# Gravity and elliptical orbits

All orbits are elliptical and special orbits are circular (like when both bodies have the same mass or when the second body's mass is negligibly small). In a circular orbit centrifugal force (which I know is just an apparent force, not a real force, but here represents the force felt due to inertia; you get the picture, and save your time admonishing me) is always equal to the gravitational force.

Assumption 1: if the "centrifugal force" equals the gravitational force, then a circular, not elliptical, orbit should be implied and follow.

In this picture (of an elliptical orbit), assume the body is orbiting clockwise.

Assumption 2: On arc ABC, kinetic energy is decreasing while potential energy is increasing. So in this segment of orbit, "centrifugal force" is higher than gravitational force. And in arc CDA, K.E. is increasing while P.E. is decreasing, so gravitational force should be greater than "centrifugal force."

Assumption 3: If assumption 2 is correct, then at points A and C (when the force-tables turn) "centrifugal force" should equal gravitational force.

Discrepancy: If both aforementioned forces are equal at points A and C that would imply a circular orbit, which is not the case.

Either assumption 1 is wrong or I don't understand kepler orbits as well as I thought I did. What's the case