On May 30, 1:24 pm, Eric Gisse wrote:
On May 29, 11:41 pm, Koobee Wublee wrote:

In spacetime with the Schwarzschild metric, the Euler-Lagrange
equation associated with r can simply be derived as the following
where the orbital motion is confined to the equatorial plane of the
gravitating body.

It isn't "spacetime", chuckles. It is an affine parameter.

d^2r/ds^2 - (1 - 3 U) r (dO/ds)^2 = - U / r

Where

** O = Longitude
** s = Spacetime
** U = G M / c^2 / r

The actual radial equation of motion is:

d^2r/dl^2 + GM/r^3 * (r - 2GM) * (dt/dl)^2 - GM/r(r-2GM) *(dr/dl)^2 -
r(r-2GM)[(d\theta/dl)^2 + sin(\theta)^2*(d\phi/dl)^2] = 0, where l is
an arbitrary affine parameter [none of this 'spacetime' bull****].

This is wrong. It should be corrected as follows using your symbols
and notations.

d^2r/dl^2 + GM/r^3 * (r - 2GM) * (dt/dl)^2 - (GM/r)/(r-2GM) *(dr/dl)^2
- (r-2GM)[(d\theta/dl)^2 + sin(\theta)^2*(d\phi/dl)^2] = 0

For simplicity without sacrificing the accuracy of the mathematical
model, we can easily establish the following.

** \theta = 0
** \phi = O
** ds = dl
** U = G M [/ c^2] / r

In doing so, your equation after my correction leads to the following.

dr^2/ds^2 - (1 - 2 U) r (dO/ds)^2 = - [c^2] (1 - 2 U) (dt/ds)^2 U / r
+ (dr/ds)^2 (U / r) / (1 - 2 U)

Furthermore, we can also easily establish the following from the
spacetime equation with the Schwarzschild metric.

** [c^2] (1 - 2 U) (dt/ds)^2 = 1 + (dr/ds)^2 / (1 - 2 U) + r^2 (dO/
ds)^2

Thus finally, your equation after my correction eventually leads to a
much simpler and elegant equation as I have already presented. Here
it is once again.

d^2r/ds^2 - (1 - 3 U) r (dO/ds)^2 = - U / r

Centrifugal force is not a farce. It is very real in direct contrast
from denials from Dr. Roberts.

Notice this isn't anywhere even close to your idiotic equation. As
usual you get even the simplest mathematics totally and completely
wrong.

You know how to copy equations without understanding them. shrug
You have no capability to copy equations correctly. sigh
You are hopelessly beyond any help. get lost

He knows not and not knows that he knows not is a fool. Shun Gisse
and his pathetic cronies.