Problem 5

An exploration probe is placed into circular orbit above an unknown planet at an altitude of 6000km and

speed 80500 km/hr. The probe discovers the planet also has a moon that orbits every 0.6 days with a

semi major axis of 120 x 10³ km and semi minor axis of 88% of this. Determine the following in order to

achieve the most efficient mission to investigate the moon outside its sphere of influence.

a) The radius and mass of the planet

b) The gravity on the surface of the planet

c) The total energy per unit mass of the probe and

moon orbits

d) The angular momentums per unit mass of the

probe and moon orbits

e) The eccentricity of the most efficient transfer

orbit for the probe to encounter the moon.

(Answers: 4.48x104 km, 3.8x1025 kg, 1.292g, -1.06,-2.5 x10³J/kg, 1.54, 1.135 x10¹²m²/s, 0.108,

23.53,18.96 km/s, 1.172km/s, -5.42 km/s, 9.42 km/s)

f) The velocities at the apoapsis and periapsis¹ of

the most efficient transfer orbit for the probe to

encounter the moon.

g) The minimum velocity increment to encounter

the moon and the relative velocity between the

moon and probe during the encounter

h) The minimum velocity increment required to

escape the planet after the moon encounter