A satellite has an orbit with pedigree 175 km and apogee 181,200 km. What is the period of the orbit?

Question

>>I'm not sure what the associated equation is. I tried the problem using the average radius in the period equation but it didn't work. Please help!

Answer 1

First of all, the word is perigee, not pedigree. Pedigrees are used to breed animals.

The numbers you gave must be altitudes, not distances from the center of the Earth. Otherwise, the satellite would come crashing to the surface of the Earth.

Add the radius of the Earth to each. I believe that is something like 6376 km, on the average. That makes the distances from the ceneter of the Earth
6551 km for perigee and 187,576 for the apogee. The average of those two distances is called the semimajor axis of the elliptical orbit, and that is what determines the period. In this case, it is 97064 km.

Assuming it is an Earth satellite, use Kepler's third law (or wht you called the "period equation") to get the period. Since the apogee is nearly half way to the Moon, it is likely that this orbit would be highly perturbed.