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

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APPENDIX

Delta-V Calculations

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