This is a table of mission parameters calculated by Jon C. Rogers for the book Spaceship Handbook. It lists round-trip missions starting at Terra's surface, traveling to and landing on the destination planet (or at low orbit for Venus, Jupiter, Saturn, Uranus, and Neptune; due to the fact that the atmospheric pressure of these planets will crush your spacecraft like a cheap beer can) then lifting off, traveling back to and landing on Terra.
Mr. Rogers is interested in comparing the different trajectory types, so the focus is on splitting the mission into standard blocks, rather than optimizing for minimum delta V. An optimized missiom will require less delta V than what is listed in the table (approximately 5% to 10% less delta V). As a verification, Mr. Rogers used his mathematical model to calculate a mission to Luna and compared it to the actual data reported by NASA for the Apollo 11 mission. His model said delta V of 16.905 km/s which is within 3% of the NASA Apollo 11 delta V of 16.479 km/s.
Six trajectories are listed, three impulse types and three constant acceleration brachistochrone types. "Impulse" means the spacecraft makes an initial burn then coasts for months.
Impulse trajectory I-1 is pretty close to a Hohmann (minimum delta V / maximum time) orbit, but with a slightly higher delta V.
Impulse trajectory I-2 is in-between I-1 and I-3 (it is equivalent to an elliptical orbit from Mercury to Pluto, the biggest elliptical orbit that will fit inside the solar system).
Impulse trajectory I-3 is near the transition between delta V levels for high impulse trajectories and low brachistochrone trajectories (it is a hyperbolic solar escape orbit plus 30 km/s).
Brachistochrone (maximum delta V / minimum time) trajectories are labeled by their level of constant acceleration: 0.01 g, 0.10 g, and 1.0 g.
The transit times are important for figuring things like how much food and life support endurance must be carried, mission radiation total dosage, and damage to astronauts due to prolonged microgravity exposure. In fact, if you have a hard limit on, say, total radiation dosage, you can examine the table and rule out any mission trajectory whose transit time exceeds it.
|☿ Mercury||48,740 (8m)||75,210 (2.5m)||106,230 (2m)||397,000 (33d)||1,205,000 (13d)||3,794,000 (4d)|
|♀ Venus||30,270 (9.6m)||63,330 (1m)||98,620 (21d)||281,000 (19d)||815,000 (8d)||2,552,000 (3d)|
|☾ Luna||16,480 (9d)||-||-||-||-||260,000 (7h)|
|♂ Mars||29,930 (17m)||52,930 (2m)||94,110 (1.5m)||370,000 (30d)||1,115,000 (12d)||3,508,000 (4d)|
|⚶ Vesta||30,300 (2y2m)||46,670 (5.5m)||92,560 (3.8m)||578,000 (54d)||1,791,000 (20d)||5,654,000 (7d)|
|⚳ Ceres||33,430 (2y7m)||44,730 (7.5m)||92,160 (5m)||655,000 (63d)||2,040,000 (23d)||6,441,000 (8d)|
|⚴ Pallas||33,110 (2y7m)||44,320 (7.5m)||91,770 (5m)||656,000 (63d)||2,043,000 (23d)||6,450,000 (8d)|
|♃ Jupiter||69,990 (5y5m)||72,690 (1y10m)||118,010 (1y)||1,000,000 (3.5m)||3,142,000 (36d)||9,930,000 (12d)|
|Io||76,220 (5y6m)||70,760 (1y10m)||78,980 (1y)||1,000,000 (3.5m)||3,143,000 (36d)||9,933,000 (12d)|
|Europa||67,390 (5y6m)||61,850 (1y10m)||71,490 (1y)||1,001,000 (3.5m)||3,144,000 (36d)||9,935,000 (12d)|
|Ganymede||61,880 (5y5m)||56,250 (1y10m)||67,130 (1y)||1,001,000 (3.5m)||3,145,000 (36d)||9,938,000 (12d)|
|Callisto||55,400 (5y5m)||49,640 (1y10m)||62,190 (1y)||1,002,000 (3.5m)||3,147,000 (36d)||9,945,000 (12d)|
|♄ Saturn||57,690 (12y1m)||55,770 (4y11m)||108,680 (2y3m)||1,420,000 (5m)||4,477,000 (52d)||14,153,000 (17d)|
|Enceladus||65,850 (12y1m)||59,880 (4y11m)||67,810 (2y3m)||1,421,000 (5m)||4,477,000 (52d)||14,155,000 (17d)|
