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.

POINT NEMO

• 

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.

• 

SPACECRAFT CEMETERY

• 

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.

SOUTH ATLANTIC ANOMALY

• 

• 

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.

Definition

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.

Effects

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.

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. So Terra's Hill Sphere fits between Earth-Sun Lagrange 1 and Earth-Sun Lagrange 2 (a radius of about 1,471,400 kilometers, centered on Terra). Luna orbits inside Terra's Hill Sphere (about 384,400 km from Terra's center), so Luna is dominated by Terra's gravity, not the Sun.

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.
• Hill Sphere: Closer than 1,471,400 kilometers to Terra's center.

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.

TERRA-LUNA LAGRANGIAN POINTS

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.

x24.96 OR TAIN'T STABLE

• 

(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 ]

where:

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.”

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.

Approximately the orbit of Mars.

Approximately the inner edge of the asteroid belt.

Approximately the outer edge of the asteroid belt.

Approximately the orbit of Saturn.

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
Mother	MERCURY	$.39
Very	VENUS	$.72
Thoughtfully	TERRA	$1.00
Made	MARS	$1.50
A	ASTEROIDS	(around $2.77)
Jelly	JUPITER	$5.20
Sandwich	SATURN	$9.50
Under	URANUS	$19.00
No	NEPTUNE	$30.00
Protest	PLUTO	$39.50

Heinlein used dollar amounts to show the distance of each from Sol (the Sun to you) in Astromical Units. He used dollars since his mind tends to pay attention to money. One AU is the distance between Terra and Sol, about 150 million kilometers.

The big thing to notice is that the planet distances tend to double. Say you are traveling from Sol to Saturn, a distance of 9.5 AU. When you get to the orbit of Jupiter (the orbit just before Saturn) you have only traveled 5.2 AU. In other words, when you have reached the orbit of Jupiter you are only half-way to Saturn!

Planetary Fact Sheets! All hail Planetary Facts Sheets! These are handy sheets from Dr. David Williams of NASA containing vital statistics of various solar system planets. Also useful is Wikipedia's List of gravitationally rounded objects of the Solar System (i.e., Sol and the planets)

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.

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.

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.

Approximately one-third of the way to Alpha Centauri.

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.

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".

Example

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? "

This is a three dimensional star map I made back in 2008 of the closest 100 stars according to the RECONS star catalog. As a shameless plug, I sell this map in poster form, where you can actually read the numbers without straining your eyes.

The map is a three dimensional XYZ cartesian graph with the grid and each star's coordinate is printed.

The map is in Galactic coordinates. The x-y plane is the plane of the galaxy. The +X axis points at the galactic core ("Coreward"), the -X axis points away from the core ("Rimward"), the +Y axis is the direction the galaxy's spiral arms move ("Spinward") and the -Y axis is the opposite direction ("Trailing"). Sol, our Sun is in the center at 0,0,0. Pretty much all 100 stars are within 20 light-years of Sol.

If using the True Distance Formula makes your head hurt, just look at the map's violet and green lines.

The stars are the colored star symbols. Each star has violet line drawn to its two closest stellar neighbors (two is an arbitrary number of neighbors, with three or more the map becomes a tangled mess of lines). The midpoint of each line is labeled with the distance between the two stars in light-years. So to get an idea of where the stars are without using mathematics, just look at the violet lines to see how they are connected.

Stars that are in the HabCat star catalog have a high probability of having quote "habitable" unqote planets. Note that "habitable" does NOT mean "planet that humans can live on in their shirt-sleeves." Also note that since the HabCat catalog was compiled, astronomers have learned that spectral class M red stars have more habitable planets than previously thought.

Anyway, each HabCat star has green lines drawn between it and its two closest HabCat star neighbors. HabCat stars have gold rings drawn around their star icons. The important point to remember is for your interstellar colonies and initial empires you should probably focus on the green lines.

Back in the early 2000s, I did some star map work for Ken Burnside's Attack Vector: Tactical "Ten Worlds universe."

Mr. Burnside was doing his worldbuilding right, by using real star data along with a specification for his universe's faster-than-light drive. So he would have that determine the strategy, tactics, and other constraints for his game universe.

The wrong way is to first decide upon the desired constraints, then desperately try to retrofit the map and FTL details so the desired constraints occur as emergent behavior. We call this the "wrong way" because it is almost impossible to plug up all the loop holes to prevent unintended consequences.

