Question

Satellites in near-earth orbit experience a very slight drag due to the extremely thin upper atmosphere. These satellites slowly but surely spiral inward, where they finally burn up as they reach the thicker lower levels of the atmosphere. The radius decreases so slowly that you can consider the satellite to have a circular orbit at all times. As a satellite spirals inward, does it speed up, slow down, or maintain the same speed? Explain.

Short answer

Speed will increase as it spiral inwards.

Step-by-step solution

Given Information

Satellites slowly but surely spiral inward, where they finally burn up as they reach the thicker lower levels of the atmosphere.

Explanation

From Keplar's law period of an orbit is given by

T² = R³

So T = R^3/2

We see as the radius decreases the time period of the orbit will also decrease. And angular velocity will increase.

As angular velocity is given by ω = 2π/T.

which is inversely proportional to the period T.

So we can conclude that as the satellite spirals inward, speed will increase.