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

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:

E_t = −f_sun/6.2 AU = −143.0894 km²/sec²

(2) Perigee velocity of transfer orbit:

V₁ = [2(f_sun/1 AU + E_t)]^.5 = 38.6171 km/sec

(3) Delta-V to enter transfer orbit:

Delta-V₁ = V₁ − V_p−sun = 8.8223 km/sec

(4) Apogee velocity of transfer orbit:

V₂ = [2(f_sun/5.2 AU + E_t)] = 7.4157 km/sec

(5) Velocity required to orbit Jupiter at an altitude of 500,000 km:

V₃ = (f_Jupiter/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:

V_3−escape = (2f_Jupiter/571370)^.5 = 21.0676 km/sec

(8) Delta-V to escape Jupiter:

Delta-V_3−esc = V_J−esc − V_J = 6.1705 km/sec

(9) Velocity of probe about sun at Jupiter distance:

V_p−sun−J = (f_sun/5.2 AU)^.5 = 13.0601 km/sec