---
title: "A satellite of mass \\(m\\) orbits a uniform spherical planet of mass \\(M\\) in a circular orbit of radius \\(R_0\\) with orbital speed \\(v_0\\) and period \\(T_0\\). The satellite is transferred into a new stable circular orbit of radius \\(4R_0\\). In terms of the initial values, what are the new orbital speed \\(v\\) and new orbital period \\(T\\) of the satellite?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/120885/"
date_modified: "2026-08-23T04:44:09+00:00"
---

# A satellite of mass \(m\) orbits a uniform spherical planet of mass \(M\) in a circular orbit of radius \(R_0\) with orbital speed \(v_0\) and period \(T_0\). The satellite is transferred into a new stable circular orbit of radius \(4R_0\). In terms of the initial values, what are the new orbital speed \(v\) and new orbital period \(T\) of the satellite?

A satellite of mass \(m\) orbits a uniform spherical planet of mass \(M\) in a circular orbit of radius \(R_0\) with orbital speed \(v_0\) and period \(T_0\). The satellite is transferred into a new stable circular orbit of radius \(4R_0\). In terms of the initial values, what are the new orbital speed \(v\) and new orbital period \(T\) of the satellite?

- **A.** \(v = \dfrac{1}{4}v_0\) and \(T = 4T_0\)
- **B.** \(v = \dfrac{1}{4}v_0\) and \(T = 8T_0\)
- **C.** \(v = \dfrac{1}{2}v_0\) and \(T = 8T_0\)
- **D.** \(v = \dfrac{1}{2}v_0\) and \(T = 4T_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120885/*