|Tetheys||62,910 (12y1m)||56,860 (4y11m)||65,600 (2y3m)||1,420,000 (5m)||4,478,000 (52d)||14,155,000 (17d)|
|Dione||59,810 (12y1m)||53,660 (4y11m)||63,270 (2y3m)||1,420,000 (5m)||4,478,000 (52d)||14,155,000 (17d)|
|Rhea||56,310 (12y1m)||50,010 (4y11m)||60,780 (2y3m)||1,421,000 (5m)||4,478,000 (52d)||14,156,000 (17d)|
|Titan||49,670 (12y1m)||42,750 (4y11m)||56,660 (2y3m)||1,421,000 (5m)||4,479,000 (52d)||14,160,000 (17d)|
|Iapetus||45,010 (12y1m)||37,590 (4y11m)||53,070 (2y3m)||1,422,000 (5m)||4,483,000 (52d)||14,173,000 (17d)|
|♅ Uranus||50,110 (32y)||44,830 (15y6m)||56,420 (5y2m)||2,069,00 (8m)||6,532,00 (76d)||20,652,000 (24d)|
|Ariel||49,910 (32y)||44,650 (15y6m)||56,150 (5y2m)||2,069,000 (8m)||6,532,00 (76d)||20,653,000 (24d)|
|Umbriel||48,010 (32y)||42,550 (15y6m)||54,870 (5y2m)||2,069,000 (8m)||6,532,000 (76d)||20,653,000 (24d)|
|Titania||46,180 (32y)||40,410 (15y6m)||53,800 (5y2m)||2,069,000 (8m)||6,532,000 (76d)||20,654,000 (24d)|
|Oberon||45,040 (32y)||38,930 (15y6m)||53,220 (5y2m)||2,069,000 (8m)||6,532,000 (76d)||20,654,000 (24d)|
|♆ Neptune||51,370 (61y3m)||48,420 (36y)||57,470 (8y5m)||2,613,000 (10m)||8,257,000 (96d)||26,108,000 (31d)|
|Triton||48,090 (61y3m)||44,780 (36y)||56,030 (8y5m)||2,614,000 (10m)||8,257,000 (96d)||26,109,000 (31d)|
|Nereid||40,620 (61y3m)||36,300 (36y)||50,400 (8y5m)||2,615,000 (10m)||7,262,000 (96d)||26,125,000 (31d)|
|♇ Pluto||39,810 (90y11m)||39,810 (88y9m)||50,140 (11y4m)||3,009,000 (11m)||9,508,000 (111d)||30,063,000 (35d)|
|Charon||39,680 (90y11m)||39,680 (88y9m)||50,080 (11y4m)||3,009,000 (11m)||9,508,000 (111d)||30,063,000 (35d)|
Using the mission table above, Mr. Rogers took a list of major propulsion systems and calculated which ones were up to the task of peforming said missions. Note that Mr. Rogers values for the exhaust v3elocity of the propulsion systems might differ slightly from the ones I have on the mission list.
- 1 Stage, Max Payload is 33% payload, 66% propellant, mass ratio of 2.94
- 1 Stage, Min Payload is 11% payload, 89% propellant, mass ratio of 9.1
- Multi Stage is 1.6% payload, 98.4% propellant, mass ratio of 62.5
Cross reference the mass ratio, propulsion system, and mission trajectory. If there is a colored box at the intersection, the propulsion system can perform that mission.
Example: For a 1 Stage minimum payload (mass ratio of 9.1), using a Nuclear Fission Gas Core reactor, with a Mars Impulse trajectory I-2, the presence of a hot pink box says that propulsion system is capable of that mission. But it is not capable of performing a Mars Constant Brachistochrone 0.01g mission.
Below are a series of tables for Hohmann transfer delta V requirments. Unlike the above table, they are for one-way trips to various destinations. For instance, the above table will give requirements for a Terra-Mars-Terra mission, but the tables below will give requirements for a Terra-Mars mission.
The tables assume that an orbit for each of the bodies is 100 km altitude (even for pointlessly tiny ones like Phobos and Deimos), and for surface launches it is presumed that all the bodies have no atmosphere (not true for, say, Titan).
- Start and destination planets are labeled along axes.
- Values are in meters per second.
- Values below the diagonal in blue are delta V's needed to go from orbit around one world to orbit around the other, landing on neither.
- Values above the diagonal in red are delta V's needed to go from the surface of one world to the surface of the other, taking off and landing. If either is a gas giant, a 100 kilometer orbit is used instead of the planet's surface.
