Question

Centripetal force (university physics 1):

At what altitude should a geosynchronous satellite be placed? A geosynchronous orbit means the satellite stays above the same point on earth...so what is its orbital period

Answer 1

Let the satellite is at a distance r from the center of the earth.

At each point in the orbit, the gravitational force is equal to the centripetal acceleration.

Let M be the mass of earth and m be that of the satellite moving with angular velocity ω

For, Geosynchronous orbits the time period of the satellite is equal to that of the rotation of earth.

Hence,

However, this distance is from the center of earth.

To calculate its altitude, we must subtract this from the radius of earth.

Orbital period as stated above is 24 hr and angular velocity is