As friction with our atmosphere causes a satellite to spiral inward, closer to Earth, its orbital speed increases. Why?

Explanation:

When we go back and look at Kepler's third law. Kepler's third law states that "the square of the period is proportional to the cube of the semi-major axis of the orbit". P²µa³

where a is the semi-major axis of orbit,

P is the period of orbit

The orbit in question is the distance from the center of Earth. If the satellite spirals in as a result of air friction, then it decreases and, so does P.

Note that P = 2πa / V or Vµ1 / a0.5 .

From the formula, we can see that a decrease in the value of a, will lead to an Increase in the value of V.