Most of them, of course, were “dead” stars, detectable at only the closest range. Six of them had planetary systems; but the planets, without exception, possessed surface temperatures below the freezing point of mercury.

That was unfortunate. To remain alive on any of these worlds would demand that he stay in the ship, and use power, for heat and light. Even such slight radiation as that would cause meant a virtual certainty of detection by even a cursory sweep of the planet on the part of a League cruiser. He had to find a place where the ship would remain at least habitably warm without aid from its own converters. He could do without light, he thought.

The problem would not have bothered a pilot of even moderate experience, of course. The ship could easily be set in a circular orbit of any desired radius about one of the stars. Unfortunately, there is a definite relation between the mass of a star, the radius of the desired orbit, and the amount of initial tangenital velocity required; and this simple relation was unknown to La Roque. Trial and error would be very unsatisfactory; the error might be unnoticeably small to start with, and become large enough to require correction when searchers were around. A worried frown began to add creases above La Roque’s black brows as the little flier raced on.

(ed note:

OrbitalVelocity = sqrt[ (G * PlanetMass) / OrbitalRadius ]


OrbitalVelocity = mean velocity of ship in its orbit (m/s)
G = Newton's gravitational constant = 6.673×10-11 (N m2 kg-2)
PlanetMass = mass of planet (kg) (Terra = 5.98×1024 kg)
OrbitalRadius = distance from station to center of planet (m)
sqrt[ x ] = square root of x


From where he was, the runaway could not lay a direct course for his chosen hide-out. His knowledge of solid geometry and trigonometry was so small that all he could do was to continue on his present course until the proper heliocentric distance was attained, then stop, put Sol exactly on his beam, hold it there while he turned in the proper direction, and again run in second-order (FTL) flight for a certain length of time—dead reckoning pure and very simple. By thus reducing his goal position to a known plane—or near plane; actually the surface of a sphere centered on Sol—he could get the course of his second leg by simply measuring, on a plane chart, the angle whose vertex was the point in the sky toward which he had been driving, and whose sides were determined, respectively, by some beacon star such as Rigel or Deneb, and the star of his destination. He dragged out a heliocentric chart and protractor, and set to work.

By the most generous estimate, his margin of clearance from the law was growing narrow, when he cut the fields at—according to his reckoning—twenty-eight point seven seven four seven light-years from the Solar System.

He snapped on plate after plate, looking around in every direction. A fifth-magnitude star on the cross wires of the rear plate was, of course, Sol. He looked for Deneb, but Cygnus was too badly distorted by a parallactic variation of nine parsecs to permit him to identify its alpha star with certainty. Orion was recognizable, since he had been moving more or less directly away from it and all its principal stars were extremely distant; so he decided to use Rigel to control his direction.

He zeroed the cross wires of one of the side plates and, using the gyros, swung the ship until Sol was centered on that plate. Rigel was, conveniently, visible on the same plate; so he snapped a switch which projected a protractor on to it, and swung the ship again until Rigel was on the proper—according to his measures—radius. Using the plate’s highest power, he placed the two stars to four decimals of accuracy, released the gyro clutches, and cut in the second-order fields before friction at the gyro bearings could throw off his heading.

His arithmetic said he had eight hours and thirty minutes of flight to his destination. Experience would have told him that his chances of stopping within detection range of his goal were less than one in a hundred thousand; as it was, the chief worry that actually disturbed him was whether or not there was risk of collision. Not too surprising! In dead reckoning, the novice navigator makes a tiny point and says, “Here we are.” The junior makes a small circle and says the same. The experienced navigator lays the palm of his hand on the chart and says, “We ought to be here.” And La Roque’s was the deadest of dead reckoning.

As things were, he took one look at the forward plate, and for the next ninety seconds used language which should really have been recorded for the benefit of future sailors. He had some excuse. The star was listed in the chart reference as single; La Roque had chosen it for that reason. However, plainly visible on the plate, revolving evidently almost in contact, were two smoky red suns—a close binary system.

Of course, no one would normally be greatly interested. The Astrographic Survey vessel which had covered the section had probably swept past fifty billion miles out, and noted the system’s existence casually as its radiometers flickered. Size? Mass? Companions, if any? Planets? Who cared!

La Roque, of course.

He was wondering how a stable orbit could be established close enough to this system to keep him from freezing without using ship’s power. The near-circular one he had planned was out; it would have had to be less than a million miles from a single sun of such late type, and the doubling of the heat source wasn’t much help.

