Page:Project Longshot - Advanced Design Program Project Report.pdf/61



Assumptions:

 * space station orbit altitude = 300 km
 * space station orbit inclination = 28.5 deg
 * obliquity = 23.5 deg
 * 1 AU = 149.6 x 106 km
 * Earth radius = 6378 km
 * fearth = GMe = 398,601.2 km2/sec2
 * fsun = GMe = 1.3271544 x 1011 km2/sec2
 * fJupiter = GMe = 1.268 x 108 km2/sec2


 * (1) Velocity of probe about the earth:
 * Vp = (GMe/Rcircular).5 = (398,601.2/6678).5 = 7.7258 km/sec


 * (2) Amount of plane change:
 * i = 61x − (28.5x + 23.5x) = 9x


 * (3) Delta-V for 9x plane change:
 * Delta-Vpc = 2 x Vp x sin(i/2) = 1.2123 km/sec


 * (4) Earth escape velocity:
 * Ve−escape = (2GMe/R).5 = 10.9260 km/sec


 * (5) Delta-V to escape earth:
 * Delta-Ve−esc = Ve−esc - Vp = 3.2002 km/sec


 * (6) Velocity of probe around sun:
 * Vp−sun = (fsun/1 AU).5 = 29.7849 km/sec


 * (7) Solar system escape velocity:
 * Vsun−escape = (2fsun/1 AU).5 = 42.1221 km/sec


 * (8) Delta-V to escape the solar system:
 * Delta-Vsun−esc = Vsun−esc - Vp−sun = 12.4273 km/sec


 * (9) Total Delta-V required to escape solar system:
 * Delta-Vtotal = 16.8398 km/sec