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# Determination of the mass of a planet from orbital dynamics

A satellite of mass 830 kg orbits a planet of unknown mass at a distance of 29100 km from the planet's center. The orbital velocity of the satellite is 14200 m/s.

* What is the mass of the planet?
* How much would potential energy (PE) and kinetic energy (KE) of this satellite change as the satellite moved from a circular orbit of radius 29100 km to a circular orbit of radius 32010 km?

Consider G = 6.67 * 10^-11 N m^2 / kg^2 .

#### Solution Preview

Satellite mass (m) in circular orbit with tangential velocity (v) of radius (r) from center of the planet has centripetal force

F = m*v^2/r (1)

To balance the satellite in orbit, this force equals the gravitational force given by (2).

F = GMm/r^2 (2)

Where M is the mass of the planet in question.

Equating (1) and (2) we ...

#### Solution Summary

The orbit of a known satellite is described (radius 29100 km) , both its mass mass (830 kg) and velocity (14200 m/s) are given to determine the mass of the accompanying planet. The changes in potential energy and kinetic energy of the satellite is explined as the satellite moves from an orbit of 29100 km to one of 32010 km

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