Randall D. Knight — Newton's Theory of Gravity: Problem 31

The Parker Solar Probe, launched in 2018, was the first spacecraft to explore the solar corona, the hot gases and flares that extend outward from the solar surface. The probe is in a highly elliptical orbit that, using the gravity of Venus, will be nudged ever closer to the sun until, in 2025, it reaches a closest approach of 6.9 million kilometers from the center of the sun. Its maximum speed as it whips through the corona will be 192 km/s. a. What is the probe’s closest approach as a multiple of \(R_s\), the sun’s radius? b. The probe’s highly elliptical orbit carries it out to a maximum distance of \(160 R_s\) with a period of 88 days. What is its slowest speed, in km/s?