# Chapter 5 - Circular Motion; Gravitation - Questions: 22

By knowing the size and time to complete orbit (period) of the moon, the gravitational attraction between the two was used to calculate the mass of Pluto.

#### Work Step by Step

Once scientists spotted one of Pluto’s 5 moons, they equated the gravitational attraction between Pluto and the moon to the centripetal force required to keep the moon in an orbit of radius R. $$\frac{G M_{Pluto}m_{moon}}{R^{2}}=\frac{ m_{moon}v^{2}}{R}$$ This allowed them to determine Pluto’s mass, $M_{Pluto}$, if they could determine the moon’s speed v. This is deduced from the radius of the orbit and the time required to complete an orbit. (The mass of the moon does not affect the calculation.)

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