---
title: "A satellite in an initially circular low Earth orbit experiences a very small atmospheric drag force that causes its trajectory to slowly decay inward through a series of nearly circular orbits of decreasing radius \\(r\\). Precise tracking data reveal that as the orbital radius decreases over many revolutions, the satellite’s orbital speed \\(v\\) increases. Which of the following best explains why the satellite speeds up despite the continuous dissipation of mechanical energy by drag?"
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url: "https://nerd-notes.com/ubq/123985/"
date_modified: "2026-09-28T13:29:58+00:00"
---

# A satellite in an initially circular low Earth orbit experiences a very small atmospheric drag force that causes its trajectory to slowly decay inward through a series of nearly circular orbits of decreasing radius \(r\). Precise tracking data reveal that as the orbital radius decreases over many revolutions, the satellite’s orbital speed \(v\) increases. Which of the following best explains why the satellite speeds up despite the continuous dissipation of mechanical energy by drag?

A satellite in an initially circular low Earth orbit experiences a very small atmospheric drag force that causes its trajectory to slowly decay inward through a series of nearly circular orbits of decreasing radius \(r\). Precise tracking data reveal that as the orbital radius decreases over many revolutions, the satellite's orbital speed \(v\) increases. Which of the following best explains why the satellite speeds up despite the continuous dissipation of mechanical energy by drag?

![A central shaded circle represents Earth of mass M. A dashed spiral curve with arrowheads oriented counterclockwise begins at an outer radius and winds inward by two complete revolutions toward Earth. A small solid circle representing the satellite is drawn along the spiral path. At the position of the satellite, a single straight arrow pointing in the clockwise direction opposite the satellite motion is labeled F_drag. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790602198-6ZGAAk.jpg)

- **A.** Because atmospheric drag acts strictly opposite to the instantaneous velocity, it exerts zero net torque about the center of Earth, requiring orbital speed to increase to conserve the satellite's angular momentum as the radial distance decreases.
- **B.** The negative work done by drag reduces the total mechanical energy, causing the orbit to decay to a smaller radius where the decrease in gravitational potential energy is twice the magnitude of the dissipated energy, with the surplus potential energy converted into kinetic energy.
- **C.** The reduction in total mechanical energy forces the orbital period to decrease, and because speed is inversely proportional to period (\(v = \dfrac{2\pi r}{T}\)), the shorter orbital period directly necessitates an increased orbital speed.
- **D.** Because a stable circular orbit strictly satisfies \(v = \sqrt{\dfrac{GM}{r}}\), the reduction in radius dictates an increase in kinetic energy even though the net work done on the satellite by all forces combined is negative.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123985/*