Mercury Precession without Space Bending Illusion
Since Kepler we know that planetary orbits are elliptical or circular. Newton explained that with his “inverse square law” formula for gravitational force between masses m and M at distance R:
F = G×m×M / R², where G is some constant.
If interested, check https://www.youtube.com/watch?v=3oGATSP1KJ0 deduction of Kepler’s laws by Newton’s calculus. For the simplest circular orbit, when distance R does not change, planetary velocity value is constant: V = sqrt(G×M/R). But what puzzled scientists is the precession of the Mercury orbit (shifting/turning of the elliptical orbit):
Einstein solved this long-standing puzzle, and that was a triumph of his General Relativity theory. I like Dr. Vivian Robinson presentation of this solution at https://www.youtube.com/watch?v=86mb-D_Sla4&t=1101s, with Newton’s insight on force weaker than G×m×M/R² not retaining a planet on its elliptical orbit (precession happens), and force stronger than G×m×M/R² pulling a planet inside its static elliptical orbit, causing orbital regression:
We will return to that insight shortly, from the angle of disbalance between centrifugal and centripetal Newton’s gravitational force. As Einstein found, time around mass slows down, so let’s explore what happens when a planet enters slower or faster time. Let’s start with a circular orbit. Time inside the orbit flows slower, and outside the orbit it flows faster than on the orbit. Velocity of the planet, where it touches faster time, is smaller than the velocity on the orbit, and velocity inside the orbit is greater than the orbital velocity V (see the picture and the explanation below):
|AB| is the distance travelled between A and B, T — time passed on the orbit, T/D1 — time passed inside the orbit, T/D2 — time passed outside the orbit. Velocity is distance |AB| divided by time passed, thus V1>V (because time dilation D1>1), and V2<V (because time dilation D2<1). For V2<V, centrifugal force decreases, thus, planet will sink from the outer blue orbit to the black/current orbit, where centrifugal force is in balance with the Newton’s centripetal force. For V1>V, centrifugal force increases, thus, planet will rise from the inner red orbit to the black/current orbit, where centrifugal force is in balance with the Newton’s centripetal force. And that line of argument holds true in general:
· When a planet enters slower time, then due to the planet’s velocity increase caused by time dilation alone, the planet is pushed outside of its (elliptical) orbit, because Newton’s gravitation does not counter the increase of centrifugal force.
· When a planet enters faster time, then due to the planet’s velocity decrease caused by time dilation alone, it is pulled inside its (elliptical) orbit, because Newton’s gravitation overpowers reduced centrifugal force.
Now we understand what happens on an elliptical orbit, when a planet enters slower time while travelling towards the Sun, and when planet drifts away from the Sun into faster time:
Or if you don’t like talking about fictitious centrifugal force, the same result will be just by the velocities change:
That leads to the orbit tilting (in the white arrows direction), along with apogee and perigee rotation, in the same direction as the planet rotates:
P.S. Next read Final Reality Check: Space Curvature vs. Time Dilation.
P.P.S. Read more in Time Matters.
