Interplanetary travel in other star systems 3
A long time ago, I did a limited comparison of our solar system with scaled versions of itself and with Kepler-62. But there are far more systems, and far more places to visit within a star system.
At the risk of being a bit table-spammy, this looks at a more or less complete set of trips between planets around: a G-dwarf (Sol), a K-dwarf (Kepler-62), an early M-dwarf (L98-59), and an ultracool dwarf (TRAPPIST-1).
The plotted trips consist of:
- Traveling from a planet’s surface to a circular 200 km orbit. Three different values are considered: orbital speed at that altitude, an idealized 2 burn trasfer from the surface, and 20% more ΔV than circular velocity. This 20% figure is a rather arbitrary (and possibly pessimistic) way of considering atmospheric and gravity losses, but is at least consistent and should be vaguely accurate. The 200 km altitude is also arbitrary (if perhaps optimistic), but works as a parking orbit for Earth. Assuming thin atmospheres and/or low scale heights, it can be applied elsewhere. I’ll try to note planets where this is silly (eg: gas giants)
- Hohmann transfers are performed to travelling between planets. Yes, this implies circular coplanar orbits. For the chosen systems, this is usually “good enough”.
- I include the Oberth effect in the typical patched conic way (orbit goes from the nominal SOI edge to 200 km altitude).
- Typical transfer and wait times are considered, but overall Δv is not added up. Just note that starting a transfer from body x to body y is the same as ending one from body y to body x (assuming no aerobraking).
Gravity assists and travel times/Δv for eg: brachistochrones are also being ignored. Things are complicated and messy enough even in the simple cases, and this is a relatively simple comparsion.
Transfer and wait times are symmetric. Transfer ΔVs are not. Start with a column, and go down to the row with your destination.
The raw spreadsheet(s), including some systems that were ultimately ignored
Our solar system
Body | Mercury | Venus | Earth‡ | Mars‡ | Jupiter | Saturn | Uranus | Neptune |
---|---|---|---|---|---|---|---|---|
Mass (kg) | 3.301E+23 | 4.868E+24 | 5.972E+24 | 6.417E+23 | 1.898E+27 | 5.683E+26 | 8.681E+25 | 1.024E+26 |
Radius (m) | 2.440E+06 | 6.052E+06 | 6.371E+06 | 3.390E+06 | 6.991E+07 | 5.823E+07 | 2.536E+07 | 2.562E+07 |
Semi-major axis (au) | 0.39 | 0.73 | 1.00 | 1.52 | 5.20 | 9.58 | 19.19 | 30.07 |
Orbital period (yr) | 0.24 | 0.62 | 1.00 | 1.88 | 11.87 | 29.66 | 84.07 | 164.89 |
Orbital speed (m/s) | 47872 | 34903 | 29785 | 24129 | 13057 | 9622 | 6799 | 5432 |
SOI (m) | 1.124E+08 | 6.204E+08 | 9.246E+08 | 5.772E+08 | 4.821E+10 | 5.481E+10 | 5.177E+10 | 8.665E+10 |
200 km orbit (m/s) | 2889 | 7209 | 7788 | 3454 | 42508† | 25479† | 15055† | 16269† |