There had been an episode in his experiences which had occurred on Hector, one of the Trojan asteroids. Circumstances had caused him to remain there for some time, and a friendly jailer had explained to him just where Hector was and why it stayed there. It was in the stability point at the third corner of an equilateral triangle whose other corners were Sol and Jupiter; and though it could—and did—wobble millions of miles from the actual point, gravitational forces always brought it back.

La Roque looked out at the twin suns. Could his ship stand the temperature at the Trojan points of this system? More important, could he stand it?

He could. His instruments gave the energy distribution curve of the suns; one of the reference charts contained a table that turned the curves into surface temperatures. He was able to measure the distance between the centers of the suns, from the scale lines on the plate and his distance, which he knew roughly. Half a million miles from the surface of a star whose radius was fifty thousand miles and whose effective radiating temperature was a thousand degrees absolute, the black-body, temperature was, according to his figures, about thirty degrees centigrade. The presence of two stars made it decidedly warmer, but his ship was well insulated and the surface highly polished. It would eventually reach an equilibrium temperature considerably above that of an ideal black body, but it would take a long time doing so.

It seemed, then, that the Trojan point was the best place for him. He could find it easily enough; getting the centers of the stars sixty degrees apart would put him at the right distance. He could find the proper plane by moving around until the two suns appeared to move across each other in straight lines. It would not take long; by varying his distance from the system he could, in a few minutes, observe it through half a revolution.

It took him, in fact, less than an hour to find the orbital plane of the suns. It took him five and a half hours of first-order acceleration at one gravity to get rid of the hundred and twenty mile per second velocity difference between Sol and this system—fortunately, the chart had mentioned the high relative velocity, or La Roque would never have thought of such a thing. In a way, he didn’t mind the necessity; it was good to have weight for the first time in nearly a month. He was, of course, a little worried at the amount of time consumed; he wished he had not wasted so much of the commodity in putting Sol so far behind.

He cut the first-order drive the instant his clock told him the speeds should be equal, headed for the twin suns, and hopped for his Trojan point. Since moving bodies were involved, he had to make five legs out of the short trip—he failed to allow for the short period of the system and the fact that he started the first leg several light-hours from his goal.

He got there eventually, however. He suddenly realized that he would have to use first-order power again, to give his ship something like the proper orbital velocity; but even he was able to understand the proper magnitude and direction of this new vector; the only unjustified assumption he had to make was that the suns were of equal masses, and this happened to be nearly the case. He wasn’t too worried; he understood that in a Trojan orbit such small variations are opposed, not helped, by the gravity of the primary bodies. He was quite right.

He cut all his power except the detector relay currents, which did not radiate appreciably. To these he connected an alarm, and set them to synchronize with the low-frequency waves which form the “wake” of a vessel cruising at second-order speeds. Then, abruptly feeling the reaction of the past days, he drifted over to a “bunk,” moored himself, and was instantly asleep.

(ed note: Later he is awakened by the alarm, warning him that a League police cruiser has entered the system, and is prowling around looking for him. Hours pass as La Roque waits for the cruiser to give up and leave.)

Time crawled on—rapidly decelerating, in La Roque’s opinion. He had nothing to do except notice his own discomfort, which was on the increase. He cursed the ship’s builders for failure to insulate it properly, and the men who had computed the tables he had used to obtain the probable temperature at this distance from the suns. He didn’t bother to curse his own arithmetic.

Once he was almost on the point of driving farther out, hoping the pursuing ship had gone; but a flicker from one of the detectors made him change his mind. He hung and sweated; and the temperature mounted.

It must have been a hundred and fifty degrees Fahrenheit when he finally gave in. He could have stood more in the open—anyone could—but the air-conditioning apparatus had been stopped along with everything else, and the air in the ship was approaching saturation. With that fact considered, he held out remarkably well; but eventually his will power gave out. He kicked his way feebly back to the board, and snapped on the vision plates.

He lacked the energy to curse. For moments he could only stare in shocked horror at the plates—and realize how misdirected his previous denunciations had been. There was nothing wrong with his ship’s insulation; the wonder was that it had held out so well. One of the suns—he never knew which—completely filled the front, top, and port plates with a blaze of sooty crimson; he must have been within thirty or forty thousand miles of its surface. His hand darted toward the activating switch of the second-order drivers, and was as quickly checked. They would only send him straight forward, into the inferno revealed by the front plate. The ship must be turned.

He started the gyros, careless now of any insulation that might result. The control knobs were hot to the touch; and a smell of burning oil reached his nostrils as the gyros wound up to speed. The ship abruptly shuddered and began to gyrate slowly, as one of them seized in its bearings. He watched tensely as the vessel went through a full rotation, his hand hovering over the board; but not once was the glow in the forward plate replaced by the friendly darkness of space. The ship was spinning on its longitudinal axis.

