Anisotropy and Mercury (2)

Max Keon wrote:
sniped

This has all been a very interesting exercise George, but it
really makes no difference in the end because gravity is _always_
entirely elastic. That's the point you seem to be missing
altogether.

-----

Max Keon

No, you are the one forgetting that gravity is always elastic.
Ever patient George keeps pointing out to you that your proposed
effect is inelastic and you keep ignoring that. Gravity is not
proportional to velocity so it is elastic. Your proposed effect
is proportional to velocity so it is inelastic. Your proposal
is dead in the water but you have been missing that altogether.

On Jun 15, 7:40 pm, doug doug@doug wrote:
Max Keon wrote:

This has all been a very interesting exercise George, but it
really makes no difference in the end because gravity is _always_
entirely elastic. That's the point you seem to be missing
altogether.

No, you are the one forgetting that gravity is always elastic.
Ever patient George keeps pointing out to you that your proposed
effect is inelastic and you keep ignoring that. Gravity is not
proportional to velocity so it is elastic. Your proposed effect
is proportional to velocity so it is inelastic. Your proposal
is dead in the water but you have been missing that altogether.

Gerber's gravity is basically a modification to the Newtonian
gravitational potential. Gerber's gravitational potential is

U = ((G M / c^2) / r) / (1 - dr/dt / c)^2

With that gravitational potential, Gerber was able to show Mercury's
orbital anomaly in terms of advance in its perihelion. The
mathematical method pioneered by Gerber to derive the advancement in
angle was adopted by Einstein almost 16 years without referencing to
GR. In fact, it is still the choice of tools among all textbooks
since then.

Thus, what you are saying just does not prove anything.

On Jun 15, 10:32 pm, Koobee Wublee wrote:
On Jun 15, 7:40 pm, doug doug@doug wrote:

Max Keon wrote:
This has all been a very interesting exercise George, but it
really makes no difference in the end because gravity is _always_
entirely elastic. That's the point you seem to be missing
altogether.

No, you are the one forgetting that gravity is always elastic.
Ever patient George keeps pointing out to you that your proposed
effect is inelastic and you keep ignoring that. Gravity is not
proportional to velocity so it is elastic. Your proposed effect
is proportional to velocity so it is inelastic. Your proposal
is dead in the water but you have been missing that altogether.

Gerber's gravity is basically a modification to the Newtonian
gravitational potential. Gerber's gravitational potential is

U = ((G M / c^2) / r) / (1 - dr/dt / c)^2

With that gravitational potential, Gerber was able to show Mercury's
orbital anomaly in terms of advance in its perihelion. The
mathematical method pioneered by Gerber to derive the advancement in
angle was adopted by Einstein almost 16 years without referencing to
GR. In fact, it is still the choice of tools among all textbooks
since then.

Gerber again?!

http://groups.google.com/group/sci.p...8?dmode=source

[Notice how I can find my own posts yet you are incapable of managing
this yourself]

http://www.mathpages.com/home/kmath527/kmath527.htm

Gerber's potential has no actual motivation. The result Gerber used is
derivable from first principles - Gerber simply postulates it. It is
fantastically untrue to say that Einstein used his result.


Thus, what you are saying just does not prove anything.

Thus, Koobe Wublee babbles about a subject he does not understand.
Again.

"Max Keon" wrote in message
u...
"George Dishman" wrote in message
oups.com...
On 12 Jun, 04:09, "Max Keon" wrote:
"George Dishman" wrote in message
...
"Max Keon" wrote in message
u...
---

... So I guess you agree with this as
it is the same as you were saying:

In fact you said the anisotropy _decreases_ the force
on the inward leg so that increases the perihelion
distance and decreases the aphelion reducing the
eccentricity. Suppose the planet would move from
A to B to C to D without the anisotropy, it goes
from A to B to E to F if the anisotropy is switched
on between B and E then off again:

A
B
E
C
F

G D

Sun

Very carefully note the gravitational potential at F compared
with D when normal gravity is reinstated.

The potential at F is a smaller negative number compared
to D. You don't need to say "normal gravity is reinstated",
the potential is the same regardless and the anisotropy
never switches off, though it goes to zero at perihelion
and aphelion of course.