Mr. Burnside started by constraining the universe to stars within 10 parsecs (32.6 light-years) of Sol, since 10 was a nice round number. We would nudge the boarder in specific spots out further if need be, or if we found anything interesting. I took my best star catalog and trimmed it down to just stars at the specified distance.

Among the data in the star catalog was certain stars were flagged as having a high probablility of hosting a human-habitable planet. This was the short list of candidates for the worlds which would become the Ten Worlds.

Mr. Burnside specified that starships could only use their FTL drive to travel between stars connected by "jump routes". There were several classes of routes, Alpha type route, Beta type route, Gamma type route, etc. Two stars were connected by a given type of jump route if the distance between was greater than the minimum route length but less than the maximum route length.

For instance: the distance between Sol and Sirius is 2.64 parsecs. Delta type routes have a minimum distance of 2.4 pc and a maximum distance of 2.7 pc, therefore Sol and Sirius are connected by a Delta jump route since 2.64 is greater than 2.4 and less than 2.7. Gamma type routes have a minimum distance of 3.9 pc and a maximum of 4.4 pc so Sol and Sirius are not connected by a Gamma jump route.

A starship's jump drive is rated according to the maximum jump level it can handle. So a Gamma drive can use Alpha, Beta, or Gamma jump routes. Naturally the higher the drive rating, the more massive and more expensive it is.

Where did the minimum and maximum distances come from? Mr. Burnside had an amusing harmonic equation which he used, just because he arbitrarily liked the spacing of the intervals.

My next task was to write a quick Python script which took the trimmed star catalog as input, and figured out which stars were connected to which other stars, and by what types of jump links. You can see a graphic representation of this in the node map below.

From a wargame standpoint, the map of jump links revealed militarily interesting locations: choke points and grand central stations. Mr. Burnside used this as one of the decision factors for figuring out which of the worlds were the Ten Worlds. He wanted star colonies that were in thought-provoking locations from a interstellar trade and combat viewpoint.

Ken specified an average rate of interstellar exploration, that is, how many years per link. This is a measure of the speed of the exploration wave. I wrote another Python script that modeled the wave. Little virtual scout starships would jump to an unexplored star, add to the master list the year that star was explored, then it would spawn new virtual scout starships that would all wait for the "years per link" period to pass then jump to all unexplored stars linked to the current star. The result was a list of the year each star was explored.

The important point was when each of the star colonies were explored, since that was the earliest year each colony could be established. This also gave a value for the relative age of each colony, which relates to their levels of industrialization.

From a gameplay standpoint, there was one fly in the ointment. Sol and Terra had the overwhelming advantage. It would be centuries before any of the colonies could come anywhere near Terra's level of industrialization. And since Sol was the start of the exploration, it had the strategic advantage of a central location. The colonies didn't stand a chance. Which would make for a very boring game.

Which is why in the Ten Worlds universe came an event called the "Whatever." For reasons only known to Ken and a few Ten Worlds game designers sworn to secrecy (not including me), on a certain day the three jump links connecting to Sol abruptly vanished. And in the decades to come there has been nary a peep out of Terra.

Armed with the node map, list of colonies, and their relative levels of industrialization, Ken could now generate the future history by using the Great Game technique.

The end result is that Ken Burnside's Ten Worlds universe is solid enough to walk on.

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.

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.

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.

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. Within the Local Bubble, the Sun is imbedded inside the Local Fluff.

For interstellar colonists, "the light of home" is the star Sol in the night sky. It is too dim to be seen by the naked eye if the colony is further than 55.7 light years away.

However, the brilliant star Sirius is a mere 8.6 light-years away from Sol. If the colony is no further than 271 light-years away from Sirius, it will have an apparent magnitude of 6.0, just barely visible to the naked eye. The colonists cannot see Sol, but they will know it is right next to Sirius.

The Sun has the misfortune to be located near the center of a huge region about 330 to 490 light-years in diameter called "The Local Bubble". The interstellar medium within the Local Bubble has a density of about 0.05 atoms/cm³, which is about ten times lower than in the rest of the galaxy. This makes a thin fuel source for a Bussard ramjet.

