Mars Academy

Aligning the planets for the comeback.

The figure shows how once again Mars and the Earth have to be in their proper positions to attempt a return trip. When the spacecraft falls back from the Martian orbit, it will enter an elliptical transfer orbit that will encompass pi radians (half an orbit) so that it is tangential to both the terrestrial and Martian orbits.

As the Earth moves around the Sun faster than Mars (its angular velocity is nearly double that of Mars, Mars must be advanced with respect to Earth to allow the Earth to intercept the slower spacecraft.

It must follow that the initial difference in angle plus pi radians must equal the angle traveled by the Earth in the time needed to effect the transfer:

which results in an angle of 75 degrees approximately (1.3 radians)