Nope. A satellite of a larger body is in free fall, but either slowly spirals down (as one of the moons of Mars is going to do in 20K years or so) or spirals up via the tidal transfer of momentum. The tidal transfer of momentum relevant here is the axial rotational energy of the Sun basically pushing the Earth away. This is the case with satellites in prograde motion. Satellites moving in retrograde auger in.
The satellite is also losing axial rotational energy via the same process, trying to push the much larger parent body.
Our own Moon did that until it wound up with a single face ‘locked’ to face the Earth, but the Earth, being almost 100 times more massive, continues to transfer momentum to the Moon.
If there’s enough energy in the parent/child combo, the child will eventually wander out of orbit.
Thanks, I get it now. The rotational spin of the Sun is flinging the Earth away. Sort of like holding the hands of a child while spinning it around, your rotational energy is imparted to the child. Poor kid, some year far in the future the Moon will be flung out of orbit from Earth.