The other gyros were working. He tried to turn the vessel with them. The result was to shift the axis of spin about thirty degrees—and increase its rate tenfold as another of the heavy wheels, spinning at full speed, jammed abruptly. Centrifugal force snatched him away from the board and against one wall; he shrieked as his flesh touched hot metal, and kicked violently. His body shot across the room, reaching the other side at about the same time his previous point of contact was carried around by the ship’s rotation.

The specks of carbon cirrus on the front plate were describing circles now—circles whose size was visibly increasing. For part of each turn the nose was now pointing into space; La Roque tried to fight his way back to the board to take advantage of one of those moments.

He might have made it, in spite of the agony, of his burns, but the overstrained insulation had done its best. It failed; and failed, of all places, over the water tanks that lined part of the hull. The tanks themselves offered only token resistance as steam pressure suddenly built up in them. La Roque never knew when scalding water shorted the control board, for a jet of super-heated steam had caught him just before he reached it.

On the enforcement cruiser, a man straightened up from a plotting board.

“That does it, I think,” he said. “He was using heavy current for a while, probably trying to turn out with his gyros; then there was a flash of S. H. F., and everything stopped. That must have taken out his second-order, and he’d have had to use about sixty gravities of first-order to pull out of that spot. I wonder what he was doing so close to those suns.”

“Could have been hiding,” suggested a second pilot. “He might have thought the suns would mask most of his radiation. I wonder how he expected to stay there any length of time, though.”

“I know what I’d have done in his place,” replied the first man. “I’d have put my ship into a Trojan position and waited the business out. He could have lasted indefinitely there. I wonder why he didn’t try that.”

“He probably did.” The speaker was a navigator, who had kept silent up to this point. “If a smart man like you would do it, a fellow like that couldn’t be expected to know any better. Have you ever seen a planet in the Trojan points of any double sun? I’ll bet you haven’t. That Trojan solution works fine for Sol and Jupiter—Sol is a thousand times the more massive. It would work for Earth and Luna, since one has about eighty times the mass of the other. But I have never seen a binary star where the mass ratio was anywhere near twenty-five to one; and if it’s less, the Trojan solution to the three-body problem doesn’t work. Don’t ask me why; I couldn’t show you the math; but I know it’s true—the stability function breaks, with surprising sharpness, right about the twenty-five-to-one mass ratio. Our elusive friend didn’t know that, any more than you did, and parked his ship right in the path of a rapidly moving sun.” He shrugged his shoulders, and turned away. “Live and learn, they say,” he finished, “but the difficulty seems to lie in living while you learn.”

From TROJAN FALL by Hal Clement (1944)

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.

1.8 AU Radius

Approximately the orbit of Mars.

2 AU Radius

Approximately the inner edge of the asteroid belt.

4 AU Radius

Approximately the outer edge of the asteroid belt.

10 AU Radius

Approximately the orbit of Saturn.

30 AU Radius

Solar System

RocketCat sez

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
AASTEROIDS(around $2.77)

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)

You have seen a scale map of our system. You know the dimensions. Forty, seventy, one hundred and one hundred-forty millions of miles are the orbits of the Minor Planets. Then — the Great Gulf. It’s five hundred million to Jupiter, nine hundred million to Saturn, a billion and three quarters to Uranus. When the Lord made this system, he used two scales. Maybe he started out with one, and didn’t like the looks of the dinky little system he got — planets with diameters measured in thousands of miles, orbits with diameters measured in millions. Maybe he threw that scale away, and decided to start all over with something worth while. The dust specks he had, he just forgot, and worked with a scale reading in billions instead of millions for the orbits, and he used tens of thousands of miles for planet diameters.

At any rate, there are two systems really, the Inner System, and the Outer System, and they’re as different as two entirely strange systems might be. Four, seven, ten and fourteen tens of millions for the Inner System. Four, eight, seventeen, twenty-eight hundreds of millions for the Outer System.

From Marooned by John W. Campbell (1976)

Notable Solar System Locations

No, the Solar System Ain't a Vortex

RocketCat sez

Aw fer the love of Science! Will you people please stop re-tweeting that idiotic video about the solar system moving through space like a vortex? It is wrong on so many levels that I'm surprised that the ghosts of Isaac Newton, Albert Einstein, and Stephen Hawking didn't rise from the grave and kick the living snot out of the guy who made it. It's that bad.

This video was comprehensively debunked by astronomer Phil Plait, piece by disinformation piece. What really cheeses me off is Dr. Plait debunked it in 2013, and as of 2020 I'm still seeing people retweeting that blasted video.

