Solution

When a satellite with mass $m$ is in a circular orbit with radius $r$ around a planet with mass $M\gg m$, the gravitational force serves as the centripetal force

$$\frac{GMm}{r^2}=\frac{mv^2}{r}.$$

In this orbit, the gravitational potential energy is

$$-\frac{GMm}{r}=-2\cdot\frac{1}{2}mv^2;$$

that is, the gravitational potential energy is negative but its magnitude is twice the kinetic energy. Consequently, if the total energy of the satellite changes by $-\Delta E$, then the gravitational potential energy changes by $-2\cdot\Delta E$ and the kinetic energy changes by $\Delta E$. Therefore, the speed of the satellite increases even though its total energy decreases.

In terms of forces, the atmospheric resistance does decrease the tangential velocity of the satellite. However, the decrese in orbital radius means that the gravitational force increases the inward radial velocity, resulting in an overall increase in the total speed of the satellite.