---
title: "A satellite of mass \\(m\\) is in a stable circular orbit of radius \\(R\\) around a planet of mass \\(M\\). The magnitude of the gravitational field strength produced by the planet at the satellite’s location is \\(g\\). Which of the following correctly compares the magnitude of the satellite’s centripetal acceleration \\(a_c\\) to \\(g\\), and provides a correct justification?"
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url: "https://nerd-notes.com/ubq/109918/"
date_modified: "2026-03-26T06:56:33+00:00"
---

# A satellite of mass \(m\) is in a stable circular orbit of radius \(R\) around a planet of mass \(M\). The magnitude of the gravitational field strength produced by the planet at the satellite’s location is \(g\). Which of the following correctly compares the magnitude of the satellite’s centripetal acceleration \(a_c\) to \(g\), and provides a correct justification?

A satellite of mass \(m\) is in a stable circular orbit of radius \(R\) around a planet of mass \(M\). The magnitude of the gravitational field strength produced by the planet at the satellite's location is \(g\). Which of the following correctly compares the magnitude of the satellite's centripetal acceleration \(a_c\) to \(g\), and provides a correct justification?

![A diagram shows a large central circle representing a planet of mass M. A dashed circular path with radius R surrounds the planet. A small square representing a satellite is positioned on the path at the top. A horizontal arrow labeled v points to the left, tangent to the path. A vertical arrow labeled Fg points from the satellite directly toward the center of the planet.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1774508193-ULdSp1.jpg)

- **A.** \(a_c = g\), because the gravitational force is the only force acting on the satellite, and the acceleration of any object in a gravitational field is equal to the field strength at that location.
- **B.** \(a_c = g\), because the satellite is in translational equilibrium where the gravitational force is balanced by the centripetal force.
- **C.** \(a_c < g\), because the satellite's tangential speed reduces the net downward acceleration compared to the local gravitational field strength.
- **D.** \(a_c = 0\), because the satellite is in a state of free fall and experiences weightlessness, meaning the net force and acceleration are both zero.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/109918/*