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← Revision 9 as of 20170301 01:46:47 ⇥
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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  
'''Note''' Launch altitude may increase to 100 km to reduce drag.   radius km sem.lat.  launch V  orbit V  kick V <2> plane change V from loop latitude   ISS  6780 km  6615 km  7480 m/s  7668 m/s  94 m/s 134 m/s/° altitude only, ISS incl. 51.65°, inaccessable  M288  12789 km  8580 km  8586 m/s  5583 m/s  1009 m/s  97 m/s/°   GEO  42164 km 11200 km  9875 m/s  3075 m/s  1490 m/s  54 m/s/°   Moon  384400 km 12700 km 10547 m/s  1018 m/s  833 m/s487 m/s maxMoon's orbit inclined compared to Earth's axial tilt  Mars  12920 km 11002 m/s   5630 m/s   eff. escape + 2.86 m/s, kick= Mars landing  
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If the launch loop is placed south of the equator, to avoid January thunderstorms in the intertropical convergence zone (ITCZ), extra delta V will be needed after apogee kick to change orbit inclination into a circular equatorial orbit. The Moon is a special case; since its inclination varies from the Earth's equatorial plane by 23.44±5.14°, the plane change relative to the equator (and relative to a southerly offset loop) will vary. The number given for the Moon is relative to the maximum 28.58°; by launching at the right time of day and month, the loop latitude inclination reduces this. 
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.
Note Launch altitude may increase to 100 km to reduce drag.

radius km 
sem.lat. 
launch V 
orbit V 
kick V 
plane change V from loop latitude 

ISS 
6780 km 
6615 km 
7480 m/s 
7668 m/s 
94 m/s 
134 m/s/° 
altitude only, ISS incl. 51.65°, inaccessable 
M288 
12789 km 
8580 km 
8586 m/s 
5583 m/s 
1009 m/s 
97 m/s/° 

GEO 
42164 km 
11200 km 
9875 m/s 
3075 m/s 
1490 m/s 
54 m/s/° 

Moon 
384400 km 
12700 km 
10547 m/s 
1018 m/s 
833 m/s 
487 m/s max 
Moon's orbit inclined compared to Earth's axial tilt 
Mars 

12920 km 
11002 m/s 

5630 m/s 

eff. escape + 2.86 m/s, kick= Mars landing 
libreoffice spreadsheet destinations.ods
If the launch loop is placed south of the equator, to avoid January thunderstorms in the intertropical convergence zone (ITCZ), extra delta V will be needed after apogee kick to change orbit inclination into a circular equatorial orbit. The Moon is a special case; since its inclination varies from the Earth's equatorial plane by 23.44±5.14°, the plane change relative to the equator (and relative to a southerly offset loop) will vary. The number given for the Moon is relative to the maximum 28.58°; by launching at the right time of day and month, the loop latitude inclination reduces this.
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.