How do you calculate the orbital period of GPS satellites located at an altitude of 20000 km above the Earth’s surface?

Asker: Anneleen, 17 years old

Answer

This can be found by applying Kepler’s 3rd law. This one says:

4 pi2 R3 = G Ma P2

R : the radius of the orbit,
= the height above the earth’s surface + the average radius of the earth
(express both in meters!)
G : the universal gravitational constant = 6.6727 10-11 m3 kg-1 s-2

Ma : the mass of the earth (express in kg !!)
P the period (in seconds)

With the correct values ​​for the radius and mass of the earth, you will find for an altitude of 20000 km above the earth’s surface:
P = 42618.77 seconds = 11.83855 hours

Important : always make sure that you use the correct units for such calculations. The height and radius of the earth are usually expressed in km in everyday life, but you have to convert them to meters because the value of G is expressed in this way everywhere. For the same reason in the mass of the earth in kg, and the period in seconds.

How do you calculate the orbital period of GPS satellites located at an altitude of 20000 km above the Earth’s surface?

Answered by

prof.dr. Paul Hellings

Department of Mathematics, Fac. IIW, KU Leuven

Catholic University of Leuven
Old Market 13 3000 Leuven
https://www.kuleuven.be/

.

Recent Articles

Related Stories