8 Planetary and Mission Data

The gravitational constants for the Sun, Earth, and Mars are given by

Earth and Mars travel around the Sun along orbits with average radii

The associated average translational velocities and angular velocities (inertial coordinates) are given by

In particular, the angular velocity difference between Earth and Mars is

For the outgoing trip, the spacecraft is to be transferred from a low Earth orbit to a low Mars orbit; for the return trip, the spacecraft is to be transferred from a low Mars orbit to a low Earth orbit. The radii of the terminal orbits are

corresponding to the altitudes

since the Earth and Mars surface radii are given by

The circular velocities at LEO and LMO (relative-to-planet coordinates) are given by

and the corresponding escape velocities (relative-to-planet coordinates) are given by