I'm getting my feet wet with orbital mechanics and have a very basic question. Kepler's 2nd Law shows that 2 objects in an elliptical orbit sweep out equal areas in equal time, implying objects increase in velocity as they get closer to one another.

This makes sense to me re: inverse square law of gravity - as radius decreases the force of gravity increases. However, the conservation of angular momentum also has a radius component showing that objects spin around a body faster the closer they get to it.

How do I separate these two concepts cleanly in my mind re: orbital bodies?

I'm getting my feet wet with orbital mechanics and have a very basic question. Kepler's 2nd Law shows that 2 objects in an elliptical orbit sweep out equal areas in equal time, implying objects increase in velocity as they get closer to one another.

This makes sense to me re: inverse square law of gravity - as distance decreases the force of gravity increases. However, the conservation of angular momentum also has a radius component showing that objects spin around a body faster the closer they get to it.

How do I separate these two concepts cleanly in my mind re: orbital bodies?