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Old Dec 19th 2017, 12:27 AM   #11
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Originally Posted by Woody View Post
43 arc-seconds in 100 years is the best part of not a lot.

Newtons equations are fine for most purposes, it is only when very strong gravitational fields are involved, or when extreme precision is necessary, that we have to resort to Einstein.

Mercury is in a fairly strong gravitational field, being close to the Sun, but even so it took extremely precise observations to detect the anomaly.
And many years to observe it.
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Old Dec 19th 2017, 08:14 AM   #12
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MERCURY---------------DATA VALUE---------------UNITS--------Data Source
orbital equation-----X^2/A^2 + Y^2/B^2 = 1---- m--------std ellipse equation
period-------------7.600521600000E+06----------seconds---Given Value
aphelion (aph)----6.981690000000E+10------------m--------Given Value
perihelion (perh)--4.600120000000E+10------------m--------Given Value
Vaph (Vy)---------3.870000000000E+04------------m/sec---Given Value
Vperh (Vy)--------5.660000000000E+04-------------m/sec---Given Value
diameter----------4.879000000000E+06-------------m--------Given Value
mass--------------3.181000000000E+23-------------kg--------Given Value
A (ellipse value)--5.790905000000E+10-------------m--------(aph +perh)/2
B (ellipse value)--5.667152001032E+10-------------m--------sqrt(A^2 -C^2)
C (ellipse value)--1.190785000000E+10
-------------m--------A - perihelion
Vavg--------------4.684910860123E-02--------------m/sec----perimeter / period
perimeter---------3.560776618644E+05-------------m---------2*pi()*B

CONSTANTS--------------VALUE-----------------------UNITS--------Data Source
G uiversal----------6.674080000000E-11--------------------------given Value
sun's mass---------1.991000000000E+30--------------kg---------given Value
sun's radius--------6.959500000000E+08--------------meters----given Value
speed of light (c)--2.997924580000E+08--------------m/sec-----given Value

The equation for the ellipse perimeter was obtained by rearranging the
equation for the ellipse to an equation for Y and then integrating over a range
of X from +A to -A.

The given value for Mercury's orbital period is the baseline value against
which GG impacted orbital periods will be compared.

Are there any problems about what is contained in this post?

Regards; wanderer

Last edited by wanderer; Dec 22nd 2017 at 09:32 AM. Reason: Corrrect exponent values
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Old Dec 23rd 2017, 12:45 AM   #13
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I'm not sure if there is anything in Wanderer's data values that take into account the precession of mercury's orbit. I imagine it would make a better value for the period of mercury's orbit than what would be predicted by the elliptic equation alone so you would need to modify the equation X^2/A^2 + Y^2/B^2 = 1 and you're probably going to be better off in polar co-ordinates. It kind of reminds me of the spirograph patters like in Spirograph Pattern Guide and I'm thinking something like:



An elliptical orbit with no precession would be the middle picture.
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Last edited by kiwiheretic; Dec 23rd 2017 at 12:49 AM.
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Old Dec 24th 2017, 11:37 AM   #14
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Mercury's orbit

The table posted for the parameters of Mercury's orbit shows how they are determined by three given (measured) values---the two apsides distances and the orbital period. Those three values were taken from a NASA site which I beleive to be accurate, However, the average orbital speed I determined as shown in the posted table does not agree with NASA's given value of Mercury' orbital speed. Why not?
Regards, wanderer
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Old Dec 29th 2017, 08:28 AM   #15
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Mercury's orbit

I have two questions about Mercury's Orbit.
1. Is it possible for Mercury's orbit to precess if its transition times between apsides are equal? I'm looking for confirmation of my belief that unequal times are necessary for precession to occur. Otherwise new identical times would appear to only create new orbital periods without any precession.
2. Is it possible for Mercury's orbit to not precess if its transition times between apsides are unequal? Also looking for confirmation that for an object's orbital period (P), any changes to the transition times between apsides which average exactly the origional value for P, will not cause any precession.
Regards; wanderer
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Old Dec 29th 2017, 03:18 PM   #16
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If you post the equations you have been using, we might be able to spot the issue.
I am not one of those people who can skip through a mathematical problem with ease,
but I can usually grind my way through to the solution if I stick at it long enough.
You will probably receive a response from someone else while I am still grinding.

