Akinbo,
That's momentum, AND inertia. It's ONLY rationalised by the hierarchy of spin. Imagine a gyroscope flywheel made up of billions of tiny gyroscopes. Let's say if the big gyroscope is spinning but held rigidly and in rectilinear motion (in rest frame K), it's very happy "spinning but at rest" in it's own centre-of-mass frame.
Now apply a force perpendicular to it's linear motion. It will NOT want to change it's vector! The spin gives it mass. Spin IS mass! (current exchange rate E=mc^2).
Now reconsider the moon as made up of billions of tiny gyroscopes per mm^3. At any instant it's very happy on it's tangential vector and left alone will continue in that inertial state K. BUT that damned annoying centrepetal force keeps trying to accelerate it laterally!! It's inertia ('momentum') is then what is balancing the gravity.
When one gets bigger than the other, as one day one surely will, it will either crash down or fly off.
Finally, that relative 'momentum' is a direct function of relative speed right? At epigee the relative speed is far higher. Does that now become intuitive? It should do unless you're hanging on to some false assumption or other.
The spin relation works hierarchically at all scales, and explains why the polystyrene car is easier for you to push than the lead car. You'd think that as gravity is pulling the lead car down far more, that it may be accelerated more when let go! It only isn't because it has more spinning particles not interested in getting out of their rest frame inertia).
That works all the way up. Including with the Earth round the sun, the sun round the AGN, etc.
Peter