Question

A 160 kg satellite is orbiting on a circular orbit 7655 km above the Earth's surface. Determine the speed of the satellite. (The mass of the Earth is 5.97×10²⁴ kg, and the radius of the Earth is 6370 km.)
(in km/s)

Answer 1

Solution: Here, gravitational force will be equal to centripetal force acting on satellite.

Thus, GMm/R² = mv²/R

( M- mass of Earth and m is mass of satellite and R is distance between centre of the Earth to satellite = radius of Earth + Height of satellite = 6370+7655 = 14025 km = 1.4025*10^7 m and G is gravitational constant = 6.674 * 10^-11 m³ kg^-1 s^-2)

=> GM/R = v²

=> v = √ (GM/R)

=> v = √ { (6.674 * 10^-11) (5.97*10²⁴ )/(1.4025*10⁷)}

=> v = 5330.01 m/s. Answer