# Find Gravity Field of a Planet and Orbital Speed of a Spacecraft

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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.

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##### Solution Summary

The solution finds the gravity of a planet and orbital speed of a spacecraft at a known height above it.

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Part a.

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 ...

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