---
title: "A satellite of mass \\(m\\) is in a stable circular orbit of radius \\(R_1\\) around a planet of mass \\(M\\). The satellite’s engines are fired to move it into a new stable circular orbit of radius \\(R_2\\), where \\(R_2 > R_1\\). Which of the following expressions represents the total work done by the engines on the satellite-planet system to achieve this transition?"
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url: "https://nerd-notes.com/ubq/109936/"
date_modified: "2026-03-26T06:57:06+00:00"
---

# A satellite of mass \(m\) is in a stable circular orbit of radius \(R_1\) around a planet of mass \(M\). The satellite’s engines are fired to move it into a new stable circular orbit of radius \(R_2\), where \(R_2 > R_1\). Which of the following expressions represents the total work done by the engines on the satellite-planet system to achieve this transition?

A satellite of mass \(m\) is in a stable circular orbit of radius \(R_1\) around a planet of mass \(M\). The satellite’s engines are fired to move it into a new stable circular orbit of radius \(R_2\), where \(R_2 > R_1\). Which of the following expressions represents the total work done by the engines on the satellite-planet system to achieve this transition?

![A central circle labeled M represents a planet. Two concentric dashed circles represent the orbits. The inner dashed circle has a radius arrow labeled R_1. The outer dashed circle has a radius arrow labeled R_2. A small dot labeled m is on the inner circle, with a spiral arrow indicating a transition toward the outer circle.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1774508226-9UkXIq.jpg)

- **A.** \(\dfrac{GmM}{2} \left( \dfrac{1}{R_1} - \dfrac{1}{R_2} \right)\)
- **B.** \(GmM \left( \dfrac{1}{R_1} - \dfrac{1}{R_2} \right)\)
- **C.** \(\dfrac{GmM}{2} \left( \dfrac{1}{R_2} - \dfrac{1}{R_1} \right)\)
- **D.** \(\dfrac{GmM}{2} \left( \dfrac{1}{R_1} + \dfrac{1}{R_2} \right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/109936/*