---
title: "A satellite of mass \\(m\\) moves in an elliptical orbit around a planet of mass \\(M\\), where \\(M \\gg m\\). The distance from the center of the planet to the satellite at periapsis is \\(r_p\\), and the distance at apoapsis is \\(r_a = 4r_p\\). What is the ratio \\(\\dfrac{v_p}{v_a}\\) of the satellite’s speed at periapsis to its speed at apoapsis?"
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url: "https://nerd-notes.com/ubq/120933/"
date_modified: "2026-08-23T04:44:24+00:00"
---

# A satellite of mass \(m\) moves in an elliptical orbit around a planet of mass \(M\), where \(M \gg m\). The distance from the center of the planet to the satellite at periapsis is \(r_p\), and the distance at apoapsis is \(r_a = 4r_p\). What is the ratio \(\dfrac{v_p}{v_a}\) of the satellite’s speed at periapsis to its speed at apoapsis?

A satellite of mass \(m\) moves in an elliptical orbit around a planet of mass \(M\), where \(M \gg m\). The distance from the center of the planet to the satellite at periapsis is \(r_p\), and the distance at apoapsis is \(r_a = 4r_p\). What is the ratio \(\dfrac{v_p}{v_a}\) of the satellite's speed at periapsis to its speed at apoapsis?

![A horizontal elliptical orbit with a dashed outline. A large solid circle labeled M is located at the right focal point of the ellipse. A small filled circle representing the satellite is shown at the rightmost vertex of the ellipse labeled periapsis, at distance r_p from M, with an upward velocity arrow labeled v_p perpendicular to the horizontal major axis. The satellite is also shown at the leftmost vertex of the ellipse labeled apoapsis, at distance r_a from M, with a downward velocity arrow labeled v_a perpendicular to the horizontal major axis. A horizontal dashed centerline connects the two vertices through M. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460264-ODzOuN.jpg)

- **A.** \(\dfrac{1}{2}\)
- **B.** \(2\)
- **C.** \(4\)
- **D.** \(16\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120933/*