On May 30, 2:54 pm, Koobee Wublee wrote:
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.

No, it isn't. This is the radial equation of motion for the
Schwarzschild metric. Refer to any relativity textbook, or derive the
damn thing yourself.


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

I was using geometrized units - there was no c, so you have no idea if
you are inserting it in the right spots.


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.

The phrase "spacetime equation" is nonsense. Quit expecting people to
understand your nonstandard and self-created vocabulary about a
technical subject which you routinely mangle.

Your inability to communicate in an understandable language says much
about your understanding of general relativity.


** [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

Wrong, and wrong.

Where did dt/ds go? Where did c go? You insisted on putting it in, why
did you remove it? Where did the free floating 1 go? Where did the "3"
come from? There is no way for you to pick up an extra (1 - U)r(dO/
ds)^2 term.

The equations of motion /eventually/ fold into a single equation of
motion with an effective potential and effective energy _after_ the
application of 3 conserved quantities - none of which you have
mentioned or show any amount of understanding. The rigorous derivation
of said equation of motion takes about a page of math, _all_ of which
you have ignored - and isn't anywhere NEAR what you have written
down.


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

Stooooopid. That's classical mechanics, which you don't even
understand.

Centrifugal force follows directly from the expression of Newton's 2nd
law in a rotating coordinate system. Tom Roberts knows this, because
he has an actual education in physics instead of whatever you pulled
from a cracker jack box. Centrifugal force exists only in coordinate
systems that are rotating - it is a fake force that arises from your
coordinate choice. Tom Roberts also knows this, and has explained this
to you and others on numerous occasions, apparently to no effect.

[snip remaining whining]