As kiwiheritic suggests, an additional term will be required to introduce the precession.
However the precession is so tiny, that I doubt this would be the cause of your observed computational discrepancy.

Note that the relativistic effect on the precession is is only one of the smaller causes.
see this link: <Wikipedia:Precession of Mercury>
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Old Dec 30th 2017, 08:28 AM   #17
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Thanks, Woody, the table in my post 12 contains the equations I used to determine the values which I calculated. the equation is shown at the end of the line for each calculated value. The equation I posted for an ellipse is for a pure mathematical ellipse. It is not meant to address or consider any classical effects caused by other planets or other bodies in the Solar system. It is also not meant to address or consider any Special or General relativity effects. However, I want to discover what relativistic changes are needed to Mercury's non-relativistic equation to make the 43 arc-seconds per century precession occur.
Best Regards; wanderer
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Old Jan 2nd 2018, 09:37 AM   #18
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I have looked at Einstein's equation for the single orbit contribution to the 100 year presession of mercury's orbit. Knowing that value does not help me in any way to understand what parameters of the orbit of mercury were affected and how they were affected. In addition Einsteins's equation produces a unitless number. How can it be considered to be arc-seconds?
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Old Jan 4th 2018, 11:33 AM   #19
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Mercury's orbit

The Sun's gravitational field is established only by its own mass and does not depend on the mass of mercury. A peanut would follow the same orbit.
As mercury is moving from perihelion to Aphelion it is continuously moving to a distance in which the Sun's gravitational field is decreasing
and therefore the amount of GR bending of spacetime is decreasing. This unbending of space should have a GR effect on the Orbital velocity
of Mercury equivalent to the change in the gravitatioal field strength over the distance between perihelion and aphelion. There is a second
factor which must also be considered in Mercury's move between perihelion and aphelion. Mercury is climbing up out of a gravity well defined by
the Gravitational field strengths between perihelion and aphelion. This should result in a reduction in its orbital speed as it climbs up out of
the gravity well. These two factors---the unbending of spacetime and the motion through the gravity well seem to create opposing effects.

The effects of the two factors are reversed while Mercury is moving between aphelion and perihelion. However, using the average orbital speed
of mercury based on the given period time and the perimeter length as defined by 2*pi*Semi minor axis, if the perimeter length and the average
orbital speeds are modified by the Lorentz factor sqrt(1-((Avg Vorb+ deltaGRVorb)/c)^2) an estimate of the 100 year precession can be made. The value determined by my process is 39.8 arc seconds per century. The value does not exactly match the value determined by Einstein's equation. Perhaps, I still have a problem with determining exactly what
Mercury's average orbital speed really is and how its orbital speed should be determined for each actual distance between Mercury and the Sun.
However, the process shows how and what Mercury's ellipse parameters are being modified by GR and that was my original goal.

Regards, wanderer
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Old Jan 15th 2018, 07:06 AM   #20
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I had an error in determining the value of Mercury’s elliptical orbit’s tangent angle in reference to the ellipse major axis. When that error was corrected, the value of Mercury’s orbital precession, due to relativistic effects only, was determined to be 43 arc-seconds per century. This matches the value as determined by Einstein’s equation. However, AE’s equation does not identify which parameters of Mercury’s orbital equation relativistic effects affect, my algorithm does that with specificity. What ellipse parameters were affected and how, was what I wanted to know, and now I do.
If anyone is interested in the mathematical processes I used, I would be pleased to email a working copy of the algorithm file to them.
Best regards, wanderer.
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