A cloud of dust in space originally occupies volume V= 3.5 x 10^26 m^3 whose average density D= .0085 kg/m^3. Over many billions of years it contracts to form a uniform spherical planet with radius r=5.5 x 10^6 m.
Part a. Find the gravity field, g, at the surface of the planet.
Part b. Find the orbital speed v, of a spacecraft in circular orbit, at height h= 80900 meters above the surface of the planet.
Step 1. Since the total mass M, is the average density times the volume, we can write:
(1) M= D V
You should substitute knowns to find M= 2.975 x 10^24 kg.
Step 2. The gravity field on the surface of a spherical planet is expressed ...