Appendix 2

Mission Delta V and Flight Times

Tales of Outer Space ed. Donald A. Wollheim, Ace D-73, 1954. Artwork by Lawrence

Spaceship Handbook Mission Table

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.

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-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). Impulse trajectory I-2 is in-between I-1 and I-3 (it is equivalent to an elliptical orbit from Mercury to Pluto).

Brachistochrone trajectories are labeled by their level of constant acceleration: 0.01 g, 0.10 g, and 1.0 g.

These values were calculated with a complicated mathematical model, and take more factors into account than the few I've covered.

I've only listed some of the planets. For the full table refer to the book.

Destination Impulse Brachistochrone
I-1 I-2 I-3 0.01g 0.10g 1.00g
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)
Ceres 33,430 (2y7m) 44,730 (7.5m) 92,1600 (5m) 655,000 (63d) 2,040,000 (23d) 6,441,000 (8d)
Jupiter 69,990 (5y5m) 72,690 (1y10m) 118,010 (1y) 1,000,000 (3.5m) 3,142,000 (36d) 9,930,000 (12d)
Ganymede 61,880 (5y5m) 56,250 (1y10m) 67,130 (1y) 1,001,000 (3.5m) 3,145,000 (36d) 9,938,000 (12d)
Saturn 57,690 (12y1m) 55,770 (4y11m) 108,680 (2y3m) 1,420,000 (5m) 4,477,000 (52d) 14,153,000 (17d)
Titan 49,670 (12y1m) 42,750 (4y11m) 56,660 (2y3m) 1,421,000 (5m) 4,479,000 (52d) 14,160,000 (17d)
All missions either start from Terra's surface or have Terra as the destination.
(i.e., the "Mars" row gives data for both the Terra-Mars-Terra and the Mars-Terra-Mars missions)
Values are delta V in m/s, with transit times in parenthesis. Y = years, M = months, D = days, H = hours

Mr. Rogers had this to say about his table:

In (the) table, I was presenting a complete round trip from the surface of the earth to any Destination and back to Earth's surface-- which included the steps of the voyage as outlined in the figure 39, i.e., roughly:

1. Launch to LEO
2 Transfer to edge of Earths gravity well
3 Transfer between planets
4 Mid course corrections
5 Capture Destination Planet
6 Transfer to Low orbit around destination planet
7 Circularize Low Orbit
8 Land on Destination planet (with allowance for atmosphere braking)
9 thru 16 And then Repeat the process in reverse to come back to Earth.

Now, one thing I'll admit to is that my numbers are NOT the most efficient possible for any particular trip. What I wanted to do was break up a round trip to anywhere into separate definable components so the Delta-Vs of those differing trajectories could be compared apples to apples. Any normal orbit analyst would have combined steps 2 and 3 (and 10 & 11) for an improved mission Delta-V. However, when you do that, you make comparing a Hohmann orbit to a "Big Ellipse Orbit" or a Hyperbolic + 30 Kms Orbit impossible--that is, they become Apples and oranges. (Don't forget...Space isn't Flat!)

By breaking the trip up into stages we can break out and compare the TRANSFER VELOCITY of the differing Orbits and compare them...and still be very close to the actual Delta V of a typical mission.

So, by this method I produced a valid statistical comparison of different orbits velocity requirements and round trip duration requirements. Real mission planners will beat my numbers by approximately 5-10% perhaps, but that only means you would have that much 'gas' left in the tanks following my flight plans.

Bottom line, dont forget to carry fuel for those mid course maneuvers (errors and asteroids-- Darn Rocks!!) and also to land or you'll find yourself in space with no fuel!

And now you know why I say: "May your jackstands strike earth before your tanks run dry!

Erik Max Francis' Mission Tables

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).

The tables were created by Erik Max Francis' amazing Hohmann orbit calculator and the easy to use Python programming language (sample program here and here).

Expedition to Earth by Sir Arthur C. Clarke, 1953
LEGEND
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 green 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.

Delta V required for travel using Hohmann orbits: Solar System

Mercury Venus Earth Mars Vesta Juno Eugenia Ceres Pallas Jupiter Saturn Uranus Neptune Pluto
Mercury 2,945 19,852 23,523 23,143 24,486 24,991 25,050 25,059 25,094 36,121 30,200 26,548 27,176 24,207
Venus 9,524 7,265 21,703 18,542 19,316 19,960 20,043 20,078 20,114 33,372 27,477 23,913 24,620 21,488
Earth 13,094 6,887 7,847 16,540 16,368 17,035 17,124 17,170 17,204 31,642 25,705 22,169 22,918 19,679
Mars 16,876 7,887 5,748 3,502 7,525 8,323 8,437 8,524 8,555 25,265 19,694 16,475 17,390 14,026
Vesta 21,371 11,832 8,756 4,041 234 1,167 1,312 1,544 1,544 20,966 15,834 12,960 14,059 10,529
Juno 21,978 12,580 9,528 4,950 933 77 233 625 578 20,367 15,253 12,423 13,558 9,968
Eugenia 22,075 12,700 9,654 5,102 1,124 127 44 496 443 20,264 15,152 12,328 13,469 9,869
Ceres 21,863 12,514 9,477 4,963 1,116 279 191 320 755 20,172 15,041 12,216 13,360 9,751
Pallas 21,943 12,596 9,558 5,041 1,160 269 172 233 242 20,175 15,051 12,229 13,374 9,764
Jupiter 33,159 26,048 24,192 21,956 20,813 20,318 20,252 19,933 19,982 42,530 28,237 24,085 24,765 20,493
Saturn 27,239 20,156 18,259 16,392 15,682 15,205 15,140 14,806 14,862 28,237 25,495 16,875 17,573 12,786
Uranus 23,588 16,594 14,726 13,177 12,809 12,374 12,316 11,982 12,041 24,085 16,875 15,082 13,153 7,760
Neptune 24,217 17,302 15,476 14,093 13,908 13,510 13,457 13,126 13,186 24,765 17,573 13,153 16,623 8,114
Pluto 20,432 13,355 11,420 9,912 9,560 9,100 9,038 8,697 8,757 19,670 11,957 6,921 7,267 802