Also note that
Mercury's orbital velocity is slower than if it had been drawn
down the normal path.

Yes that is correct as well

Mercury's fall to the radius of C, which is now labeled F, has
been delayed, ...

Yes that is correct again.

but the prevailing conditions are exactly as they
would have been at C. It will now begin the same fall to the Sun
as it would have from C.

No, that is where you are missing a subtlety. The
path from B to F has fallen the same distance (same
change of radius) but Mercury moved farther round in
its orbit. If you imagine a circular orbit passing
through C and F, the path BC meets it at a larger
angle than the path BF. That change of direction is
critical to understanding what happens: the path with
the anisotropy has a direction that is more like the
circular orbit than the path without.

The journey from D to the perihelion radius obviously takes less
time than the journey from F to the perihelion radius, but the F
based Mercury will have still accelerated up to the same orbital
speed as the D based Mercury when it arrives at a consequently
advanced perihelion radius.

This gets difficult to illustrate and the diagram is
going to be wrong so please read all this paragraph
before commenting, you really need to use the program
to investigate it. I have added G, the next point
after F. As Mercury moves from D inward to perihelion
without the anisotropy, you are right, it would speed
up. With the anisotropy however, the path is flattened
so the next point G is actually farther from the Sun
so F becomes the perihelion. Now you are right, the
perihelion moves farther round the orbit but I can't
easily alter the diagram to show that so you will
have to imagine that the segment ABEFG ahs been moved
anticlockwise round from where it should be just for
comparison (or ease of drawing).

It doesn't matter to which part of the orbit your logic is
applied, no energy will be shifted from the Sun-Mercury closed
gravitating system.

A small amount is lost but it is almost negligible in
this context, energy really only becomes important
when considering the "rest of the universe" question.
Your point above is correct, at F the planet has less
kinetic energy and more potential energy so the total
is virtually the same as at point C.

The major effect is not on the energy of the orbit but
on the eccentricity. The perihelion has moved outward
by 2010938 m compared to the orbit without anisotropy.

The anisotropy doesn't immediately switch on or off of course,

It doesn't switch off at all, it is always there, but
we can switch it in and off for comparison of course.

but it can be pictured as a multitude of minute on or off steps
that increment and decrement proportionally to radial velocity
change. Each rise step has a counteractory fall step over each
half cycle.

Perhaps you can understand what I mean now?

I don't dispute any of what you said but you have
missed the key point again, the direction of
motion (angle relative to a circular orbit or to
the planet-Sun line) at F is not the same as at C,
and that change increases the perihelion as you
said in your previous post.

To explain the point about velocity and vectors above,
if the locations shown he

A
B
P
Q

are one second apart then the mean velocity during the first
second would be an arrow from A to B and during the next
second it would be from B to P if there was no acceleration.
So I can write B-P = A-B.

If the acceleration is an arrow from P to Q, then the
new velocity is B-Q = B-P + P-Q.

Anyway, you presumably also agree this:

The same happens on the outward leg, the slight
_increase_ in gravity as the planet is moving away
pulls it round to point more towards the Sun again
reducing the aphelion.

Sun

A

B

E
C F

D

Can you then see that it implies this:

I can see very clearly that Mercury at F is in a position of
lower gravitational potential when the anisotropy is switched
off and is orbiting faster than if it had arrived at D.

Yes that's right, it is really a mirror of the inward
leg only this time the aphelion is reduced rather than
perihelion being increased. Again it reduces eccentricity.

Remember
that the anisotropy is just like any other gravity, acting along
a direct line to the Sun, and if the pull holds Mercury more to
the Sun its orbital velocity must remain higher, around a tighter
curve.

That's right, that's why it turns it back at a lower
aphelion value.

Try to remember that the anisotropy is only gravity.

It is additional to it but that's semantics.

