---
title: "A satellite of mass \\(m\\) is in a bound, elliptical orbit with semimajor axis \\(a\\) around a planet of mass \\(M\\), where \\(M \\gg m\\). The satellite moves between its periapsis distance \\(r_p\\) and apoapsis distance \\(r_a\\) with no nonconservative forces present. Which of the following correctly describes the graphs of the gravitational potential energy \\(U(r)\\), kinetic energy \\(K(r)\\), and total mechanical energy \\(E(r)\\) of the satellite-planet system as functions of the orbital distance \\(r\\) over the interval \\(r_p \\le r \\le r_a\\)?"
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/120879/"
date_modified: "2026-08-23T04:44:06+00:00"
---

# A satellite of mass \(m\) is in a bound, elliptical orbit with semimajor axis \(a\) around a planet of mass \(M\), where \(M \gg m\). The satellite moves between its periapsis distance \(r_p\) and apoapsis distance \(r_a\) with no nonconservative forces present. Which of the following correctly describes the graphs of the gravitational potential energy \(U(r)\), kinetic energy \(K(r)\), and total mechanical energy \(E(r)\) of the satellite-planet system as functions of the orbital distance \(r\) over the interval \(r_p \le r \le r_a\)?

A satellite of mass \(m\) is in a bound, elliptical orbit with semimajor axis \(a\) around a planet of mass \(M\), where \(M \gg m\). The satellite moves between its periapsis distance \(r_p\) and apoapsis distance \(r_a\) with no nonconservative forces present. Which of the following correctly describes the graphs of the gravitational potential energy \(U(r)\), kinetic energy \(K(r)\), and total mechanical energy \(E(r)\) of the satellite-planet system as functions of the orbital distance \(r\) over the interval \(r_p \le r \le r_a\)?

- **A.** \(U(r)\) is negative, increasing, and concave downward; \(K(r)\) is positive, decreasing, and concave upward; \(E(r)\) is a constant negative value.
- **B.** \(U(r)\) is negative, increasing, and concave upward; \(K(r)\) is positive, decreasing, and concave downward; \(E(r)\) is a constant negative value.
- **C.** \(U(r)\) is negative, increasing, and concave downward; \(K(r)\) is positive, decreasing, and concave upward; \(E(r)\) is negative and increases linearly with \(r\).
- **D.** \(U(r)\) is positive, decreasing, and concave upward; \(K(r)\) is positive, decreasing, and concave upward; \(E(r)\) is a constant positive value.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120879/*