The following seeks to identify which alternate accelerations act ( gravitational, tangential, centrifugal) in Feynman's dynamics scheme leading to the same position of planet once again at the Newton classical position.
Request you to please help in drawing a new force diagram including the perpendicular bisector accelerations leading to this alternate dynamic derivation.
Feynman's Lost nb (30 - 50 sec)
A geometrical verification is made below using elimination by p- discriminant method
A variable point P (in above rough sketch) on a circle radius $2a$ centered at origin and focal point F $(2c,0)$. Finding envelope of perpendicular bisectors of PF.
$$ ( 2a\ \cos t, 2a \sin t), (c+ a \cos t,a \sin t)$$
Equation of perpendicular bisector through center point $Q$of $PF$.
$$ \dfrac{a \cos t- c}{a\sin t}= \dfrac{y-a \sin t}{x-c- a \cos t} \tag1 $$
Let $ a^2-c^2=b^2.$ Cross multiplying and simplifying
$$ \dfrac{b^2+x \cos t}{a}= ( x \cos t+ y \sin t) \tag 2$$
Using p-discriminant method partially differentiate with respect to $t$
$$ \tan t = \dfrac{y}{x} \tag 3 $$
Plug into (1) using
$$ x = r \cos t, y=r \sin \theta , p= b^2/a , r= \sqrt{x^2+y^2} \; e = c/a \tag4 $$
we arrive at
$$ e x +p=r \to \dfrac{1}{r}=\dfrac{1- e \cos \theta}{p}. \tag5 $$