How do you find the orbital radius of a satellite (GPS) if you are only given the speed at which it orbits?
March 7th, 2010 | by admin |-grade 12 physics
-formulas would be greatly appreciated
To be on an orbit of radius R the satellite shoud experience centripetal acceleration V^2/R. This acceleration is provided by gravity force and equal GM/R^2. On the Earth surface this acceleration is g = 9.8 m/s^2, so GM/r^2 = g, where r=6.4*10^6 m is Earth radius. Then GM = gr^2 and acceleration on distance R is gr^2/R^2 and equal to V^2/R. Now we have an equation:
gr^2/R^2 = V^2/R. Solve over R and get R = gr^2/V^2.
One Response to “How do you find the orbital radius of a satellite (GPS) if you are only given the speed at which it orbits?”
By Alexey V on Mar 7, 2010 | Reply
To be on an orbit of radius R the satellite shoud experience centripetal acceleration V^2/R. This acceleration is provided by gravity force and equal GM/R^2. On the Earth surface this acceleration is g = 9.8 m/s^2, so GM/r^2 = g, where r=6.4*10^6 m is Earth radius. Then GM = gr^2 and acceleration on distance R is gr^2/R^2 and equal to V^2/R. Now we have an equation:
gr^2/R^2 = V^2/R. Solve over R and get R = gr^2/V^2.
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