---
title: "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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url: "https://nerd-notes.com/ubq/19557/"
date_modified: "2025-09-23T04:43:10+00:00"
---

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

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

**Part 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 \(\#2\)? *(3 points)*

**Part 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 \(\#1\)? *(3 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/19557/*