From time to time I like to post nice physics problems on here. Here is a quickie that I used to use in my first-year Astrophysical Concepts course which has now been discontinued, so I don’t need to keep it to myself it any longer.

A simple way to travel from one planet in the solar system to another is to inject a spacecraft into an elliptical transfer orbit, like the one shown by the dashed curve, which is described by Kepler’s Laws in the same way that the planetary orbits (solid curves) are.

Kepler’s Third Law states that the period of an elliptical orbit is given by where is the semi-major axis of the ellipse. Assuming that the orbits of Earth and Mars are both approximately circular and the radius of Mars’ orbit is 50% larger than Earth’s, and without looking up any further data, calculate the time taken to travel in this way from Earth to Mars.