'-------------------------------------
x = x + dt * (vx + .5 * dt * ax) ' Updated method.
y = y + dt * (vy + .5 * dt * ay)
' x = x + dt * vx ' Previous method.
' y = y + dt * vy ' Swap the switches in both programs.
'-------------------------------------
The equations apply to a single small time step
lasting dt seconds. Take some simple numbers for
the x values as an example, suppose the step is
dt = 3 seconds, the speed at the start is
vx = 100 m/s and the acceleration is ax = 6 m/s^2.

I've just read read your other reply and you appear to have
addressed minor error problems in only a few orbits so that
those errors won't escalate too much over time. But if you
run your program using the "updated method", it really doesn't
work at all over time. Run the program and see for yourself.

I put a lot of information into these two posts and
you would do well to read them carefully and be sure
you understand each part, you'll learn quite a bit
about numerical methods from them.

I have run the program over many orbits and I'll upload a
plot showing both aphelion and perihelion of the first few
thousand orbits, probably tomorrow as I'm out tonight. I
also ran it for about a week at the end of May with some
adjustments to cope with the low eccentricity. That version
also included your "rest of the universe" mass based on the
Pioneer Anomaly and I can see the gradual decay of the orbit

I imagine that you have again not included a normal orbit as a
test of your program, so I've attached a version of your program
to the end of this post which does.

I approached it a different way, I set a breakpoint
on the detection of aphelion and perihelion and
commented out the anisotropy or left it in for each
part and changed the colour of the plot points. I
haven't found a way to do screen grabs from XP yet
but the sequence was this:

1) Run a full orbit with anisotropy off.
2) Run an inward leg only with anisotropy on.

You can see it reaches perihelion later and
it is farther from the Sun.

3) Run a full orbit with anisotropy off.

That lets you see the new reference elliptical
orbit and how the increased perihelion means
the aphelion has to decrease for the same total
energy.

4) Run an outward leg only with anisotropy on.

The path falls inside the ellipse of step 3 so
the aphelion is reduced even farther. It falls
9262870 m inside the original aphelion and is
again later in the orbit.

5) Run a full orbit with anisotropy off.

That lets you see how the reduced aphelion means
another increase of perihelion for the same energy.

It is important that each time you just change the
anisotropy calculation and then continue because the
speeds and location need to carry through to the next
step. The display is clearer if you multiply the
anisotropy by 3000 but use 1 times if you are saving
actual numbers.

It's based on your most
recent method update, which I assume hasn't changed.

I explained the penultimate refinement regarding
mean acceleration. The final one hasn't been posted
yet (I think) but is the same approach applied to
the anisotropy. Both changes only make a difference
of a few metres so I'll not bother posting the details
unless you are interested.

This time it's set up to plot every one second step of an
orbit which is more eccentric than that of Mercury so as to
highlight any possible problems. As well as showing the supposed
anisotropic decay, it clearly shows a fairly rapid decay in the
normal orbit (blue curve) in the very first cycle. Is that what
you expected?

I couldn't get the second leg to run but maybe
because I edited it incorrectly. I'll include my
version below. The pure elliptical paths without
anisotropy are green, blue and magenta. The
transitional paths with anisotropy are grey then
red. In reality, only the grey then red would
occur of course, the others are just for reference.

Note "mag" is set to 3000, change it to 1 for real
values (no effect on the display). K = 0 if the
anisotropy is 0 when anisotropy is of or K = mag
when it is on.

This has all been a very interesting exercise George, but it
really makes no difference in the end because gravity is _always_
entirely elastic. That's the point you seem to be missing
altogether.

I'm not missing it at all, what you are missing
is that your anisotropy is inelastic so there are
two possibilities, either there is anisotropy in
gravity and gravity is _not_ elastic, or gravity
_is_ elastic and there is no anisotropy. Your
equation describes the first.

Here's the program - just copy in and run then
watch the effects. Oh, it also adds a crossing
yellow line at aphelion and perihelion. (I have
deleted some print statements and file output
to reduce the clutter.)

