A satelite that goes around the earth once every 24 hours is called a geosynchro

Question

A satelite that goes around the earth once every 24 hours is called a geosynchronous satelite. If a geosynchronous satelite is in an equatorial orbit, its position appears stationary with respect to a ground station, and it is known as a geostationary satelite. Find the radius R of the orbit of a geosynchronous satelite that circles the earth. (Note that R is measured from the center of the Earth, not the surface.) Use the following constants to calculate the orbital radius in meters to three significant figures: Universal Gravitational Constant G is 6.67 x 10^-11 Nm^2/kg^2; Mass of the Earth is 5.98 x 10^24 kg; Radius of the Earth is 6.38 x 10^6 m.

Explanation / Answer

Fcp = mrw^2

where m is the mass of the satellite,

r the orbital radius and

w is the angular velocity.

This F b/w earth and satellite

F = GMm/r^2

Equating:

rw^2 = GM/r ^2

r^3 = GM/w^2

w = 2pi/T , T is the orbital period (= 24 * 3600 seconds)

r^3 = GM* T^2/(2pi)^2

r ~ 4.225 * 10^7 metres

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