Ideal Δv (surface to 200 km orbit, m/s) | 3121 | 7445 | 8031 | 3655 | 42630† | 25566† | 15174† | 16395† |
200 km orbit with 20% margin (m/s) | 3467 | 8650 | 9346 | 4145 | 51010† | 30574† | 18066† | 19522† |
Time between launch windows (yr) | Mercury | Venus | Earth‡ | Mars‡ | Jupiter | Saturn | Uranus | Neptune |
---|---|---|---|---|---|---|---|---|
Mercury | 0.39 | 0.32 | 0.28 | 0.25 | 0.24 | 0.24 | 0.24 | |
Venus | 0.39 | 1.64 | 0.93 | 0.66 | 0.63 | 0.63 | 0.62 | |
Earth‡ | 0.32 | 1.64 | 2.14 | 1.09 | 1.03 | 1.01 | 1.01 | |
Mars‡ | 0.28 | 0.93 | 2.14 | 2.23 | 2.01 | 1.92 | 1.90 | |
Jupiter | 0.25 | 0.66 | 1.09 | 2.23 | 19.79 | 13.82 | 12.79 | |
Saturn | 0.24 | 0.63 | 1.03 | 2.01 | 19.79 | 45.84 | 36.17 | |
Uranus | 0.24 | 0.63 | 1.01 | 1.92 | 13.82 | 45.84 | 171.53 | |
Neptune | 0.24 | 0.62 | 1.01 | 1.90 | 12.79 | 36.17 | 171.53 |
Transfer time (yr) | Mercury | Venus | Earth‡ | Mars‡ | Jupiter | Saturn | Uranus | Neptune |
---|---|---|---|---|---|---|---|---|
Mercury | 0.21 | 0.29 | 0.47 | 2.34 | 5.56 | 15.31 | 29.71 | |
Venus | 0.21 | 0.40 | 0.60 | 2.55 | 5.85 | 15.72 | 30.21 | |
Earth‡ | 0.29 | 0.40 | 0.71 | 2.73 | 6.09 | 16.04 | 30.62 | |
Mars‡ | 0.47 | 0.60 | 0.71 | 3.08 | 6.54 | 16.67 | 31.39 | |
Jupiter | 2.34 | 2.55 | 2.73 | 3.08 | 10.05 | 21.30 | 37.03 | |
Saturn | 5.56 | 5.85 | 6.09 | 6.54 | 10.05 | 27.28 | 44.14 | |
Uranus | 15.31 | 15.72 | 16.04 | 16.67 | 21.30 | 27.28 | 61.12 | |
Neptune | 29.71 | 30.21 | 30.62 | 31.39 | 37.03 | 44.14 | 61.12 |
Transfer Δv (m/s) | Mercury | Venus | Earth‡ | Mars‡ | Jupiter | Saturn | Uranus | Neptune |
---|---|---|---|---|---|---|---|---|
Mercury | 4487 | 5523 | 6577 | 18121 | 11197 | 6917 | 7184 | |
Venus | 5048 | 3455 | 3331 | 17924 | 11032 | 6801 | 7125 | |
Earth‡ | 7536 | 3273 | 2089 | 17828 | 10943 | 6735 | 7090 | |
Mars‡ | 10327 | 4426 | 3575 | 17715 | 10825 | 6639 | 7038 | |
Jupiter | 15016 | 7997 | 6275 | 4183 | 10568 | 6361 | 6869 | |
Saturn | 16048 | 9031 | 7261 | 5545 | 17591 | 6267 | 6795 | |
Uranus | 16688 | 9715 | 7951 | 6530 | 17656 | 10565 | 6744 | |
Neptune | 16924 | 9975 | 8220 | 6921 | 17696 | 10603 | 6243 |
There’s nothing really new here, but it’s a good reference.1 The rescaled variants just add messiness, so are staying in the spreadsheet.
Kepler-62
Kepler-62 is a K2V star with 6 known planets orbiting it. Two of them (Kepler-62 e and Kepler-62 f) are a pair of super-earths with insolations that make them plausibly habitable. The masses are generally poorly measured, with only maximum estimates.2 As such, I am using plausible values found via a mass-radius relation3. Specifically, b and c are considered terrestrial, while the rest are neptunian. Even so, Kepler-62 d is the only one that I’m relatively certain is an ice giant.