System Lagrange points

These are Lagrange points where the Sun is the primary body. These are good locations to site space stations. They also tend to accumulate debris over millions of years so they should be looked at in case there are clutches of asteroids with valuable mineral deposits, derelict spacecraft, ancient NASA space probes, ancient alien interstellar probes, or alien trash left by alien interstellar expeditions that were just passing through.

In science fiction, writers are fond of using the clutch of asteroids in Jupters L4 and L5 points as a setting. The are called the "Trojan" asteroids as a group, with the ones at Sol-Jupiter L4 called the Greek camp and the ones at Sol-Jupiter L5 called the Trojan camp. At last count there were over a million known Trojans with a diameter larger than one kilometer.

Only nine Mars trojans, 22 Neptune trojans, two Uranus trojans, and a single Earth trojan, have been found to date. Numerical orbital dynamics stability simulations indicate that Saturn and Uranus probably do not have any primordial trojans.

Please note there are only 22 known Neptune trojans, but computer simulations predict that the Neptune trojans outnumber the Jovan trojans by an order of magnitude (i.e., ten million of the little darlings).

Sun - Lagrange distances
SecondaryL1L2L3L4, L5, and
Sun - 2ndary
☿ Mercury5.7689×1010 m5.813×1010 m5.7909×1010 m5.7909×1010 m
♀ Venus1.072×1011 m1.0922×1011 m1.0821×1011 m1.0821×1011 m
⊕ Earth1.4811×1011 m1.511×1011 m1.496×1011 m1.496×1011 m
♂ Mars2.2686×1011 m2.2903×1011 m2.2794×1011 m2.2794×1011 m
♃ Jupiter7.2645×1011 m8.3265×1011 m7.7791×1011 m7.7834×1011 m
♄ Saturn1.3625×1012 m1.4928×1012 m1.4264×1012 m1.4267×1012 m
♅ Uranus2.8011×1012 m2.9413×1012 m2.8706×1012 m2.8707×1012 m
♆ Neptune4.3834×1012 m4.6154×1012 m4.4983×1012 m4.4984×1012 m


Surface Gravity0.003 m/s
(306 μg)
Escape velocity5.556 m/s
LEO to Deimos1.8 km/s delta-V
270 days transit
Deimos to LEO5.6 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


The atmosphere of Saturn is a rich source of Helium-3, valuable as fuel for fusion reactors using the 3He+D reaction. It can be harvested by atmospheric scooping.

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.

Solar Gravitational Lens

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.

Delta-V Maps

RocketCat sez

All those cute spaceship spec sheets you see with moronic entries like "range" or "maximum distance" betray a dire lack of spaceflight knowledge. Spacecraft ain't automobiles, if they run out of gas they don't drift to a halt. DeltaV is the key.

The point is that the distance between Start Planet and Destination Planet ain't anywhere near as important as the delta-V cost.

Why? Because the distance just tells you the time the trip will take. Delta-V will tell you if your spacecraft is capable of making the trip at all.

Each mission is composed of rocket maneuvers, each of which has a "cost" in terms of delta-V. Your rocket has a "wallet" containing your delta-V budget. Once you've spent all the delta-V money in your wallet, you are broke and cannot buy any more maneuvers. Your ship will just drift forever in its orbital trajectory until you are rescued or until alien archeologist intercept your ship in a few million years so they can point fingers and laugh at your dessicated remains.

Your rocket's "wallet" can be re-filled with delta-V at refueling stations and orbital propellant depots. Keeping in mind that a spaceship's wallet can only hold so much delta-V. Once it is full, you cannot add any more.

Once you have calculated or looked up your spacecraft's delta V, all you need is find the delta V cost for the mission manuevers. Delta-V maps are a big help.

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.
Evolvable Lunar Architecture

ed note:

Space system performance, deltaV, was defined for each leg of the space transfer as shown in Figure T-2. For Earth-moon transfer, the deltaV is taken the maximum actually used for the seven Apollo moon missionsviii. However, for the Apollo descent trajectory, there was a flight path angle hold for the pilot to view the landing site for large boulders or small craters (7% penalty); and for the final approach, there were six hover maneuvers for pilot attitude and speed corrections. In addition, there were additional contingencies for engine-valve malfunction, redline low-level propellant sensor, and redesignation to another site (9% penalty). In this study, it was assumed that the landing sites are fully defined, advanced laser sensors for remote site debris and crater checkout, and modern propellant and engine sensors for measuring and establishing final engine performance. In addition, the final descent time was reduced from the 45 seconds baselined in Apollo to 30 seconds at a decent velocity of 0.1 m/s. For polar lunar missions, the cis-lunar performance was taken from NASA’s Exploration Systems Architecture Study that provided the baseline systems for NASA’s Constellation programix.

