---
title: "A satellite of mass \\(m\\) travels in a circular orbit of radius \\(R_0\\) around a planet of mass \\(M\\). The satellite is transferred to a new stable circular orbit of radius \\(\\dfrac{1}{4}R_0\\). What is the ratio of the satellite’s new orbital frequency to its initial orbital frequency, \\(\\dfrac{f_{\\text{new}}}{f_0}\\)?"
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url: "https://nerd-notes.com/ubq/124345/"
date_modified: "2026-09-28T14:04:55+00:00"
---

# A satellite of mass \(m\) travels in a circular orbit of radius \(R_0\) around a planet of mass \(M\). The satellite is transferred to a new stable circular orbit of radius \(\dfrac{1}{4}R_0\). What is the ratio of the satellite’s new orbital frequency to its initial orbital frequency, \(\dfrac{f_{\text{new}}}{f_0}\)?

A satellite of mass \(m\) travels in a circular orbit of radius \(R_0\) around a planet of mass \(M\). The satellite is transferred to a new stable circular orbit of radius \(\dfrac{1}{4}R_0\). What is the ratio of the satellite's new orbital frequency to its initial orbital frequency, \(\dfrac{f_{\text{new}}}{f_0}\)?

![A top-down schematic view of two concentric circular orbits centered on a solid shaded circle representing a planet of mass \(M\). The outer orbit is drawn as a thin dashed circle of radius \(R_0\), indicated by a straight radial line from the center of the planet to the outer orbit labeled \(R_0\). A small solid black dot representing the satellite is located on the outer dashed circle. An inner orbit is drawn as a smaller concentric thin dashed circle of radius \(\dfrac{1}{4}R_0\), indicated by a radial arrow pointing from the center of the planet to the inner orbit labeled \(\dfrac{1}{4}R_0\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604295-89dBFV.jpg)

- **A.** \(4\)
- **B.** \(8\)
- **C.** \(16\)
- **D.** \(64\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124345/*