Kepler 62 | b | c | d | e‡ | f‡ |
---|---|---|---|---|---|
Mass (kg) | 1.528E+25 | 6.376E+23 | 2.665E+25 | 3.199E+25 | 1.989E+25 |
Radius (m) | 8.355E+06 | 3.444E+06 | 1.244E+07 | 1.027E+07 | 8.993E+06 |
Semi-major axis (au) | 0.0553 | 0.0292 | 0.12 | 0.427 | 0.718 |
Orbital period (yr) | 0.0156 | 0.0341 | 0.0497 | 0.3351 | 0.7318 |
Orbital speed (m/s) | 105208 | 144784 | 71420 | 37861 | 29198 |
SOI (m) | 8.636E+07 | 1.280E+07 | 2.341E+08 | 8.962E+08 | 1.246E+09 |
200 km orbit (m/s) | 10917 | 3417 | 11863† | 14281† | 12016 |
ideal Δv (surface to 200 km orbit, m/s) | 11177 | 3613 | 12053† | 14558† | 12281 |
Δv (200 km orbit w/ 20% margin, m/s) | 13100 | 4101 | 14235† | 17138† | 14419 |
Time between launch windows (yr) | b | c | d | e‡ | f‡ |
---|---|---|---|---|---|
Kepler-62 b | 0.029 | 0.023 | 0.016 | 0.016 | |
Kepler-62 c | 0.029 | 0.108 | 0.038 | 0.036 | |
Kepler-62 d | 0.023 | 0.108 | 0.058 | 0.053 | |
Kepler-62 e‡ | 0.016 | 0.038 | 0.058 | 0.618 | |
Kepler-62 f‡ | 0.016 | 0.036 | 0.053 | 0.618 |
Transfer time (yr) | b | c | d | e‡ | f‡ |
---|---|---|---|---|---|
Kepler-62 b | 0.005 | 0.016 | 0.071 | 0.145 | |
Kepler-62 c | 0.005 | 0.012 | 0.066 | 0.137 | |
Kepler-62 d | 0.016 | 0.012 | 0.086 | 0.163 | |
Kepler-62 e‡ | 0.071 | 0.066 | 0.086 | 0.261 | |
Kepler-62 f‡ | 0.145 | 0.137 | 0.163 | 0.261 |
Transfer Δv (m/s) | b | c | d | e‡ | f‡ |
---|---|---|---|---|---|
Kepler-62 b | 17837 | 10094 | 13869 | 12809 | |
Kepler-62 c | 12096 | 19460 | 17252 | 14986 | |
Kepler-62 d | 12211 | 35642 | 9521 | 9683 | |
Kepler-62 e‡ | 26832 | 50049 | 12299 | 5376 | |
Kepler-62 f‡ | 29960 | 52662 | 15586 | 6304 |
If these look different last time, it’s from using (I think) more accurate masses. While treating the estimate as a point value instead of a distribution is wrong3 (as is arbitrarily picking between the Neptunian and Terran options), it should be considerably better than the very broad lower mass limits:
Planet | b | c | d | e‡ | f‡ |
---|---|---|---|---|---|
Radius (\(R_🜨\)) | 1.31 ± 0.04 | 0.54 ± 0.03 | 1.95 ± 0.07 | 1.61 ± 0.05 | 1.41 ± 0.07 |
Maximum (\(M_🜨\)) | 9 | 4 | 14 | 36 | 35 |
Terrestrial (\(M_🜨\)) | 2.558 | 0.1068 | 10.645 | 5.357 | 3.330 |
Neptunian (\(M_🜨\)) | 2.271 | 0.5044 | 4.462 | 3.223 | 2.573 |
L98-59
A less well known M-dwarf system, but also with some rocky planets.4 At ~4x the mass of TRAPPIST-1 (M3V vs M8V), it also helps to fill in a gap in my cross-system comparsion.
