You are very persistent in your beliefs, but first of all the math does need to work and you make me work harder as a result. The equation you cite as force equation for an elliptical orbit left out a dimension of r that you had in a previous reply. At any rate, for an elliptical orbit, the force of gravity is out of balance with the centripetal force of motion and both KE and PE vary with r as you have shown
Ftotal =½ mv2(r) / r = (GMs m/r)(2/r - 1/a)
and then you contrast that with the force equation for a circular orbit where KE = PE and centripetal force equals gravity is always true
Frad = ½mv2 / r = GMs m/r2
and then you wonder which equation is true?
You are rightly confused because the math is a little more complex for an elliptical orbit than a circular orbit since r varies and so centripetal and gravity forces both vary. So both equations are valid since r changes v as long as you use force as a vector, not a scalar. Since force is a vector and depends on direction and energy is a scalar and does not depend on direction, a total force has different meaning for circular and elliptical orbits. So force has both radial and axial components and there are really two force equations, not just one.
One force is due to gravity at r, which is exactly the 1/r2 version as you rightly declare. However, there is another force equation called centripetal force and gravity and centripetal forces are not always equal for an elliptical orbit.
Your simplistic elliptic force simply divides KE by r, which assumes that there is no axial centripetal force. For an elliptic orbit, though, there are both radial and axial accelerations and forces. That is why I added the subscripts to the forces in the equations.
In essence, the kinetic energy at apogee gives a centripetal force that is less than the gravity force and so the earth tends to fall into the sun after it reaches apogee. The kinetic energy at perigee gives a centripetal force that is greater than the gravity force and so the earth tends to escape from the sun after it reaches the perigee.
Instead of contradicting Newton's gravity, elliptic orbits affirm the nature of Newton's 1/r2 force.
