Find an expression for the kinetic energy of a satellite of mass m in an orbit of radius r about a planet of mass m .

Explanation:

The gravitational force on the satellite provides the centripetal force that keeps the satellite in circular orbit around the satellite, so we can write

(1)

where

G is the gravitational constant

M is the mass of the planet

m is the mass of the satellite

r is the radius of the orbit

v is the speed of the satellite

The formula for the kinetic energy of the satellite is

which can also be written as

So we can substitute the expression that appears in (1) with 2K, and we find:

b would be the answer

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west