Fig. 1. Local cavity and LB in the plane of the Galactic equator. The filled contours show the Na i distribution (Sfeir et al. 1999), with white used for low-density regions and dark gray for high-density ones. The black contour shows the present size of the LB as determined from X-ray data (Snowden et al. 1998), with the dashed lines indicating contaminated areas where the limits of the LB cannot be accurately determined. The hatched ellipse shows the approximate position of the Ophiuchus molecular cloud (de Geus et al. 1989; Loren 1989a, 1989b). The present and past x- and y-coordinates of the center of the three subgroups of the Sco-Cen association are shown. For LCC and UCL, the past positions shown are those of 5 and 10 Myr ago, while for US only the position of 5 Myr ago is shown. The dimensions of the filled ellipses indicate the uncertainties in the past positions. Coordinates are expressed in units of parsecs.

Translation into English:

View is looking down on the galactic plane. Sol is dot in the center. Coreward is to the right (labeled "To the GC"), Spinward is to the top (labeled "Rotation Direction"). Scale on the edges are in parsecs, map is area plus or minus 200 parsecs (652 light-years).

The black dotted line is the boarder of the Local Bubble. As near as I can tell the black square icon tracked with arrows (the Sco-Cen OB association UCL subgroup) is the same as the Pleiades subgroup B1 mentioned below.

Fig. 2. Sketch of the solar neighborhood seen from above the galactic plane. The center of mass position of Pleiades subgroup B1 is labeled with “B1”. The solid line, ending at the actual position of B1, provides the trajectory of the moving group during the past 30 Myrs in the epicyclic approximation (see Sect. 3); center of mass positions 13, 20, and 30 Myrs ago are labeled with -13, -20, and -30. Approximately 13 Myrs ago the most massive B1 star(s) (M ≈ 20 M_⊙) must have exploded. The local cavity contours as derived from Nai absorption line studies by Sfeir et al. (1999) are shown as thick solid lines (dashed lines denote directions of uncertain local cavity borders). As can be seen, existing B1 member stars (or at least some of them, given their spatial spread) should have crossed the region, which now forms the Local Bubble.

Translation into English:

View is looking down on the galactic plane. Sol is dot in the center. Coreward is to the right (labeled "GC"), Spinward is to the top. Scale on the axes are in parsecs, map is area plus or minus 200 parsecs (652 light-years).

The large gray disc is the Local Bubble. B1 is the Pleiades subgroup B1. It trails an arc showing its path through the galaxy, labeled with marks for -13, -20, and -30 million years ago. α Per (Alpha Persei Cluster), Pleiades cluster, Praesepe (Beehive) cluster, NGC 2451 cluster, IC 2391 (Omicron Velorum) cluster, and IC 2602 ( Theta Carinae or Southern Pleiades) cluster are marked.

Spiral Arms

The most noticable feature of a spiral galaxy is the spiral arms. For decades, scifi authors assumed that all the stars were in the arms, separated by giant black star-less rifts.

Rifters

EVEN to the men of the flying city, the Rift was awesome beyond all human experience. Loneliness was natural between the stars, and starmen of all kinds were used to it—the star-density of the average cluster was more than enough to give a veteran Okie claustrophobia. But the enormous empty loneliness of the Rift was unique.

To the best of Amalfi's knowledge, no human being, let alone a city, had ever crossed the Rift before. The City Fathers, who knew everything, agreed. Amalfi was none too sure that it was wise, for once, to be a pioneer.

Ahead and behind, the walls of the Rift shimmered, a haze of stars too far away to resolve into individual points of light. The walls curved gently toward a starry floor, so many parsecs "beneath" the granite keel of the city that it seemed to be hidden in a rising haze of star dust.

"Above" there was nothing; a nothing as final as the slamming of a door. It was the empty ocean of space that washes between galaxies.

The Rift was, in effect, a valley cut in the face of the galaxy. A few stars swam in it, light millennia apart—stars which the tide of human colonization could never have reached. Only on the far side was there likely to be any inhabited planet, and, consequently, work for the city.

On the near side there was still the police. It was not, of course, the same contingent which had consolidated Utopia and the Duchy of Gort; such persistence by a single squadron of cops, over a trail which had spanned nearly three centuries, would have been incredible for so small a series of offenses on the city's part. Nevertheless, there was a violation of a Vacate order still on the books, and a little matter of a trick ... and the word had been passed. To turn back was out of the question for the city.

Whether or not the police would follow the city even as far as the Rift, Amalfl did not know. It was, however, a good gamble. Crossing a desert of this size would probably be impossible for so small an object as a ship, out of a sheer inability to carry enough supplies; only a city which could grow its own had much chance of surviving such a crossing. (ed note: transit time of a few centuries)

Soberly Amalfi contemplated the oppressive chasm which the screens showed him. The picture came in from a string of proxies, the leader of which was already parsecs out across the gap. And still the far wall was featureless, just beginning to show a faintly granular texture which gave promise of resolution into individual stars at top magnification.

