CAS PY 105 Study Guide - Orbital Period

Communications satellites are placed in a circular orbit where they stay directly over a fixed point on the equator as the earth rotates. These are geosynchronous orbits. The radius of the earth is 6.37 x 10⁶ m and the altitude of the synchronous orbit is 3.58 x 10⁷ m.  What is the magnitude of the acceleration of a satellite in a geosynchronous orbit?

Calculate the height from the Earth's surface that a satellite must attain in order to be in geosynchronous orbit and the satellite's velocity?

A geosynchronous orbit is one in which the satellite remains "in place" above the same spot on the Earth's surface.

The radius of the Earth- 6.38×10^6m

Gravitation Constant- 6.67×10−11m^3/kgs^2

Mass of the Earth- 5.97×10^24 kg

Communications satellites are placed in a circular orbit where they stay directly over a fixed point on the equator as the earth rotates. These are called geosynchronous orbits. The altitude of a geosynchronous orbit is 3.58×10⁷ m(≈22,000 miles).

Part A
What is the period of a satellite in a geosynchronous orbit?

Part B
Find the value of g at this altitude.

Part C
What is the weight of a 2000 kg satellite in a geosynchronous orbit?