What's ratio of the orbital period for a satellite in a geosynchronous orbit around the Earth...

What's ratio of the orbital period for a satellite in a geosynchronous orbit around the Earth to that of a satellite in an orbit slightly above the surface of the Earth? The Earth has a radius of 6371km, and a satellite in a circular geosynchronous orbit has a radius of 42000km from the center of the earth. The mass of the Earth is 5.792*10^24kg, and Newton's gravitation constant is G=6.674*10^-11N*m^2/kg^2

Solutions

Expert Solution

Gravitational constant = G = 6.674 x 10^-11 N.m²/kg²

Mass of Earth = M = 5.792 x 10²⁴ kg

Mass of the geosynchronous orbit = m₁

Mass of the satellite orbiting slightly above the surface of the Earth = m₂

Radius of orbit of the geosynchronous satellite = R₁ = 42000 km = 42000 x 10³ m = 4.2 x 10⁷ m

Radius of Earth = R₂ = 6371 km = 6371 x 10³ m

Orbital speed of the geosynchronous satellite = V₁

Orbital speed of the satellite orbiting slightly above the surface of the Earth = V₂

Orbital period of the geosynchronous satellite = T₁

Orbital period of the satellite orbiting slightly above the surface of the Earth = T₂

For the geosynchronous satellite,

The gravitational acceleration of the Earth on the satellite provides the centripetal force for it's circular motion.

Similarly for the satellite orbiting slightly above the surface of the Earth,

Ratio of the orbital period of the geosynchronous satellite and the satellite orbiting slightly above the Earth = 16.93

genius_generous answered 2 years ago

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