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?

Answer 1

According to my research, a satellite in a circular Earth orbit is subject to a very tiny constant friction force, due to the atmosphere. As it spirals inward, it slowly decreases its orbital radius.
So as long as a satellite moves in a circular orbit, it's velocity is inversely proportionate to the square root of the orbital radius-it speeds up as it spirals inward. I hope my answer proves of some help to you.

Answer 2

As the satellite spirals inward ; The speed of the satellite increases ( i.e. speeds up )

As the satellites continually to move inward in a circular earth orbit, its orbital radius will continually decrease because of the constant friction between the satellite and the atmosphere, while the centripetal force acting on the satellite is the force of gravity.   Also

The velocity of the satellite as it moves around its circular orbit inwardly is inversely proportional to the $\sqrt{orbital radius}$  of the satellite.

Hence we can conclude that As the satellite spirals inward the satellite speeds up.

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