Atmospheric drag gradually removes mechanical energy and angular momentum from a satellite, causing its orbit to shrink. Although drag instantaneously slows the satellite, its mean orbital speed increases as it moves into a lower orbit, eventually leading to atmospheric re-entry.
The mechanism
This is an Additional Higher Level (AHL) concept in D.1 Gravitational fields. The upper atmosphere is extremely thin, but its particles exert a small force opposite the satellite's velocity.
Because drag opposes the displacement, it does negative work. The satellite's total orbital energy therefore decreases and becomes more negative. For a satellite in a circular orbit,
where is Earth's mass, is the satellite's mass, and is the orbital radius. A more negative corresponds to a smaller , so the satellite loses altitude.
| Stage | Effect on the satellite |
|---|---|
| Drag acts | The satellite loses kinetic energy and angular momentum locally. |
| Orbit decays | Its orbital radius and altitude decrease. |
| Lower orbit develops | Its mean speed increases because . |
| Period changes | Its orbital period decreases, consistent with Kepler's third law. |
| Final stage | Denser air produces stronger drag, causing rapid decay and re-entry. |
The apparent contradiction is important: drag initially reduces the satellite's speed at its current position, making it fall inward. As it descends, gravitational potential energy is transferred to kinetic energy. A stable circular orbit at the new, smaller radius requires a greater orbital speed.
The common misconception is that drag must make the satellite move progressively more slowly. In fact, drag removes total mechanical energy, while the satellite's lower orbit generally has a greater mean speed.
Exam technique
For an Explain question, link the steps clearly: drag does negative work, orbital energy becomes more negative, orbital radius decreases, and mean orbital speed increases. Do not state only that the satellite “slows down and falls”; distinguish the immediate slowing effect from the long-term increase in speed as the orbit decays.
