F Gm1m r2 1 ac 2 T T GM R 1 Vesc 2GM R Gm1m KE mv U E KE U

Last updated: 5/15/2023

F Gm1m r2 1 ac 2 T T GM R 1 Vesc 2GM R Gm1m KE mv U E KE U Ecircular Gm m 1 2r T G 6 674 x 10 1 N m kg Problem 1 You are the science officer on a visit to a distant solar system Prior to landing on a planet you measure its radius to be 9 x 100 m and its rotation period to be 22 3 hours You have previously determined that the planet orbits 2 2 x 10 m from its star with a period of 402 days 3 473 x 107 sec Once on the surface you find that the free fall acceleration is 12 2 m sec a What is the mass of the planet Answer 1 5 x 1025 kg b What is the mass of the star Answer 5 2 x 1030 kg