Distance of a satellite from the earths surface.

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SUMMARY

The distance of a television satellite in a circular orbit around the Earth with a sidereal period of 24 hours can be calculated using Kepler's Laws and gravitational equations. The relevant formulas include GMm/r² = ω²r and GM/r = ω², where G is the gravitational constant and M is the mass of the Earth. By determining the angular velocity (ω) from the period of 24 hours, one can derive the satellite's orbital radius and subsequently the distance from the Earth's surface.

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  • Understanding of Kepler's Laws of planetary motion
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1. A television satellite is in circular orbit about the Earth, with a sidereal period of exactly 24h. What is the distance from the Earths surface?



2. I think I have to use Kepler's Laws. Confused as to how to do it without the mass of each. I guess I could find out the mass of the Earth but then..? Can anyone point me in the right direction?
 
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pwphysics101 said:
1. A television satellite is in circular orbit about the Earth, with a sidereal period of exactly 24h. What is the distance from the Earths surface?



2. I think I have to use Kepler's Laws. Confused as to how to do it without the mass of each. I guess I could find out the mass of the Earth but then..? Can anyone point me in the right direction?

GMm/r2 = ω2r

GM/r = ω2

You know G and M (or can look them up)

ω is the angular velocity. If the period is 24 hours then you know 24 hours is the amount of time it takes for the satellite to travel 2∏ radians. You should probably convert that into radians/sec
 
Thanks! :)
 

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