The force of gravity is always orthogonal to the direction of motion when in orbit. So never loses momentum. Which is why the moon is still going around the earth a billion years later and has not 'fallen' into it.
This is only true for circular orbits. It’s pretty transparently obvious that elliptical orbits move closer to and farther from the center of mass (and lose and gain momentum accordingly).
If I'm wrong, I'd love to hear exactly why, but regurgitating basic physics doesn't resolve the difficulties in modelling a straight flight path around a curved surface, in relation to a dropped object.
