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## Homework Statement

A satellite in low-Earth orbit is not truly traveling through a vacuum. Rather, it moves through very thin air. Does the resulting air friction cause the satellite to slow down?

## Homework Equations

## The Attempt at a Solution

Evidently, the answer is, "Air resistance causes a decrease in the energy of the satellite-Earth system. This reduces the diameter of the orbit, bringing the satellite closer to the surface of the Earth. A satellite in a smaller orbit, however, must travel faster. Thus, the effect of air resistance is to speed up the satellite!"

However, when I consider the relationship [itex]E = \frac{-Gm_1m_2}{2r}[/itex], which becomes [itex]r = \frac{-Gm_1m_2}{2E}[/itex], I am not convinced that the radius becomes smaller, thereby causing the diameter to become smaller. Am I considering the wrong relationship in order to solve this problem?