How Much Energy Was Lost to Friction for a Falling Satellite?

[Sheneron]

Homework Statement

A 500 kg satellite is in a circular orbit at an altitude of 500km above the Earth's surface. Because of air friction, the satellite eventually falls to the Earth's surface where it hits the ground with a speed of 2000 m/s. How much energy was transformed to internal energy by means of friction.

The Attempt at a Solution

Ki + Ui = Kf + Uf loss

$$-\frac{\frac{1}{2}GM_SM_E}{Ri} = \frac{1}{2}M_SV_f^2 - \frac{\frac{1}{2}GM_SM_E}{Rf}+ loss$$

$$-\frac{\frac{1}{2}(6.67e-11)(500)(5.98e24)}{6.37e6 + 500,000} - \frac{1}{2}(500)(2,000)^2 +\frac{\frac{1}{2}(6.67e-11)(500)(5.98e24)}{6.37e6} = loss$$
Is this how to go about this problem, or did I miss a concept at the beginning? thanks

 

[Sheneron]

Is this the right process?

 

[alphysicist]

Hi Sheneron,

I don't believe the factor of 1/2 should be in your expression for Uf.