- Diagonal values in gold are delta V's needed to take off from the surface of a world and go into circular orbit around it, or to land from a circular orbit.
Here are some Synodic Periods and Transit Times for Hohmann Travel tables. Remember that Synodic periods are how often Hohmann launch windows occur. These too were created by Erik Max Francis' Hohmann orbit calculator.
- In both sections, "y" means "years", "m" means "months", "d" means "days", and "h" means "hours"
- Synodic periods (i.e., frequency of Hohmann launch windows) are above the diagonal in red
- Transit times are below the diagonal in blue
|Earth||3.5m||4.8m||2y, 1.6m||1y, 4.6m||1y, 3.6m||1y, 3.4m||1y, 3.3m||1y, 3.3m||1y, 1.1m||1y, 0.4m||1y, 0.1m||1y, 0.1m||1y, 0.0m|
|Mars||5.6m||7.1m||8.5m||3y, 10.8m||3y, 3.7m||3y, 2.9m||3y, 2.2m||3y, 2.1m||2y, 2.8m||2y, 0.1m||1y, 11.1m||1y, 10.8m||1y, 10.7m|
|Vesta||9.7m||11.5m||1y, 1.1m||1y, 4.2m||21y, 8.2m||18y, 11.7m||17y, 2.4m||16y, 11.6m||5y, 2.7m||4y, 1.6m||3y, 9.5m||3y, 8.5m||3y, 8.2m|
|Juno||11.3m||1y, 1.2m||1y, 2.9m||1y, 6.2m||1y, 11.9m||151y, 11.1m||83y, 1.8m||77y, 11.1m||6y, 10.6m||5y, 1.3m||4y, 7.1m||4y, 5.7m||4y, 5.2m|
|Eugenia||11.6m||1y, 1.6m||1y, 3.2m||1y, 6.5m||2y, 0.3m||2y, 2.5m||183y, 8.3m||159y, 11.8m||7y, 2.5m||5y, 3.4m||4y, 8.9m||4y, 7.3m||4y, 6.8m|
|Ceres||11.9m||1y, 1.8m||1y, 3.5m||1y, 6.8m||2y, 0.6m||2y, 2.9m||2y, 3.3m||1239y, 8.2m||7y, 6.1m||5y, 5.3m||4y, 10.4m||4y, 8.8m||4y, 8.2m|
|Pallas||11.9m||1y, 1.9m||1y, 3.5m||1y, 6.9m||2y, 0.7m||2y, 2.9m||2y, 3.3m||2y, 3.6m||7y, 6.6m||5y, 5.6m||4y, 10.6m||4y, 9.0m||4y, 8.5m|
|Jupiter||2y, 4.0m||2y, 6.6m||2y, 8.8m||3y, 1.0m||3y, 8.1m||3y, 10.9m||3y, 11.3m||3y, 11.7m||3y, 11.8m||19y, 9.6m||13y, 9.9m||12y, 9.5m||12y, 5.7m|
|Saturn||5y, 6.8m||5y, 10.2m||6y, 1.0m||6y, 6.5m||7y, 3.6m||7y, 7.0m||7y, 7.5m||7y, 8.0m||7y, 8.1m||10y, 0.6m||45y, 9.8m||36y, 2.1m||33y, 8.8m|
|Uranus||15y, 3.9m||15y, 8.7m||16y, 0.6m||16y, 8.1m||17y, 8.4m||18y, 0.9m||18y, 1.7m||18y, 2.4m||18y, 2.5m||21y, 3.8m||27y, 3.6m||171y, 12.0m||127y, 11.2m|
|Neptune||29y, 8.2m||30y, 2.1m||30y, 7.0m||31y, 4.3m||32y, 7.4m||33y, 0.9m||33y, 1.9m||33y, 2.7m||33y, 2.8m||36y, 12.0m||44y, 1.2m||61y, 1.1m||499y, 4.3m|
|Pluto||44y, 1.1m||44y, 7.8m||45y, 1.4m||46y, 0.0m||47y, 5.1m||47y, 11.4m||48y, 0.5m||48y, 1.4m||48y, 1.6m||52y, 4.4m||60y, 3.6m||78y, 11.6m||101y, 11.3m|
|Io||11h||11h||13h||3d, 13h||2d, 8h||1d, 23h||1d, 19h||1d, 19h|
|Europa||20h||20h||22h||1d, 7h||7d, 1h||4d, 12h||3d, 14h||3d, 14h|
|Ganymede||1d, 12h||1d, 12h||1d, 14h||2d, 2h||2d, 15h||12d, 12h||7d, 9h||7d, 9h|
|Callisto||3d, 6h||3d, 6h||3d, 9h||3d, 24h||4d, 16h||5d, 19h||17d, 21h||17d, 20h|
|Himalia||45d, 2h||45d, 2h||45d, 9h||46d, 19h||48d, 6h||50d, 16h||55d, 16h||7050d, 0h|
|Elara||46d, 17h||46d, 17h||47d, 1h||48d, 11h||49d, 23h||52d, 9h||57d, 11h||127d, 16h|
|Epimetheus||1405d, 13h||2d, 16h||1d, 10h||1d, 2h||22h||20h||17h||17h|
|Janus||8h||2d, 16h||1d, 10h||1d, 2h||22h||20h||17h||17h|
