Calculation of change in velocity required to enter the transfer orbit for the return trip

Expression (2) supplied a formula for calculating the velocity at any point of a heliocentric orbit with the Earth at perihelion and Mars at aphelion :

The velocity at aphelion will then be found by replacing r by dMars:

The value we are really interested in is the change in velocity (negative, for we will drop orbits and so the thrusters will have to be fired in opposite direction to the direction of the Martian orbit), that is, the difference between the velocity at aphelion that has just been calculated and Mars orbital velocity.

The velocity of Mars supposing a circular orbit would be :

So the change in velocity would then be :

Substituting, the change in velocity required is of -3.2 km/s.