# Gravitation of a Satellite

If a satellite is in a sufficiently low orbit, it will encounter air drag from the earth's atmosphere. Since air drag does negative work (the force of air drag is directed opposite the motion), the mechanical energy will decrease. According to the following equation: (See attached file for full problem description)

E= - GmEm/ 2r

, if E decreases (becomes more negative), the radius r of the orbit will decrease. If air drag is relatively small, the satellite can be considered to be in a circular orbit of continually decreasing radius.

A) A satellite with mass m is initially in a circular orbit a distance h1 above the earth's surface. Due to air drag, the satellite's altitude decreases to h2 . Calculate the initial orbital speed.

Express your answer to four significant figures. Take the gravitational constant to be G, the mass of the Earth to be ME , the radius of the Earth to be RE .

V =

B) Calculate the increase in orbital speed.

Calculate the answer correctly to two significant figures. If you decide to compute the individual velocities separately, you may need to compute them to a higher degree of accuracy, in order to get the difference accurate to this degree.

delta V =

C) Calculate the initial mechanical energy.

E =

D) Calculate the change in kinetic energy.

delta K =

E) Calculate the change in gravitational potential energy.

delta U =

F) Calculate the change in mechanical energy.

delta E =

G) Calculate the work done by the force of air drag.

W =

#### Solution Summary

This solution contain step-by-step calculations to determine the multiple variables of the satellite. All workings and formulas are shown in a clear manner.