"I hope the food holds out," he muttered. "If we make this one, it'll make the most colossal story any Okie ever had to tell. They'll be calling us the Rifters from one end of the galaxy to the other."

Alas for all those scifi writer, It Just Ain't So!

The star density (stars per cubic parsec) of a spiral arm is not much more than the density in the gaps between arms. The difference of the spiral arms is they are places where new stars are born more frequently than elsewhere, so the spiral arms have more young and brighter stars. The brighter the star, the shorter the lifespan. So the bright stars die out before they leave the spiral arms, the only stars that live long enough to leave the arms and enter the gaps are the longer-lived but dimmer stars. The result is most of the stars in the arms are intensely bright and the stars in the gaps are easily overlooked dim things.

A typical spiral arm has only about 10% more stars than the gap region.

Why are more stars born in the spiral arms? According to Density Wave Theory, spiral regions that are more dense with interstellar gas are formed by galactic rotation. The more gas in a section of space, the more stars form in it.

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:

• Scales are in light-years
• Origin is at the Sun
• Positive Z-axis points at the celestial north pole (x-y plane is parallel to Terra's equator), positive X-axis points at the First point of Aries

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 to the astronomer's galactic north or nadir 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) in the plane of the Galaxy. The baseline is a line connecting the galactic center (Sagittarius A*) with Sol (which is actually not on the galactic plane, but close). Theta is analogous to longitude on a globe of Terra. (The angle is measured in radians instead of degrees, 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. This measures the object's "altitude" above or below the plane of the galaxy. Phi is analogous to latitude on a globe of Terra. (Note that in mathematics, they confusingly measure phi as the separation from the north-south axis, not from the plane, don't be fooled)

Rho (ρ) is the object's distance from the galactic center, measured in parsecs. Rho is analogous to altitude on a globe of Terra, except it is measured from the planet's core not the planet's surface.

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 galactic "longitude" 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 ("altitude") (green arc with arrows) of 20° from the galactic plane. This is π/9 radians or 0.349 radians. So the galactic "latitude" phi is positive 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.

Astronomer's Galactic North

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 right hand around the spin so that the fingers point 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.

When looking at a picture of a galaxy, you can tell the spin direction by looking at the spiral arms. Pick an arm and see where it attaches to the galactic core. Starting at the attachment point, trace the rest of the arm. The direction you are tracing in is the anti-spinward direction. The spin direction is the opposite.

However, if you examine at the galactic maps below, which are done from the astronomical 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 this turned out to be the wrong choice, since Terra's axis of rotation has nothing to do with the galactic axis.

Bottom line: Astronomer's North is the same as my South and Nadir.

Just outside of the Milky Way galaxy.

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.

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.

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.

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.

The current most distant candidate astronomical object is a galaxy called UDFj-39546284 with a redshift z=11.9 (though some astronomers suspect it is a nearby object with a peculiar spectrum). This would give it a light-travel distance of 13.37 billion light-years.

The current most distant "proven" astronomical object is some as-yet unseen galaxy or something that emitted Gamma Ray Burst 090423. it has a redshift z=8.2. When the GRB occured, the universe was only 630 million years old.

The universe is only 13.798±0.037 billion years old, which is quite a bit less than 46.6 billion. However, due to the expansion of space astronomers are observing objects that were originally much closer but are "now" considerably farther away. That explains the discrepancy.

Astronomers technically make a distinction between the visible universe and the observable universe. When the Big Bang occured, the universe was wall-to-wall plasma that was opaque to light and other electromagnetic radiation. About 377,000 years after the Big Bang the universe had expanded to a point where all the electrons and protons in the plasma suddenly combined into hydrogen atoms (called the Recombination). No more plasma meant the universe was abruptly transparent to light.

So the visible universe only has a radius of 45.7 billion light-years (starting at recombination) while the observable universe has a radius of 46.6 billion light-years (starting at the Big Bang). To be vislbe means you need light, and there ain't none available before recombination. However, the observable universe could theoretically be observed even before recombination using gravitational waves, neutrinos, or something like that. Yes, I know, it is really nit-picky but scientists have to be precise or major break-throughs are overlooked.