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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?

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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

User Kevin Russell
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