Determining the Orbital Altitude

By combining Newton's Universal Law of Gravity with the centripetal force that causes an object to move in a circle, we can solve the equation for "r".  Then, the altitude is determined by subtracting the radius of Earth, Eradius, from the total distance of the satellite from Earth's center, "r".

Newton's Universal Law of Gravity

Central Force Causing an Object to Move in a Circle

Altitude,  Hheight

Fgravity=Gm Earthmsatellite / r2 

equation 1

Fcircl = msatellite v2 / r  

equation 2

Hheight = r - Eradius 

equation 3

G = 6.672 X 10-11 Nm2/kg2 
mEarth = 5.98 X 1024 kg 
r = distance of satellite from center of Earth
velocity, v = 2pr / t 

period, t = time to orbit Earth once (from Part I)

Eradius  = 3960 X 10 m

First, set Fgravity = Fcircle (i.e., set equation 1 equal to equation 2).  Second, solve the equation algebraically for the distance that the satellite orbits from the center of Earth, r.  Finally, determine the altitude, Hheight from equation 3. Determine the altitude of the Yohkoh spacecraft.

Back to the Orbital Velocity or onward to Satellite Network Monitoring

Lesson designed by the YPOP Team

For questions about this lesson, please contact Tim Slater