|Mimas||10h||10h||3d, 1h||1d, 21h||1d, 11h||1d, 5h||1d, 0h||23h|
|Enceladus||12h||12h||14h||5d, 0h||2d, 18h||1d, 23h||1d, 12h||1d, 9h|
|Tethys||15h||15h||17h||19h||6d, 2h||3d, 6h||2d, 3h||1d, 22h|
|Dione||19h||19h||21h||1d, 0h||1d, 4h||6d, 23h||3d, 7h||2d, 20h|
|Rhea||1d, 4h||1d, 4h||1d, 6h||1d, 10h||1d, 13h||1d, 19h||6d, 7h||4d, 19h|
|Titan||3d, 9h||3d, 9h||3d, 12h||3d, 16h||3d, 22h||4d, 5h||4d, 20h||19d, 23h|
|Iapetus||14d, 22h||14d, 22h||15d, 3h||15d, 11h||15d, 19h||16d, 8h||17d, 6h||21d, 20h|
|Miranda||4d, 4h||2d, 13h||1d, 22h||1d, 19h|
|Ariel||1d, 0h||6d, 11h||3d, 14h||3d, 3h|
|Umbriel||1d, 9h||1d, 16h||7d, 23h||6d, 0h|
|Titania||2d, 8h||2d, 16h||3d, 3h||24d, 13h|
|Oberon||3d, 7h||3d, 15h||4d, 4h||5d, 12h|
These are "maps" of the delta-V cost to move from one "location" to another (instead of maps of the ditance from one location to another). Keep in mind that some of the locations are actually orbits. If there is a planet with an atmosphere involved, "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).
- LEO: Low Earth Orbit. Earth orbit from 160 kilometers to 2,000 kilometers from the Earth's surface (below 200 kilometers Earth's atmosphere will cause the orbit to decay). The International Space Station is in an orbit that varies from 320 km to 400 km.
- GEO: Geosynchronous Earth Orbit. Earth orbit at 42,164 km from the Earth's center (35,786 kilometres from Earth's surface). Where the orbital period is one sidereal day. A satellite in GEO where the orbit is over the Earth's equator is in geostationary orbit. Such a satellite as viewed from Earth is in a fixed location in the sky, which is intensely desirable real-estate for telecommunications satellites. These are called "Clarke orbits" after Sir. Arthur C. Clarke. Competition is fierce for slots in geostationary orbit, slots are allocation by the International Telecommunication Union.
- EML1: Earth-Moon Lagrangian point 1. On the line connecting the centers of the Earth and the Moon, the L1 point is where the gravity of the two bodies cancels out. It allows easy access to both Earth and Lunar orbits, and would be a good place for an orbital propellant depot and/or space station. It has many other uses. It is about 344,000 km from Earth's center.
Rocket Flight Delta-V Map
In the also regrettably out of print game Rocket Flight the map is ruled off in hexagons of delta V instead of hexagons of distance (wargames use hexagons instead of squares so that diagonal movement is the same distance as orthogonal). Moving from one hex to an adjacent hex represents a delta V of 3 kilometers per second. This also means that in this map each hexagon represents an entire orbit (instead of a location), due to "rotating frames of reference" (no, I do not quite understand that either; but people I know who are more mathematically knowledgable than I have assured me that it is a brilliant idea).
