Question

The mean radius of earth is R, and its angular speed on its axis is 'omega'. What will be the radius of orbit of a geostationary satellite?

Answer 1

Hey mate,

● Answer-
r = cuberoot(GM/w^2)

● Solution-
Consider a geostationary satellite rotating about earth at height h, radius r, and angular velocity w.

For stationary speed -
Centripetal force = Gravitational force
mrw^2 = GMm/r^2
r^3 = GM/w^2
r = (GM/w^2)^(1/3).
r = cuberoot(GM/w^2)

Radius of orbit of geostationary satellite is (GM/w^2)^(1/3).

Hope this helps...

Answer 2

For a geostationary satellite it's angular velocity should be same as earth's angular velocity ω

Centripetal acceleration of geostationary satellite

here 'r' is the radius of satellite v is the linear velocity of satellite

Now v=ωr since angular velocity of geostationary satellite must be equal to angular velocity of earth.

substituting the value of v in above equation we get

Now g=GM/R2

GM=gR2 substituting value in above equation we get