The performances of transfers from Earth to Earth-moon L2 and from there to Mars orbit were taken from various referencesx, xi, xii, xiii. The selected data are for direct missions only. Performance can be optimized for specific dates of transfer using gravity turns but cannot be used in this study because specific missions and dates are not available.

Simple orbital mechanics defined the 1-body orbit around Earth to a periapsis of Earth-moon L2 to compute the periapsis deltaV and the atmospheric entry speed of 11km/s.

Finally for all deltaVs in Figure T-2, an additional 5 percent reserve is used.

viii Richard W. Orloff. “Apollo By The Numbers”. NASA SP-2000-4029, 2000.
ix Exploration Systems Architecture Study Final Report. NASA-TM-2005-214062, 2005. xi E. Canalis, “Assessment of Mission Design Including Utilization of Libration Points and Weak Stability Boundaries”. Approved by Dario, Advanced Concetps Team, Contract Number 18142/04/NL/MV
xii John P. Carrico, “Trajectory Sensitivities for Sun-Mars Libration Point Missions”, AAS 01-327, 2001
xiii D. F. Laudau, “Earth Departure Options for Human Missions to Mars”, Concepts and Approaches for Mars Exploration, held June 12-14, 2012 in Houston, Texas. LPI Contribution No. 1679, id.4233, June 2012

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:

Dry Mass
0 to 5
Dry Mass
6 to 10
Dry Mass
11 to 20
Dry Mass
21 to 30
Dry Mass
31 to 99
800 km/s00000.1
100 km/s00000.5
32 km/s000.50.51
16 km/s00.5112
8 km/s0.51224
4 km/s11347
3 km/s124610
2 km/s234915
1 km/s48162440

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.

Gravity Well Maps

These maps display Gravity Wells, the gravitational potential for the positions of planets in the solar system. While pretty to look at, they are not particularly useful for calculating the delta-V costs for space missions (for that use delta-V maps).

For instance, a gravity well map shows the delta-V cost to move a spacecraft from the surface of Terra to a position 400 kilometers above the surface. But this is NOT the delta-V cost to enter a 400 km orbit. This is because if you transport an object to 400 km altitude and let go, the object will plummet back to Terra and make a crater. In order to insert the object into orbit so it stays there requires an additional delta-V to rev up the thing into orbital velocity. The gravity well map shows the move delta-V but not the orbital velocity delta-V.

Gravity well maps are typically graphs with the abscissa the distance from Sol and the ordinate the potential energy.

The XKCD map is a bit different. Its abscissa has length of each gravity well scaled to the diameter of the planet and the spacing between the planets is not to scale with distance from the Sol. Because the distances between the planets are condensed, the gravitational potential - from the gravity pulling toward the sun - accumulates quicker. This is the reason for the large peaks between the planets. Its ordinate potential energy is scaled to kilometers via the gravitational potential an object has at the given height assuming at a constant acceleration due to Earth's surface gravity.

50 AU Radius

Approximate orbit of Pluto

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.

1 Light-Year Radius

Oort Cloud

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.

1.6 Light-Year Radius

Approximately one-third of the way to Alpha Centauri.

3.4 Light-Year Radius

Interstellar Space

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.

But the scale factor involved in space travel is strongly counter-intuitive.

Here's a handy metaphor: let's approximate one astronomical unit — the distance between the Earth and the sun, roughly 150 million kilometres, or 600 times the distance from the Earth to the Moon — to one centimetre. Got that? 1AU = 1cm. (You may want to get hold of a ruler to follow through with this one.)

The solar system is conveniently small. Neptune, the outermost planet in our solar system, orbits the sun at a distance of almost exactly 30AU, or 30 centimetres — one foot (in imperial units). Giant Jupiter is 5.46 AU out from the sun, almost exactly two inches (in old money).

We've sent space probes to Jupiter; they take two and a half years to get there if we send them on a straight Hohmann transfer orbit, but we can get there a bit faster using some fancy orbital mechanics. Neptune is still a stretch — only one spacecraft, Voyager 2, has made it out there so far. Its journey time was 12 years, and it wasn't stopping. (It's now on its way out into interstellar space, having passed the heliopause some years ago.)

The Kuiper belt, domain of icy wandering dwarf planets like Pluto and Eris, extends perhaps another 30AU, before merging into the much more tenuous Hills cloud and Oort cloud, domain of loosely coupled long-period comets.

