How and why does a geostationary satellite stay above the same point on the Earths surface?
First I think it is useful to look at the definition of a geostationary satellite to find out why it appears to stay in the same place above the earths surface. It is an object that is above the equator, has a period of close to 24 hours (importantly the same duration as a day on Earth!) and moves in the direction of the rotation of the earth. As the earth rotates the satellite travels a longer distance above the earth so that it appears motionless in the sky.The satellite travels in a circular orbite. The Force towards the earth due to gravity = MeMsG/r^2 and the force due to the circular motion of the satellite = MsVs^2/r therefoe the speed of the satellite is equal to root(MeG/r).
TS
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