A satellite is orbiting close to the earth such that it is travelling through a very thin air, not vaccum. Will the resulting air friction slow down the satellite?

Explanation

The energy of a satellite revolving around the earth is given by
`T.E. = -(GMm)/( r)`
where r is the distance of satellite from the centre of earth (orbital radius ).
Now, due to air drag, the energy of the satellite decreases, i.e. it becomes more negative. This results in decrease in orbital radius and hence, the satellite would jump into a lower orbit . As a result, the moment of inertia of the satellite about the centre of earth decreases. According to law of conservation of angular momentum, decrease in moment of inertia results in increase in angular velocity. So, the angular velocity and hence the linear velocity of the satellite will increase. So, the satellite will start moving faster.