A sports satellite is circularly orbiting planet $XÆ A-12$ in a geostationary orbit ready to bounce game signal all over the planet. The planet's mass is $2.41 * 10^{24}$. The satellite is orbiting the planet at a speed of 2732 m/s and the orbital distance is $3.65 * 10^6$ and a day lasts for 18 hours on planet $XÆ A-12$. A pro basketball player has just traveled to $XÆ A-12$ to compete in the CBA (Cosmic Basketball Association) and is having troubleshooting free throws. What velocity must the player shoot with if they launch the basketball from a height of 2.8 meters? (you cannot assume that $XÆ A-12$ has the same acceleration due to gravity as Earth).

A good solution is not just equations and numeric predictions but will include commentary and discussion of those equations and predictions and reflections on what those predictions mean. We encourage you to use the simplest model that correctly captures the essential physics.