# Work done by a force changing the distance of a satellite's orbit

## Homework Statement

A 5530-kg satellite is in a circular earth orbit that has a radius of 1.81 × 10^7 m. A net external force must act on the satellite to make it change to a circular orbit that has a radius of 8.01 × 10^6 m. What work must the net external force do?

## Homework Equations

Orbital Speed:
v = sqrt( G * M_e / r )
where G is the gravitational constant and M_e is earth's mass

Work-Kinetic Energy Theorem:
W = K_f - K_i = .5*m*v_f^2 - .5*m*v_i^2

## The Attempt at a Solution

v_i = sqrt( 6.674e-11 * 5.98e24kg / 1.81e7m )
v_i = 4695.74m/s

v_f = sqrt( 6.674e-11 * 5.98e24kg / 8.01e6m )
v_f = 7058.74m/s

W = .5*m*v_f^2 - .5*m*v_i^2
W = .5*5530kg*7058.74m/s^2 - .5*5530kg*4695.74m/s^2
W = 7.68002e10J

Last edited:

Simon Bridge
Homework Helper
Work = change in energy.

Work = change in energy.

I incorrectly found the work to be the difference between the initial and final kinetic energies above.

Simon Bridge