George



DIM c AS DOUBLE, GM AS DOUBLE
DIM time AS DOUBLE, dt AS DOUBLE, sinceTurn AS DOUBLE
DIM x AS DOUBLE, y AS DOUBLE
DIM px AS DOUBLE, py AS DOUBLE, lastPx AS DOUBLE, lastPy AS DOUBLE
DIM lastX AS DOUBLE, lastY AS DOUBLE
DIM prevX AS DOUBLE, prevY AS DOUBLE
DIM scale AS DOUBLE, xOffset AS DOUBLE, yOffset AS DOUBLE
DIM vx AS DOUBLE, vy AS DOUBLE, vr AS DOUBLE, lastVr AS DOUBLE
DIM ax AS DOUBLE, ay AS DOUBLE, ar AS DOUBLE
DIM axPrev AS DOUBLE, ayPrev AS DOUBLE
DIM axMean AS DOUBLE, ayMean AS DOUBLE
DIM radiusSquared AS DOUBLE, radius AS DOUBLE, turnRadius AS DOUBLE
DIM lastRadius AS DOUBLE, prevRadius AS DOUBLE
DIM Newton AS DOUBLE, acceleration AS DOUBLE, anisotropy AS DOUBLE
DIM simLength AS DOUBLE, orbitnum AS DOUBLE
DIM hemi AS INTEGER, show AS INTEGER
DIM K AS DOUBLE, mag AS DOUBLE, colour AS INTEGER

SCREEN 12
CLS

K = 0
mag = 3000
colour = 2

REM Constants - all values are in SI units. Note
REM that the GM product is negative as the Newtonian
REM force pulls the body towards the Sun.

c = 299792458#
GM = -1.327D+20

REM Simulation timestep of 30s and maximum duration.

dt = 100
simLength = 10000000000#

REM Screen scaling factors.

scale = 2E-09
xOffset = 320
yOffset = 240

PSET (xOffset, yOffset)

REM Initial values

x = 69820000000#
y = 0
vx = 0
vy = 38855

REM Internal variables

time = 0
orbitnum = 0

lastRadius = x
prevRadius = x
lastX = x
lastY = y
prevX = x
prevY = y

REM ==========================
REM ==== Start the loop ====
REM ==========================

timestep:

REM Find the square of the radius then the radius.

radiusSquared = x * x + y * y
radius = SQR(radiusSquared)

REM ================================================== ====
REM ==== Detect the aphelion and perihelion points. ====
REM ================================================== ====

IF hemi = 1 THEN
IF radius lastRadius THEN ' Found aphelion
hemi = 0
show = 1

IF orbitnum .7 THEN
K = mag
colour = 8
ELSEIF orbitnum 1.7 THEN
' continue second ellipse
ELSEIF orbitnum 2.7 THEN
K = 0
colour = 5
ELSE
END
END IF
END IF
ELSE
IF radius lastRadius THEN ' Found perihelion
hemi = 1
show = 1

IF orbitnum .2 THEN
' continue first ellipse
ELSEIF orbitnum 1.2 THEN
K = 0
colour = 3
ELSEIF orbitnum 2.2 THEN
K = mag
colour = 4
END IF
END IF
END IF

IF show = 1 THEN
PSET (px - 1, py), 14
PSET (px + 1, py), 14

show = 0
orbitnum = orbitnum + .5
END IF

REM ================================================== =
REM ==== Do the physics to move to the next step ====
REM ================================================== =

REM Find the Newtonian acceleration.

Newton = GM / radiusSquared

REM ================================================== =
REM The anisotropy depends on the radial speed which is
REM the rate of change of radius or change divided by
REM delta time.
REM ================================================== =

lastVr = vr
vr = (radius - lastRadius) / dt

REM ================================================== =
REM ==== Modify acceleration for the anisotropy. ====
REM ================================================== =

anisotropy = Newton * (3 * vr - lastVr) / (2 * c)
acceleration = Newton + anisotropy * K

REM ================================================== ====
REM Capture the current values for use in various places
REM before moving on a step.
REM ================================================== ====

prevRadius = lastRadius
prevX = lastX
prevY = lastY

lastRadius = radius
lastX = x
lastY = y
axPrev = ax
ayPrev = ay

REM ================================================== =
REM ==== Integrate the acceleration and velocity ====
REM ================================================== =

REM Find the present acceleration components.

ax = acceleration * (x / radius)
ay = acceleration * (y / radius)