L98-59 | b | c | d | e | f‡ |
---|---|---|---|---|---|
Mass (kg) | 2.747E+024 | 1.194E+025 | 9.794E+024 | 1.684E+025 | 1.672E+025 |
Radius (m) | 5.338E+06 | 8.476E+06 | 1.038E+07 | 9.057E+06 | 9.121E+06 |
Semi-major axis (au) | 0.0223 | 0.0309 | 0.0494 | 0.0712 | 0.1052 |
Orbital period (yr) | 0.0062 | 0.0101 | 0.0204 | 0.0351 | 0.0631 |
Orbital speed (m/s) | 107832 | 91605 | 72450 | 60348 | 49647 |
SOI (m) | 2.472E+07 | 6.166E+07 | 9.106E+07 | 1.630E+08 | 2.402E+08 |
200 km orbit (m/s) | 5754 | 9585 | 7861 | 11019 | 10943 |
Ideal Δv (surface to 200 km orbit, m/s) | 5967 | 9810 | 8012 | 11261 | 11181 |
200 km orbit with 20% margin (m/s) | 6904 | 11502 | 9434 | 13223 | 13131 |
Time between launch windows (yr) | b | c | d | e | f‡ |
---|---|---|---|---|---|
L98-59 b | 0.0158 | 0.0088 | 0.0075 | 0.0068 | |
L98-59 c | 0.0158 | 0.0200 | 0.0142 | 0.0120 | |
L98-59 d | 0.0088 | 0.0200 | 0.0487 | 0.0301 | |
L98-59 e | 0.0075 | 0.0142 | 0.0487 | 0.0791 | |
L98-59 f‡ | 0.0068 | 0.0120 | 0.0301 | 0.0791 |
Transfer time (yr) | b | c | d | e | f‡ |
---|---|---|---|---|---|
L98-59 b | 0.0040 | 0.0063 | 0.0093 | 0.0149 | |
L98-59 c | 0.0040 | 0.0074 | 0.0107 | 0.0164 | |
L98-59 d | 0.0063 | 0.0074 | 0.0137 | 0.0199 | |
L98-59 e | 0.0093 | 0.0107 | 0.0137 | 0.0242 | |
L98-59 f‡ | 0.0149 | 0.0164 | 0.0199 | 0.0242 |
Transfer Δv (m/s) | b | c | d | e | f‡ |
---|---|---|---|---|---|
L98-59 b | 5168 | 10675 | 13013 | 14388 | |
L98-59 c | 5281 | 5861 | 9193 | 11247 | |
L98-59 d | 14318 | 6478 | 5162 | 7206 | |
L98-59 e | 20487 | 11217 | 4330 | 5045 | |
L98-59 f‡ | 25761 | 16005 | 8105 | 5104 |
TRAPPIST-1
Ah, yes. That infamous M8V system with 8 planets, 3 of which are in the habitable zone.5
TRAPPIST-1 | b | c | d | e‡ | f‡ | g‡ | h |
---|---|---|---|---|---|---|---|
Mass (kg) | 6.074E+24 | 6.904E+24 | 1.774E+24 | 4.611E+24 | 5.578E+24 | 6.856E+24 | 1.977E+24 |
Radius (m) | 7.150E+06 | 6.984E+06 | 5.000E+06 | 5.804E+06 | 6.671E+06 | 7.322E+06 | 4.930E+06 |
Semi-major axis (au) | 0.0115 | 0.0158 | 0.0223 | 0.0293 | 0.0385 | 0.0469 | 0.0619 |
Orbital period (yr) | 0.0041 | 0.0066 | 0.0111 | 0.0167 | 0.0252 | 0.0338 | 0.0514 |
Orbital speed (m/s) | 82686 | 70655 | 59528 | 51925 | 45265 | 41039 | 35704 |
SOI (m) | 2.829E+07 | 4.078E+07 | 3.336E+07 | 6.425E+07 | 9.124E+07 | 1.205E+08 | 9.685E+07 |
200 km orbit (m/s) | 7426 | 8009 | 4771 | 7159 | 7361 | 7799 | 5071 |
Ideal Δv (surface to 200 km orbit, m/s) | 7633 | 8236 | 4960 | 7404 | 7580 | 8011 | 5275 |
200 km orbit with 20% margin (m/s) | 8912 | 9610 | 5725 | 8591 | 8833 | 9359 | 6085 |
Time between launch windows (yr) | b | c | d | e‡ | f‡ | g‡ | h |
---|---|---|---|---|---|---|---|
TRAPPIST-1 b | 0.0110 | 0.0066 | 0.0055 | 0.0049 | 0.0047 | 0.0045 | |
TRAPPIST-1 c | 0.0110 | 0.0165 | 0.0110 | 0.0090 | 0.0082 | 0.0076 | |
TRAPPIST-1 d | 0.0066 | 0.0165 | 0.0330 | 0.0198 | 0.0165 | 0.0141 | |
TRAPPIST-1 e‡ | 0.0055 | 0.0110 | 0.0330 | 0.0495 | 0.0330 | 0.0247 | |
TRAPPIST-1 f‡ | 0.0049 | 0.0090 | 0.0198 | 0.0495 | 0.0989 | 0.0495 | |