Delta V required for travel using Hohmann orbits: Moons of Mars

Phobos Deimos
Phobos 3 745
Deimos 744 1

Delta V required for travel using Hohmann orbits: Moons of Jupiter

Metis Adrastea Amalthea Io Europa Ganymede Callisto Himalia Elara
Metis 7 109 4,970 13,485 15,561 17,006 17,380 15,589 15,574
Adrastea 85 8 4,877 13,410 15,495 16,949 17,330 15,549 15,534
Amalthea 4,922 4,826 54 9,392 11,876 13,814 14,596 13,367 13,355
Io 11,768 11,690 7,625 1,761 5,689 8,022 9,431 9,560 9,558
Europa 14,182 14,113 10,452 2,545 1,388 5,504 6,855 7,705 7,709
Ganymede 15,107 15,047 11,871 4,385 2,177 1,902 5,772 6,626 6,636
Callisto 15,676 15,624 12,850 6,004 3,748 2,127 1,691 5,065 5,083
Himalia 15,542 15,499 13,279 7,806 6,281 4,676 3,305 59 158
Elara 15,558 15,515 13,297 7,834 6,316 4,717 3,355 41 20

Delta V required for travel using Hohmann orbits: Moons of Saturn

Epimetheus Janus Mimas Enceladus Tethys Dione Rhea Titan Iapetus
Epimetheus 15 72 1,521 3,156 4,374 5,552 6,768 9,230 8,481
Janus 17 26 1,515 3,149 4,368 5,546 6,762 9,224 8,475
Mimas 1,428 1,416 92 1,676 2,943 4,188 5,514 8,302 7,703
Enceladus 3,044 3,031 1,490 112 1,384 2,653 4,077 7,249 6,827
Tethys 4,121 4,108 2,617 1,023 258 1,568 2,969 6,422 6,132
Dione 5,216 5,203 3,780 2,217 971 333 1,891 5,559 5,391
Rhea 6,340 6,328 5,016 3,553 2,297 1,116 422 4,565 4,469
Titan 7,367 7,355 6,369 5,292 4,321 3,371 2,276 1,832 3,977
Iapetus 8,104 8,093 7,258 6,359 5,523 4,698 3,681 1,736 360

Delta V required for travel using Hohmann orbits: Moons of Uranus

Miranda Ariel Umbriel Titania Oberon
Miranda 115 1,215 1,889 2,834 3,137
Ariel 720 364 1,332 2,218 2,533
Umbriel 1,431 593 338 1,629 1,918
Titania 2,194 1,312 730 514 1,566
Oberon 2,530 1,663 1,060 496 483
Art by the legendary Wally Wood

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.

LEGEND
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 green
Transit times are below the diagonal in blue

Synodic Periods and Transit Times for Hohmann Travel: Solar System

Mercury Venus Earth Mars Vesta Juno Eugenia Ceres Pallas Jupiter Saturn Uranus Neptune Pluto
Mercury 4.7m 3.8m 3.3m 3.1m 3.1m 3.1m 3.0m 3.0m 2.9m 2.9m 2.9m 2.9m 2.9m
Venus 2.5m 1y, 7.2m 11.0m 8.9m 8.6m 8.6m 8.5m 8.5m 7.8m 7.5m 7.4m 7.4m 7.4m
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

Synodic Periods and Transit Times for Hohmann Travel table for Moons of Mars

Phobos Deimos
Phobos 10h
Deimos 9h

Synodic Periods and Transit Times for Hohmann Travel table for Moons of Jupiter

Metis Adrastea Amalthea Io Europa Ganymede Callisto Himalia Elara
Metis 31d, 21h 17h 9h 8h 7h 7h 7h 7h
Adrastea 4h 18h 9h 8h 7h 7h 7h 7h
Amalthea 5h 5h 17h 14h 13h 12h 12h 12h
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

Synodic Periods and Transit Times for Hohmann Travel table for Moons of Saturn

Epimetheus Janus Mimas Enceladus Tethys Dione Rhea Titan Iapetus
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

Synodic Periods and Transit Times for Hohmann Travel table for Moons of Uranus

Miranda Ariel Umbriel Titania Oberon
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