Now for the first scale shock: using our handy metaphor the Kuiper belt is perhaps a metre in diameter. The Oort cloud, in contrast, is as much as 50,000 AU in radius — its outer edge lies half a kilometre away.

Got that? Our planetary solar system is 30 centimetres, roughly a foot, in radius. But to get to the edge of the Oort cloud, you have to go half a kilometre, roughly a third of a mile.

Next on our tour is Proxima Centauri, our nearest star. (There might be a brown dwarf or two lurking unseen in the icy depths beyond the Oort cloud, but if we've spotted one, I'm unaware of it.) Proxima Centauri is 4.22 light years away. A light year is 63.2 × 103 AU, or 9.46 × 1012 Km. So Proxima Centauri, at 267,000 AU, is just under two and a third kilometres, or two miles (in old money) away from us.

But Proxima Centauri is a poor choice, if we're looking for habitable real estate. While exoplanets are apparently common as muck, terrestrial planets are harder to find; Gliese 581c, the first such to be detected (and it looks like a pretty weird one, at that), is roughly 20.4 light years away, or using our metaphor, about ten miles.

Try to get a handle on this: it takes us 2-5 years to travel two inches. But the proponents of interstellar travel are talking about journeys of ten miles. That's the first point I want to get across: that if the distances involved in interplanetary travel are enormous, and the travel times fit to rival the first Australian settlers, then the distances and times involved in interstellar travel are mind-numbing.

From The High Frontier, Redux by Charles Stross (2007)

Interstellar Map Notes

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.

Three-Dimensional Maps

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.

With such maps the stars are generally plotted using Cartesian coordinate systems (in the form of x,y,z coordinates), though occasionally one will find maps using Spherical coordinate systems.

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".


If Wolf 359 has xyz coordinates of -1.9,-3.9,+6.5; and Tau Ceti has xyz coordinates of -3.4,+0.4,-11.4 then:

  • DIST = SQRT[ (X1-X2)^2 + (Y1-Y2)^2 + (Z1-Z2)^2 ]
  • DIST = SQRT[ ((-1.9)-(-3.4))^2 + ((-3.9)-0.4)^2 + (6.5-(-11.4))^2 ]
  • DIST = SQRT[ (1.5)^2 + (-4.3)^2 + (17.9)^2 ]
  • DIST = SQRT[ 2.25 + 18.49 + 320.41 ]
  • DIST = SQRT[ 341.15 ]
  • DIST = 18.5 light-years

Node Maps

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.

"That Bergenholm is in bad shape, believe me. We can hold her together for a while by main strength and awkwardness, but before very long she's going out for keeps — and when she does you don't want to find yourself fifty years from a machine shop instead of fifty minutes."

"I'll say not," the Lensman agreed. "But on the other hand, we don't want those birds jumping us the minute we land, either. Let's see, where are we? And where are the bases? Um . . . um . . . Sector bases are white rings, you know, sub-sector bases red stars . . . . . " Three heads bent over charts.

"The nearest red-star marker seems to be in System 240.16-37 " Kinnison finally announced. "Don't know the name of the planet — never been there . . .

"Too far, interrupted Thorndyke. "We'll never make it — might as well try direct for Prime Base on Tellus. If you cant find a red closer than that, look for an orange or a yellow."

"Bases of any kind seem to be scarce around here," the Lensman commented. "You'd think they'd be thicker. Here's a violet triangle, but that wouldn't help us — just an outpost . . . How about this blue square? It's just about on our line to Tellus, and I can't see anything any better that we can possibly reach."

"That looks like our best bet," Thorndyke concurred, after a few minutes of study. "It's probably several breakdowns away, but maybe we can make it — sometime. Blues are pretty low-grade space-ports but they've got tools, anyway. What's the name of it, Kim — or is it only a number?"

"It's that very famous planet, Trenco," the Lensman announced, after looking up the reference numbers in the atlas.

"Trenco!" exclaimed Thorndyke in disgust. "The nuttiest dopiest wooziest planet in the galaxy — we would draw something like that to sit down. on for repairs, wouldn't we? "

From Galactic Patrol by E. E. "Doc" Smith (1938)

Interstellar Empire Math

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 Gregersen4.0×10-3 s/ly359.680.017
HabCat5.14×10-4 s/ly3464.460.002
Globular Cluster2.02×100 s/ly30.1188.461
Omega Centauri
3.8×100 s/ly30.06315.917
Omega Centauri
8.6×101 s/ly30.003360.236
Omega Centauri
1.8×102 s/ly30.001753.982
Galactic Core2.88×100 s/ly30.08312.064
Galactic Center8.5×101 s/ly30.003356.047

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

Kuramesu Drift

Kuramesu Drift: A modestly-sized modular drift-habitat located in the Omane (First Expanses) System, at the Solar-Diageri (Omane IV) trailing libration point.

