---
title: "A small moon orbits a large spherical planet of uniform density \\(\\rho\\) in a circular path. The moon’s orbit is very close to the planet’s surface, such that the orbital radius can be considered approximately equal to the planet’s radius \\(R\\). Which of the following is a correct expression for the orbital period \\(T\\) of the moon in terms of \\(\\rho\\), \\(G\\), and physical constants?"
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url: "https://nerd-notes.com/ubq/114665/"
date_modified: "2026-07-03T04:47:04+00:00"
---

# A small moon orbits a large spherical planet of uniform density \(\rho\) in a circular path. The moon’s orbit is very close to the planet’s surface, such that the orbital radius can be considered approximately equal to the planet’s radius \(R\). Which of the following is a correct expression for the orbital period \(T\) of the moon in terms of \(\rho\), \(G\), and physical constants?

A small moon orbits a large spherical planet of uniform density \(\rho\) in a circular path. The moon’s orbit is very close to the planet’s surface, such that the orbital radius can be considered approximately equal to the planet’s radius \(R\). Which of the following is a correct expression for the orbital period \(T\) of the moon in terms of \(\rho\), \(G\), and physical constants?

![A large grey circle representing a planet with radius R. A small moon, depicted as a small black dot, is positioned on a dashed circular line representing an orbit that is just slightly larger than the planet's circumference. A velocity vector v is shown tangent to the orbit, and a force vector Fg points from the moon directly toward the center of the planet.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1783054024-NXOgCe.jpg)

- **A.** \( \sqrt{\dfrac{3 \pi}{G \rho}} \)
- **B.** \( \sqrt{\dfrac{3}{4 \pi G \rho}} \)
- **C.** \( \sqrt{\dfrac{\pi}{G \rho}} \)
- **D.** \( \sqrt{\dfrac{3}{G \rho}} \)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/114665/*