Ageosynchronous earth satellite is one that remains above the same point on earth (provided it orbits in the equatorial plane in the same direction as earth's rotation). such orbits are useful for communication and weather observation. calculate the radius of such an orbit. mass of earth = me = 5.97 1024 kg.

Explanation:

A geosynchronous satellite's time period is T = 24 hours = 86,400 s

T² = 4 π² R³ / G M

G = Universal gravitational constant = 6.67 × 10⁻¹¹ N m² / kg²

M = Mass of earth = M = 5.97 × 10²⁴ kg

⇒ R =  ∛ [ T² G M / 4 π² ] = ∛ (86400)² ( 6.67 × 10⁻¹¹ ) ( 5.97 × 10²⁴ ) / 4 π²

        =  4.22 × 10⁷ m = 4.22 × 10⁴ km

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