In order to move to an adjacent hexagon in one turn, the spacecraft has to expend propellant mass points. To discover how much, refer to the table and cross reference the spacecraft propulsion's specific impulse with the spacecraft's dry mass points:
0 to 5
6 to 10
11 to 20
21 to 30
31 to 99
If you want to move two hexes in one turn, you have to burn four times the specified number of propellant points. You can move three hexes for eight times the propellant, four hexes for 16 times the propellant, and 5 hexes for 32 times the propellant. Which is why most people opt to just move one hex per turn unless it is an emergency.
However, the various propulsion systems have a maximum mass flow rate, which is the maximum number of propellant points it can expend in one turn. This corresponds to the spacecraft's acceleration rate.
High Frontier Delta-V Map
The black hexagons are sites, which are planets, moons, and asteroid spacecraft can land on. some planets are composed of several sites, e.g., the planet Mars is composed of three sites: North Pole, Hellas Basin Buried Glaciers, and Arsia Mons Caves.
Sites are connected by lines called routes which are paths that spacecraft can move along. During the turn, a spacecraft can move as far as it wants along a path, until it encounters a pink circle. In order to enter a pink circle it has to expend one "burn" (paying the 2.5 km/sec delta V cost and also expending a unit of propellant). At the beginning of each turn, a spacecraft is given an allotment of "burns" equal to its acceleration rating. These burns can be used during its turn, unused burns are lost. Remember in order to use a burn the spacecraft must pay a point of propellant.
When a spacecraft runs out of burns, it can no longer enter pink circles during this turn. It has to stop on any "Intersections" on its current path prior to the pink circle. And when a spacecraft runs out of propellant, it can no longer make burns at all until it is refueled no matter what turn it is.
The number of propellant units and the acceleration rating of a spacecraft depends upon its propulsion system and mass ratio.
Different routes cross each other. If one of the routes has a gap (so it appears that one route goes "over" and the other goes "under", see "No Intersection" in the diagram) the two routes are not connected. If both routes have no gaps they are connected, this is called a "Hohmann Intersection". If the place the two routes cross is marked with a circle they are connected, this is called a "Lagrange Intersection." At the end of a turn all spacecraft must be occupying either an Intersection or a Site.
A spacecraft can turn at an Interstection to switch from the route it is on to the route it was crossing (otherwise it has to stay on its current route). It costs one burn to turn at a Hohmann intersection, turning at a Lagrange intersection is free (due to gravity being negated by a nearby planet).
Some Lagrange intersections are marked with symbols:
- Skull and Crossed Bones: a Crash Hazard. Spacecraft has to roll a die to see if it crashes and is destroyed.
- Parachute: an Aerobrake Hazard. Spacecraft has to roll a die. If it rolls 2 to 6, it successfully areobrakes, and can now move to land on a Site with no cost in propellant. If it rolls a 1, it burns up in reentry and is destroyed. Spacecraft with Atmospheric ISRU Scoops are immune to Aerobrake Hazards, they are automatically successful. In addition such spacecraft can refuel if they ends their move there. A spacecraft using one of the three kinds of lightpressure sail propulsion is automatically destroyed if it enters an Aerobrake Hazard.
- Number: Gravitational Slingshot. Spacecraft obtains that number of extra burns which do not require propellant to be expended. These burns can be used in the remainder of the game turn. NASA loves gravitational slingshots and use them at every opportunity.
- Lunar Crescent: Moon Boost. As per Gravitational Slingshot, except it only gives +1 extra propellant-free burn.
- Nuclear Trefoil: Radiation Belt. Spacecraft entering this suffer a radiation attack. Roll one die and subtract the spacecraft's modified thrust to find the radiation level (the faster you can fly the lower the radiation dose). All spacecraft systems with a radiation hardness lower than the radiation level are destroyed. If sunspots are active add 2 to the die roll. The UN Cycler is immune to the Earth radiation belt. Spacecraft with a sail propulsion system are immune to radiation belts. Spacecraft with Magnetic Sails are immune and in addition get a Moon Boost.
High Trader Delta-V Map
A pity this game never saw the light of day.
Each triangle or diamond shape is an Orbital. Spacecraft in orbitals must always be facing one of the sides of the orbital. Turning to face an adjacent side requires one burn of 2.5 km/s delta V. Spacecraft can move from the orbital they are in, jumping over the face they are pointing at, and enter the next orbital. There is no cost to do so unless the face has a Burn Dot on it. In that case the spacecraft must expend one burn of 2.5 km/s delta V. If the spacecraft does not have that much delta V left it is forbidden to cross the Burn Dot.
Each new orbital entered adds 2 months to the spacecraft's travel time.