The Return Trip
The return trip will be made by using a similar Hohmann minimum energy transfer orbit that will boost the spacecraft out of the Martian orbit, letting it fall towards the Earth.
Again an initial thrust must be provided, this time in the opposite direction to the Martian orbit so that the spacecraft reduces its orbital speed and thus enters an orbit of lower radius.
The transfer orbit will be again a heliocentric orbit with aphelion at the point where the spacecraft leaves Mars and perihelion when it intercepts the Earth's orbit.
Determining the parameters for the return trip is essential for it will not only allow us to calculate the total time for the expedition, which is obviously fundamental in terms of overall planning but as the planets have to be again favorably aligned for the return leg this will determine the stay time on the surface of Mars.