---
title: "A satellite of mass \\(m\\) is in a circular orbit of radius \\(R\\) about a planet of mass \\(M\\), where \\(M \\gg m\\). Thrusters on the satellite are fired over a brief interval to place the satellite on an escape trajectory that allows it to just reach an infinite separation from the planet. Which of the following statements correctly identifies the minimum work done by the thrusters on the satellite and provides the correct justification?"
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url: "https://nerd-notes.com/ubq/120877/"
date_modified: "2026-08-23T04:44:03+00:00"
---

# A satellite of mass \(m\) is in a circular orbit of radius \(R\) about a planet of mass \(M\), where \(M \gg m\). Thrusters on the satellite are fired over a brief interval to place the satellite on an escape trajectory that allows it to just reach an infinite separation from the planet. Which of the following statements correctly identifies the minimum work done by the thrusters on the satellite and provides the correct justification?

A satellite of mass \(m\) is in a circular orbit of radius \(R\) about a planet of mass \(M\), where \(M \gg m\). Thrusters on the satellite are fired over a brief interval to place the satellite on an escape trajectory that allows it to just reach an infinite separation from the planet. Which of the following statements correctly identifies the minimum work done by the thrusters on the satellite and provides the correct justification?

- **A.** The minimum work done is \(\dfrac{GMm}{R}\) because the thrusters must supply an amount of energy equal to the magnitude of the gravitational potential energy to reach zero potential energy at infinity.
- **B.** The minimum work done is \(\dfrac{GMm}{R}\) because the satellite's orbital speed must be doubled to reach the escape velocity.
- **C.** The minimum work done is \(\dfrac{GMm}{2R}\) because the thrusters must remove all initial orbital kinetic energy so the satellite comes to rest relative to the planet.
- **D.** The minimum work done is \(\dfrac{GMm}{2R}\) because the initial total mechanical energy is \(-\dfrac{GMm}{2R}\) and escape requires a final total mechanical energy of zero.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120877/*