REM This is a modified Verlet integrator using a
REM linear forward estimator for the acceleration.
REM The Mean values are over the coming time step
REM based on assuming the same rate of change of
REM acceleration as over the previous step.

axMean = (3 * ax - axPrev) / 2
ayMean = (3 * ay - ayPrev) / 2

REM The locations change by the mean velocity times the
REM step duration which is given by Newton's equation:
REM s = ut + 1/2 a t^2.

x = x + dt * (vx + .5 * dt * axMean)
y = y + dt * (vy + .5 * dt * ayMean)

REM The velocity changes by the mean acceleration
REM multiplied by the timestep duration.

vx = vx + dt * axMean
vy = vy + dt * ayMean

REM Finally step the time forward. Time is not currently

time = time + dt

REM ======================================
REM ==== Show the graphical display ====
REM ======================================

REM Convert location to screen coordinates.

px = xOffset + x * scale
py = yOffset - y * scale

IF (px lastPx) OR (py lastPy) THEN
PSET (px, py), colour
lastPx = px
lastPy = py
END IF

REM ================================================== =====
REM ==== Check for completion of the desired orbits. ====
REM ================================================== =====

REM The time check is a safeguard in case the
REM aphelion/perihelion detection gets broken.

IF (orbitnum 10000.6) AND (time simLength) GOTO timestep

END

On Jun 16, 12:03 am, Eric Gisse wrote:
On Jun 15, 10:32 pm, Koobee Wublee wrote:

Gerber's gravity is basically a modification to the Newtonian
gravitational potential. Gerber's gravitational potential is

U = ((G M / c^2) / r) / (1 - dr/dt / c)^2

With that gravitational potential, Gerber was able to show Mercury's
orbital anomaly in terms of advance in its perihelion. The
mathematical method pioneered by Gerber to derive the advancement in
angle was adopted by Einstein almost 16 years without referencing to
GR. In fact, it is still the choice of tools among all textbooks
since then.

Gerber again?!

Yes, Mr. Keon's modification of the Newtonian gravitational potential
is very similar to what Gerber did. shrug

http://groups.google.com/group/sci.p...sg/3a57c809c15...

[Notice how I can find my own posts yet you are incapable of managing
this yourself]

Maybe I just don't have all this free time as you do. shrug

Hint: I have a life.

http://www.mathpages.com/home/kmath527/kmath527.htm

Gerber's potential has no actual motivation.

Bullsh*t! His motivation was to explain Mercury's orbital anomaly.
shrug

The result Gerber used is
derivable from first principles - Gerber simply postulates it.

Einstein did exactly the same crap before GR. shrug

GR is the same crap. shrug

It is
fantastically untrue to say that Einstein used his result.

The result is the 43" of observation. I said Einstein and modern
physicists all have used Gerber's methodology to derive Mercury's
orbital anomaly. In Gerber's circumstance, it is valid. However,
under the concept of spacetime, it is not. Why?

Hint:

** ds^2 = g_11 dt^2 - g_22 dr^2 - g_33 dO^2

And

** d^2r/dO^2 = d^2r/dOds ds/dO + dr^2r/dOdt dt/dO

Thus, what you are saying just does not prove anything.

Thus, Koobe Wublee babbles about a subject he does not understand.
Again.

You are so wrong again. shrug

On Jun 16, 7:40 pm, Koobee Wublee wrote:
[...]


It is
fantastically untrue to say that Einstein used his result.

The result is the 43" of observation. I said Einstein and modern
physicists all have used Gerber's methodology to derive Mercury's
orbital anomaly. In Gerber's circumstance, it is valid. However,
under the concept of spacetime, it is not. Why?

The question is based upon the false premise that physicists use
"Gerber's methodology". This is not true - consult any intermediate
text on general relativity.

Way back in February I gave you a /good/ reference on Gerber's
gravity:

http://www.mathpages.com/home/kmath527/kmath527.htm

There is an explicit comparison of the equations of motion - read the
following:

"It just so happens that the term +3mu2 in the GR equation of motion
and the term -6mu d2u/dq2 in Gerber's equation of motion both result
in a first-order precession of 6pm/L in the slow weak-field limit.
Thus Gerber did not in any way anticipate the two-body equation of
motion predicted by general relativity, let alone the field equations
from which the relativistic equation of motion is derived."

