Using Kepler's laws and Rutherford scattering to chart the seven gravity assists in the epic sunward journey of the Parker Solar Probe

Abstract

On August 12, 2018, NASA launched the Parker Solar Probe (PSP) to explore regions very near the Sun. Losing enough energy and angular momentum to approach the Sun requires either an impractical amount of fuel or a maneuver called a gravity assist. A gravity assist is essentially an elastic collision with a massive, moving target—Rutherford scattering from a planet. Gravity assists are often used to gain energy in missions destined for the outer solar system, but they can also be used to lose energy. Reaching an orbit sufficiently close to the Sun requires that PSP undergoes not one but seven successive gravity assists off the planet Venus. This simple description poses several conceptual challenges to the curious physics student. Why is it so much more challenging to get to the Sun than to leave the Solar System? Why does it take more than one gravity assist to achieve this, and why does it require seven? Would it be more effective to use Mercury instead of Venus? These questions can be answered using the basic physics principles of Kepler's laws and Rutherford scattering. The reasoning can be presented in an illuminating graphical format to show that these and other seemingly arcane aspects of interplanetary exploration can be understood at the undergraduate level.