Question

The radius of the orbit of a geostationary satellite is (mean radius of the earth R, angular velocity about an axis in ω and acceleration due to gravity on earth's surface is (g) ______.

Options

• `"gR"^2/omega^2`

• `("gR"^2/omega^2)^(1/2)`

• `("gR"^2/omega^2)^(1/3)`

• `("gR"^2/omega^2)^(2/3)`

Answer 1

The radius of the orbit of a geostationary satellite is (mean radius of the earth R, angular velocity about an axis in ω and acceleration due to gravity on earth's surface is (g) `underline(("gR"^2/omega^2)^(1/3))`.

Explanation:

If r is the radius of the orbit of the satellite and ro is the angular velocity which is same as the angular velocity of the earth about its axis then we have

`mromega^2="GMm"/r^2`

`thereforeomega^2="GM"/r^3="gR"^2/r^3`

`thereforer^3="gR"^2/omega^2`

`thereforer=("gR"^2/omega^2)^(1/3)`