The explicit derivation of the equations of motion is he

http://www.mathpages.com/rr/s6-02/6-02.htm

You continue to talk about stuff you just /do not understand/.

[snip crap]

On Jun 16, 9:16 pm, Eric Gisse wrote:
On Jun 16, 7:40 pm, Koobee Wublee wrote:

The result is the 43" of observation. I said Einstein and modern
physicists all have used Gerber's methodology to derive Mercury's
orbital anomaly. In Gerber's circumstance, it is valid. However,
under the concept of spacetime, it is not. Why?

The question is based upon the false premise that physicists use
"Gerber's methodology". This is not true - consult any intermediate
text on general relativity.

The following website quoted describes exactly how Gerber did it.

http://www.mathpages.com/home/kmath527/kmath527.htm

The methodology is exactly what modern physicists do to derive
Mercury's orbital anomaly. shrug

Way back in February I gave you a /good/ reference on Gerber's
gravity:

http://www.mathpages.com/home/kmath527/kmath527.htm

I know about that one for years. Thank you.

There is an explicit comparison of the equations of motion - read the
following:

"It just so happens that the term +3mu2 in the GR equation of motion
and the term -6mu d2u/dq2 in Gerber's equation of motion both result
in a first-order precession of 6pm/L in the slow weak-field limit.
Thus Gerber did not in any way anticipate the two-body equation of
motion predicted by general relativity, let alone the field equations
from which the relativistic equation of motion is derived."

When Gerber derived the result, GR was still 16 years in the future.
shrug

However, the term, 3mu2 (3 G M /c^2 U^2), describes in term of orbital
speed that Mercury will complete a circle in exactly sqrt(3 G M /
c^2 / R) in radian faster than the Newtonian result. This translates
to half of 43" per century!!!

The explicit derivation of the equations of motion is he

http://www.mathpages.com/rr/s6-02/6-02.htm

The equation right below (5) is not valid because r can also be a
function of t and O according to the spacetime equation. shrug

You continue to talk about stuff you just /do not understand/.

This appears to you so because you don't understand the stuff.
shrug

On Jun 16, 10:37 pm, Koobee Wublee wrote:

[...]


When Gerber derived the result, GR was still 16 years in the future.
shrug

However, the term, 3mu2 (3 G M /c^2 U^2), describes in term of orbital
speed that Mercury will complete a circle in exactly sqrt(3 G M /
c^2 / R) in radian faster than the Newtonian result. This translates
to half of 43" per century!!!

No, it doesn't.

Of course, if you want to argue the point I will gladly look at your
derivation. If you don't have a derivation to show me, then I am
uninterested in your assertions.


The explicit derivation of the equations of motion is he

http://www.mathpages.com/rr/s6-02/6-02.htm

The equation right below (5) is not valid because r can also be a
function of t and O according to the spacetime equation. shrug

The phrase "spacetime equation" is nonsense.

The spatial variable r is trivially a function of time and angle, but
those functionalities are unimportant because of the conserved
quantities associated with the manifold.


You continue to talk about stuff you just /do not understand/.

This appears to you so because you don't understand the stuff.
shrug

I can point to a handful of books and resources and say 'this is where
I have learned general relativity'. Why don't you point to the
resources _YOU_ learned GR from so I can see where your coming from?
If you don't have them, why are you even arguing?

On Jun 17, 1:58 am, Eric Gisse wrote:
On Jun 16, 10:37 pm, Koobee Wublee wrote:

When Gerber derived the result, GR was still 16 years in the future.
shrug

However, the term, 3mu2 (3 G M /c^2 U^2), describes in term of orbital
speed that Mercury will complete a circle in exactly sqrt(3 G M /
c^2 / R) in radian faster than the Newtonian result. This translates
to half of 43" per century!!!

No, it doesn't.

I meant sqrt(1 + 3 G M / c^2 / R).

Of course, if you want to argue the point I will gladly look at your
derivation. If you don't have a derivation to show me, then I am
uninterested in your assertions.

