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A 1000 kg satellite travels with an orbital speed of 500 m/s around a planet at an orbital radius of 8000 km.  What is the mass of the planet?

Sagot :

Everest2017
The satellite revolves in a circular orbit and has a centripetal acceleration. This centripetal acceleration is caused by the gravitational attraction force  of the planet.

m = mass of satellite            M mass of planet      R radius of the orbit
V linear velocity tangential to the orbit                   G = gravitational constant

Centripetal force = m V² / R 
                         =  gRGravitational Force = G Mm / R²
So,  V² = G M/R
So,   M =  V² R / G        =  500²  * 8000 * 1000 / 6.67 * 10^-11
             = 2.998 * 10^22  Kg

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