Question

This problem concerns the properties of circular orbits for a satellite of mass m orbiting a planet of mass M in an almost circular orbit of radius r. In doing this problem, you are to assume that the planet has an atmosphere that causes a small drag due to air resistance. "Small" means that there is little change during each orbit so that the orbit remains nearly circular, but the radius can change slowly with time. The following questions will ask about the net effects of drag and gravity on the satellite's motion, under the assumption that the satellite's orbit stays nearly circular. Use G if necessary for the universal gravitational constant.

What is the potential energy U of the satellite?Express your answer in terms ofm, M, G, and r.What is the kinetic energy K of the satellite?Express the kinetic energy in termsof m, M, G, and r.

Answer 1

A) U = - GMm/r

B) K = 0.5 mGM/r

Step-by-step explanation:

A) The potential energy U of the satellite

U = - GMm/r

G = universal gravitational constant which is ( 6.67e-11 Nm^2/c^2 )

M = mass of the planet

m = mass

r = distance ( radius )

B) Kinetic energy

kinetic energy expressed as K = 0.5 m Vo^2

NOTE : Vo^2 = GM / r

hence kinetic energy will be expressed as

K = 0.5 mGM/r