This is not my derivation. This is the derivation you have posted
from the website below. shrug

http://www.mathpages.com/rr/s6-02/6-02.htm

The equation right below (5) is not valid because r can also be a
function of t and O according to the spacetime equation. shrug

The phrase "spacetime equation" is nonsense.

The equation is the familiar one describing a segment of spacetime.
shrug

You are jumping on the same wagon of the ones who blame their
ignorance on vocabularies after been presented with the proper math.
shrug

The spatial variable r is trivially a function of time and angle, but
those functionalities are unimportant because of the conserved
quantities associated with the manifold.

Wrong! Understand the model calling out for geodesics following the
maximum accumulated spacetime does not allow a conserved quantity in
energy. There is only one conserved quantity associated with angle
--- conservation of angular momentum. You are falling into the
matheMagical realm created by the ones who choose Einstein as the
Messiah of GR. shrug

This appears to you so because you don't understand the stuff.
shrug

I can point to a handful of books and resources and say 'this is where
I have learned general relativity'.

But you cannot point out one that does not contradict itself. shrug

Why don't you point to the
resources _YOU_ learned GR from so I can see where your coming from?

This is not about who can find the most popular references. shrug

If you don't have them, why are you even arguing?

This is about GR and SR themselves. shrug

On Jun 17, 8:01 pm, Koobee Wublee wrote:
On Jun 17, 1:58 am, Eric Gisse wrote:

On Jun 16, 10:37 pm, Koobee Wublee wrote:
When Gerber derived the result, GR was still 16 years in the future.
shrug

However, the term, 3mu2 (3 G M /c^2 U^2), describes in term of orbital
speed that Mercury will complete a circle in exactly sqrt(3 G M /
c^2 / R) in radian faster than the Newtonian result. This translates
to half of 43" per century!!!

No, it doesn't.

I meant sqrt(1 + 3 G M / c^2 / R).

Of course, if you want to argue the point I will gladly look at your
derivation. If you don't have a derivation to show me, then I am
uninterested in your assertions.

This is not my derivation. This is the derivation you have posted
from the website below. shrug

Plug in the numbers.

You get 43" or so, not 21.5".


http://www.mathpages.com/rr/s6-02/6-02.htm

The equation right below (5) is not valid because r can also be a
function of t and O according to the spacetime equation. shrug

The phrase "spacetime equation" is nonsense.

The equation is the familiar one describing a segment of spacetime.
shrug

You are jumping on the same wagon of the ones who blame their
ignorance on vocabularies after been presented with the proper math.
shrug

I am in no way confused about how to obtain the equations of motion.
I'm just pointing out what you are saying is nonsense.

YOUR vocabulary is the faulty one - it is inconsistent with how the
entire physics community uses and describes things.


The spatial variable r is trivially a function of time and angle, but
those functionalities are unimportant because of the conserved
quantities associated with the manifold.

Wrong! Understand the model calling out for geodesics following the
maximum accumulated spacetime does not allow a conserved quantity in
energy. There is only one conserved quantity associated with angle
--- conservation of angular momentum. You are falling into the
matheMagical realm created by the ones who choose Einstein as the
Messiah of GR. shrug

There are two conserved quantities - angular momentum and energy [per
unit mass, depending if the path is timelike or null].

You get conservation of energy because \partial_t * g_tt = 0 and
conservation of angular momentum because \partial_\phi * g_\phi\phi =
0. Familiarize yourself with killing vectors, and don't whine about
Einstein because Einstein has nothing to do with the modern
formulation of general relativity.


This appears to you so because you don't understand the stuff.
shrug

I can point to a handful of books and resources and say 'this is where
I have learned general relativity'.

But you cannot point out one that does not contradict itself. shrug

None of them do. You cannot claim differently because you don't own
any textbooks on GR.


Why don't you point to the
resources _YOU_ learned GR from so I can see where your coming from?

This is not about who can find the most popular references. shrug

Who said anything about popular? I am yet to see you post even ONE
reference that I have not already given you.


If you don't have them, why are you even arguing?

This is about GR and SR themselves. shrug