TRAPPIST-1 g‡ | 0.0047 | 0.0082 | 0.0165 | 0.0330 | 0.0989 | 0.0990 | |
TRAPPIST-1 h | 0.0045 | 0.0076 | 0.0141 | 0.0247 | 0.0495 | 0.0990 |
Transfer time (yr) | b | c | d | e‡ | f‡ | g‡ | h |
---|---|---|---|---|---|---|---|
TRAPPIST-1 b | 0.0008 | 0.0011 | 0.0015 | 0.0020 | 0.0025 | 0.0035 | |
TRAPPIST-1 c | 0.0008 | 0.0013 | 0.0017 | 0.0022 | 0.0028 | 0.0038 | |
TRAPPIST-1 d | 0.0011 | 0.0013 | 0.0021 | 0.0027 | 0.0032 | 0.0043 | |
TRAPPIST-1 e‡ | 0.0015 | 0.0017 | 0.0021 | 0.0031 | 0.0037 | 0.0049 | |
TRAPPIST-1 f‡ | 0.0020 | 0.0022 | 0.0027 | 0.0031 | 0.0044 | 0.0056 | |
TRAPPIST-1 g‡ | 0.0025 | 0.0028 | 0.0032 | 0.0037 | 0.0044 | 0.0063 | |
TRAPPIST-1 h | 0.0035 | 0.0038 | 0.0043 | 0.0049 | 0.0056 | 0.0063 |
Transfer Δv (m/s) | b | c | d | e‡ | f‡ | g‡ | h |
---|---|---|---|---|---|---|---|
TRAPPIST-1 b | 3767 | 7286 | 8923 | 10280 | 10808 | 12099 | |
TRAPPIST-1 c | 3540 | 3376 | 5653 | 7316 | 8182 | 9623 | |
TRAPPIST-1 d | 7767 | 3775 | 3150 | 4584 | 5603 | 6905 | |
TRAPPIST-1 e‡ | 11248 | 6237 | 2560 | 3148 | 4015 | 4881 | |
TRAPPIST-1 f‡ | 14416 | 8945 | 4947 | 3072 | 3077 | 3197 | |
TRAPPIST-1 g‡ | 16410 | 10798 | 6810 | 4033 | 2879 | 2364 | |
TRAPPIST-1 h | 18845 | 13179 | 9332 | 5749 | 3827 | 3229 |
Final Thoughts
TRAPPIST-1 is the only system where the transfer Δvs don’t seem to jump enormously when compared with Sol’s. I think this shows the planets being tightly packed and low mass when compared with the others. The planet masses have a huge effect in terms of getting to orbit also, dominating over transfer numbers if one plans to land. This might mean that most places are actually harder from an interplanetary travel perspective than Earth, but could also be observation bias.
Transfer times and transfer window frequency are more or less monotonic with stellar mass^-1. Likewise SOI sizes. Planet orbital speeds aren’t quite, but that’s in part because of how the distributions of the 4 systems vary.
Mission times could potentially be in ‘easy’ reach, being no more than some proposed lunar missions or actual space station ones, though how that interacts with the Δv numbers for Kepler-62 and L98-59 would require far more detailed analysis that I feel like doing. Maybe Project Rho has some useful heuristics.
It was surprisingly hard to find good exo-earth analogs. I know that we’ve found far more hot jupiters and neptunes, but still… (eg: Kepler-90 was initially intriguing, but the planets closest to having reasonable instellations were gas giants. Similarly, all of Kepler-80’s planets are also quite hot)
† Planet is (or probably is) a gas or ice giant, so don’t take these figures too seriously.
‡ Planet is or may be relatively habitable.
Data Sources
-
Wikipedia, as the solar system bodies are generally known well to high precision. ↩
-
Probabilistic Forecasting of the Masses and Radii of Other Worlds ↩ ↩2
-
A 2018 update on the masses of the TRAPPIST-1 planets, and a 2017 study of TRAPPIST-1 with Spitzer data for their periods and the star’s properties. ↩