Page:Project Longshot - Advanced Design Program Project Report.pdf/62

Rh

Rough calculations for Delta-V's for orbit changes to take the probe out to Jupiter (to take on fuel) are made using Hohmann transfer equations as an approximation (actual orbits would be patched-conics). The first six calculations are the same for this analysis:


 * (1) Energy of Hohmann transfer orbit:
 * Et = −fsun/6.2 AU = −143.0894 km2/sec2


 * (2) Perigee velocity of transfer orbit:
 * V1 = [2(fsun/1 AU + Et)].5 = 38.6171 km/sec


 * (3) Delta-V to enter transfer orbit:
 * Delta-V1 = V1 − Vp−sun = 8.8223 km/sec


 * (4) Apogee velocity of transfer orbit:
 * V2 = [2(fsun/5.2 AU + Et)] = 7.4157 km/sec


 * (5) Velocity required to orbit Jupiter at an altitude of 500,000 km:
 * V3 = (fJupiter/571370).5 = 14.8971 km/sec


 * (6) Delta-V to inject into orbit about Jupiter:
 * V3 − V2 = 7.4814 km/sec


 * (7) Jupiter escape velocity:
 * V3−escape = (2fJupiter/571370).5 = 21.0676 km/sec


 * (8) Delta-V to escape Jupiter:
 * Delta-V3−esc = VJ−esc − VJ = 6.1705 km/sec


 * (9) Velocity of probe about sun at Jupiter distance:
 * Vp−sun−J = (fsun/5.2 AU).5 = 13.0601 km/sec