Exploring Our Universe: From the Classroom to Outer Space II. The FUSE Satellite Activity #2 Solutions

Finding the Fata Frequency

R = radius of Earth + 50 km = 6.42 x 10⁶ m
Using Kepler's Law of Periods: T =  5117 s = 0.05923 days
f = 1/T = 16.8 revolutions/day.

Fitting the Data
 

1.  Revolutions/day = 1.665 x 10^-5 time + 14.39

2.

Substitute 16.9 revolutions/day  in the equation above and solve for time.
Destruction time = 1.508 x 10⁵  days = 4.1 x 10² years.

3.  You expect the lifetime calculated in this activity to be greater than a more realistic prediction. This is because as the frequency increases and the period decreases,  the average radius also decreases. As FUSE gets closer to Earth's surface it faces a thicker atmosphere, drag forces on the satellite increase, and  the orbit will decay faster.