# Properties of Circular Orbits for a Satellite Orbiting a Planet of Mass M

The motivation for Isaac Newton to discover his laws of motion was to explain the properties of planetary orbits that were observed by Tycho Brahe and analyzed by Johannes Kepler. A good starting point for understanding this (as well as the speed of the space shuttle and the height of geostationary satellites) is the simplest orbit--a circular one. This problem concerns the properties of circular orbits for a satellite orbiting a planet of mass M.

The motivation for Isaac Newton to discover his laws of motion was to explain the properties of planetary orbits that were observed by Tycho Brahe and analyzed by Johannes Kepler. A good starting point for understanding this (as well as the speed of the space shuttle and the height of geostationary satellites) is the simplest orbit--a circular one. This problem concerns the properties of circular orbits for a satellite orbiting a planet of mass M.

A. Find the orbital speed for a satellite in a circular orbit.

B. Find the kinetic energy of a satellite in a circular orbit.

B. Find the orbital period.

C. Find the magnitude of the angular momentum of the satellite with respect to the center of the planet.

D. Represent the physical quantities characterizing the orbit that depend on the radius. Indicate the exponent (power) of the radial dependence of the absolute value of each.

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#### Solution Summary

This solution identifies how to simplify or evaluate the formulas related to the properties of circular orbits.