Kuramesu Drift is an independent drift, unaffiliated with any of the polities or law providers of Omane Actual, the freesoil world with which it shares a system. Rather, Kuramesu Drift is chartered to the Microstatic Commission, providing a data haven and negotiation space for the Worlds’ many micronations and small freeholds to play politics out from under the eyes of their much larger cousins. Omane, one link outside the Empire’s border, protected from intimidation by other polities by its position in an isolated loop route only accessible by passing through an Imperial border world – Ionai (First Expanses) – and yet only 13 links from the Conclave Drift by optimal routing, is essentially perfect for these purposes.

Naturally, Kuramesu Drift has a very high density of spies per capita. In fact, gentle reader, you may find it easiest to assume that everyone not an actual delegate or you, yourself, is a spy for someone.

The drift is, however, well worth visiting for reasons other than espionage. The lifestyles of even minor notables ensure that Kuramesu Drift is blessed with excellent shopping districts, banking facilities, and cultural events, including a spintronic symphony orchestra, tholin baths, and microgravity ballet, and the Commission offsets the running costs of the Drift by renting out their facilities to a variety of conferences (especially those seeing an advantage in a location near, but not within, the Empire) and conventions when they are not otherwise in use.

Meanwhile, the Agent’s Rest offers one of the finest polyspecific selections of liquors and other hedonics to be found in the central Worlds. Just don’t ask for a double – everyone’s heard that one already.

– Leyness’s Worlds: Guide to the Ecumene

15 Light-Year Radius

Sol's Interstellar Neighborhood

Scroll for star list. Artwork by Karl Tate

20 Light-Year Radius

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.

30 Light-Year Radius

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.

Jump Routes
LevelMinimum Distance
Maximum Distance

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.

These are older 3D star maps I made. Some stars are tagged as "habitable", which means "star exists in Jill Tarter and Margaret Turnbull's HabCat database" which means "Jill Tarter and Margaret Turnbull think these stars can possibly host a habitable planet." Please note that "habitable" does not necessarily mean "shirt-sleeve habitable by human beings", it means "it is not out of the question that some extremophile form of life could exist there." The HabCat database was created in 2002, it is admittedly a little dated.

These maps are more recent, I made them in 2016.

They contain stars within 13 parsecs (42 light-years) that the Planetary Habitability Laboratory at the University of Puerto Rico at Arecibo has classified as either "Conservatively Potentially Habitable Exoplanets" or "Optimistically Potentially Habitable Exoplanets" as of 2016. For more details go here.

55.7 Light-Year Radius

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.

65 Light-Year Radius

100 Light-Year Radius

Brighter stars visible from Terra.

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.

200 Light-Year Radius

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.

Interstellar Empire Framework

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.

Here are:

Have fun with it. Distances on the map are in parsecs, sorry about that.

271 Light-Year Radius

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.

400 Light-Year Radius

650 Light-Year Radius

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.

800 Light-Year Radius

1500 Light-Year Radius

3000 Light-Year Radius

10,000 Light-Year Radius

25,000 Light-Year Radius

Half The Galaxy

30,000 Light-Year Radius

50,000 Light-Year Radius

Milky Way Galaxy

Galactic Directions

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

Now, understand that these labels make less and less sense the farther away you are from the galactic quadrant that Sol is in. On the opposite side of the galaxy the direction of Coreward, Rimward, Spinward, and Trailing all reverse. This is because these are not absolute directions, they are relative directions. It is the difference between saying an object is to the northwest, and saying an object is to the left of you.

For absolute directions, the common usage is to use Cartesian or Spherical coordinate systems.

Cartesian coordinate give an object's location in terms of X, Y, and Z coordinates. They are defined by the units the x, y, and z scales use, the origin of the system (i.e., what is at the exact center of the x, y, and z axes), and what are the x, y , and z axes aimed at.

The old and busted Equatorial cartesian system has:

In other words it is parochially based around Terra, and is not particularly useful. Warning: you will find that many cartesian star maps use this system, because the math is easier. Equatorial cartesian maps can be identifed by the fact that Barnard's Star is dead on the -Y axis (XYZ 0,-6,0 in light-years).

