Imagine a hypothetical planet that has two moons. Moon \(\#1\) is in a circular orbit of radius \(R\) and has a mass \(M\).(a) Suppose Moon \(\#2\) has a mass \(M\), equal to Moon \(\#1\), but has an orbital radius twice that of Moon \(\#1\), \(2R\). What is the ratio of the force the planet exerts on Moon \(\#1\) compared to the force the planet exerts on Moon \(\#2\)? , (b) Moon \(\#1\) has an orbital radius of \(R\). Suppose that Moon \(\#2\) has a mass of \(3M\) (three times greater than Moon \(\#1\)). Where must Moon \(\#2\) be located (in terms of \(R\)) such that it experiences the same gravitational force as Moon \(\#1\)? :

\(4:1\) \(r = \sqrt{3} R\) (Moon 2 must be place 1.73 times further than Moon 1)

Imagine a hypothetical planet that has two moons. Moon \(\#1\) is in a circular orbit of radius \(R\) and has a mass \(M\). • Nerd Notes

AP Physics 1

6.6 Motion of Orbiting Satellites

2.9 Circular Motion

2.6 Gravitational Force

Multi-Unit

IntermediateFRQMathematicalProportional Analysis24.4k

Imagine a hypothetical planet that has two moons. Moon \(\#1\) is in a circular orbit of radius \(R\) and has a mass \(M\).

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