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Comment:

1785

Deletions are marked like this.  Additions are marked like this. 
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Launch at 80 km altitude, 6458 km radius. GM is 3.986e14 m^2^/s^2^, day is 86164 seconds, escape velocity is 11111 m/s. rotation velocity 471 m/s, effective escape 10640 m/s . '''Not including air drag on the way out, which will be significant.'''  Launch at 80 km altitude, 6458 km radius. GM is 3.986e14 m^3^/s^2^, day is 86164 seconds, escape velocity is 11111 m/s. rotation velocity 471 m/s, effective escape 10640 m/s . '''Not including air drag on the way out, which will be significant.''' 
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  radius km  launch V  kick V   ISS  6780 km  7480 m/s  94 m/s  inclination 51.65°, inaccessable from equatorial plane launch   M288  12789 km  8586 m/s  1009 m/s   GEO  42164 km  9875 m/s  1490 m/s   Moon  384400 km  10547 m/s  833 m/s  Moon's orbit inclined compared to Earth's axial tilt   Mars   11002 m/s  5630 m/s  sum of squares, eff. escape + 2.86 m/s  
  radius km  launch V  orbit V  kick V <2> plane change V from loop latitude   ISS  6780 km  7480 m/s  7668 m/s  94 m/s 134 m/s/°  altitude only, ISS inclination 51.65°, inaccessable   M288  12789 km  8586 m/s  5583 m/s  1009 m/s  97 m/s/°   GEO  42164 km  9875 m/s  3075 m/s  1490 m/s  54 m/s/°   Moon  384400 km  10547 m/s  1018 m/s  833 m/s  18 m/s/°  Moon's orbit inclined compared to Earth's axial tilt   Mars   11002 m/s   5630 m/s   kick=Mars landing, eff. escape + 2.86 m/s  
Launch Loop Destinations
Launch at 80 km altitude, 6458 km radius. GM is 3.986e14 m^{3}/s^{2}, day is 86164 seconds, escape velocity is 11111 m/s. rotation velocity 471 m/s, effective escape 10640 m/s . Not including air drag on the way out, which will be significant.

radius km 
launch V 
orbit V 
kick V 
plane change V from loop latitude 

ISS 
6780 km 
7480 m/s 
7668 m/s 
94 m/s 
134 m/s/° 
altitude only, ISS inclination 51.65°, inaccessable 
M288 
12789 km 
8586 m/s 
5583 m/s 
1009 m/s 
97 m/s/° 

GEO 
42164 km 
9875 m/s 
3075 m/s 
1490 m/s 
54 m/s/° 

Moon 
384400 km 
10547 m/s 
1018 m/s 
833 m/s 
18 m/s/° 
Moon's orbit inclined compared to Earth's axial tilt 
Mars 

11002 m/s 

5630 m/s 

kick=Mars landing, eff. escape + 2.86 m/s 
libreoffice spreadsheet destinations.ods
Note that gravity assist from the Moon reduce the Mars launch velocity a tiny bit  but not much, because the vehicle must leave the Moon at precisely the right direction (tangential to Earth's orbit) and velocity ( 2860 m/s added to the Earth's 29,800 m/s solar orbital velocity to be in a Hohmann orbit to Mars, and this must happen at precisely the right window to reach Mars when it gets there. These windows happen every 780 days, and the Moon will be in the wrong place most of those days. The vehicle can take a faster orbit than a Hohmann (with a higher delta V at each end) and accomodate some "wrongness") but not much.
Saving perhaps 200 m/s of delta V on a Mars rocket launch is significant. Not for a launch loop. It is more important to save delta V for the kick.