The new hotness is the Terra-Galactic cartesian system:

  • Scales are in light-years
  • Origin is at the Sun
  • Positive Z-axis points at the north galactic pole (x-y plane is parallel to plane of the galaxy), positive X-axis points at the center of the galaxy, more or less at Sagittarius A*

In theory a more universal system would be the Galactic-Terra cartesian system:

  • Scales are in light-years
  • Origin is at the center of the galaxy (Sagittarius A*)
  • Positive Z-axis points at the north galactic pole (x-y plane is parallel to plane of the galaxy), positive X-axis points at Terra

This system will have to cope with the fact that the solar system is NOT in the plane of the galaxy. It is northward of the plane, values I've seen include between 75 and 101 light-years, 66.83±11.41 light-years, between 42.38 and 91.28 light-years, and 55.75±16.3 light-years. Do your own research, the figure keeps changing.

Very rarely you will see the scales measured in parsecs instead of light-years. There are 3.26 light-years in one parsec. The parsec is commonly used by astronomers but science fiction fans hate it.

Isaac Asimov used a Spherical coordinate system in his novel THE STARS LIKE DUST.

Theta (θ) is the object's angular separation from the Standard Galactic Baseline (orange line) along the plane of the Galaxy. The baseline is a line connecting the galactic center (Sagittarius A*) with Sol. The angle is measured in radians, which is quite useful for physicists and mathematicians but difficult for science fiction fans. Isaac Asimov figured his fans could learn things the right way or go elsewhere.

Phi (φ) is the object's angular separation from the plane of the galaxy in a plane perpendicular to the galaxy. Also measured in radians. Note that in mathematics, they instead measure phi as the separation from the north-south axis, don't be confused.

Rho (ρ) is the object's distance from the galactic center, measured in parsecs.

In the diagram above, planetary nebula IC 5117 is plotted.

In the plane of the galaxy, the projection of IC 5117 onto the galactic plane is at an angular separation (yellow arc with arrows) of 45° from the Standard Galactic Baseline. This is π/4 radians or 0.785 radians. So the theta is 0.785.

In a plane perpendicular to the galactic plane which passes through both IC 5117 and the galactic center, IC 5117 is at an angular separation (green arc with arrows) of 20° from the galactic plane. This is π/9 radians or 0.349 radians. So the phi is 0.349.

IC 5117 is 35,900 light-years from the galactic center (blue line with arrows), or 11,000 parsecs. So the rho is 11,000.

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.

80,000 Light-Year Radius

Just outside of the Milky Way galaxy.

300,000 Light-Year Radius

3 Million Light-Year Radius

5 Million Light-Year Radius

Local Group">Local Group of Galaxies

30 Million Light-Year Radius

100 Million Light-Year Radius

150 Million Light-Year Radius

200 Million Light-Year Radius

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.

550 Million Light-Year Radius

These are from Cosmicflows-3: Cosmography of the Local Void.

The subject of the paper is galaxies within 550 million light-years of our Milky Way galaxy, with a focus on areas of galaxy clumps and voids. They studied a dataset of about 18,000 galaxies to create these maps.

In most of the following maps are a set of three colored arrows. The Milky Way galaxy is at the origin of the arrows. Each arrow is 218 million light-years long (recessional velocity= 5,000 km/sec). The arrows define the axes of the Supergalactic coordinate system. Red arrow points toward +SGX, green toward +SGY, and blue toward +SGZ

There is a movie of the map here.

There are two interactive Sketchfab models here and here.

Converting Recessional Velocity into Light-Years

Because distances to celestial objects is extremely difficult to measure at such ranges, the report uses recessional velocity instead of distance in light-years as a unit of measurement. Such velocity is easily determined by measuring red-shift. To calculate distance from recessional velocity one uses the Hubble Constant (H0). This is usually given in terms of recessional velocity in kilometers/sec per megaparsec (km s-1 Mpc-1). Divide the recessional velocity by H0 to get the distance in megaparsecs. Multiply the result by 3.262×106 to convert into light-years.

The fly in the ointment is that the various ways of measuring H0 give quite different values. The paper figures that 75 km s-1 Mpc-1 for the Hubble Constant is currently the best value to use.

I'm only telling you this in case you actually read the paper and get frustrated at all the distance measurements being in kilometers per second.

Example: the colored arrows are 5,000 km/sec long in terms of recessional velocity. Divide by 75 km s-1 Mpc-1 to get a length of 66.7 megaparsecs. Multiply by 3.262×106 to convert into 217,600,000 light-years or 218 million light-years.

600 Million Light-Year Radius

1 Billion Light-Year Radius

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.

1.5 Billion Light-Year Radius

10 Billion Light-Year Radius

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.

13.798 Billion Light-Year Radius

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.

18 Billion Light-Year Radius

46.6 Billion Light-Year Radius

Observable Universe

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.

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