[Kryptid]

There is no equation in your referred article.

You didn't look very hard, did you? Look at the attached file:

[jsaldea12 (OP)]

Saw it but can you translate it to simple math equation that is very easy to understand  to KNOW how Dr. Einstein solved the anomalous precession of Mercury..jsaldea12 February 15, 2019

[Kryptid]

Saw it but can you translate it to simple math equation that is very easy to understand  to KNOW how Dr. Einstein solved the anomalous precession of Mercury..jsaldea12 February 15, 2019

It's a bit late for me to do this tonight, but I'll try to do so tomorrow when I get the chance (assuming no one else does it first).

[mad aetherist]

Saw it but can you translate it to simple math equation that is very easy to understand  to KNOW how Dr. Einstein solved the anomalous precession of Mercury..jsaldea12 February 15, 2019

It's a bit late for me to do this tonight, but I'll try to do so tomorrow when I get the chance (assuming no one else does it first).

And also show how it works, ie how it changes the 1/RR relationship, or how it drags the frame, or something (ie something mechanical)(ie not an equation).

[jsaldea12 (OP)]

Quoted:"It's a bit late for me to do this tonight, but I'll try to do so tomorrow when I get the chance (assuming no one else does it first).."  That is what I want to know. But please show us how Dr. Einstein did it, outwitting the whole astronomical societies for 5o years !!!.. jsaldea   Feb. 17, 2019

[Kryptid]

Saw it but can you translate it to simple math equation that is very easy to understand  to KNOW how Dr. Einstein solved the anomalous precession of Mercury..jsaldea12 February 15, 2019

This is what the symbols in the equation represent:

“σ” represents the precession in radians per revolution
“L” represents the semi-major axis in meters
“T” represents the orbital period in seconds
“c” represents the speed of light in meters per second
“e” represents the orbital eccentricity (a value between 0 and 1)

So now I will put in the values known for Mercury:

σ = (24π³L²)/(T²c²(1-e²))
σ = (24π³(57,909,050,000 m)²)/((7,600,530.24 s)²(299,792,458 m/s)²(1-(0.20563²))
σ = ((744.1506)(3.3534581 x 10²¹))/((5.776806 x 10¹³)(8.9875518 x 10¹⁶)(1-0.0422836969)
σ = (2.4954779 x 10²⁴)/((5.1919343 x 10³⁰)(0.9577163031))
σ = (2.4954779 x 10²⁴)/(4.9724001 x 10³⁰)
σ = 5.0186587 x 10^-7 radians/revolution

Since 1 radian equals 206,265 arcseconds, that would be 0.10351736367 arcseconds per revolution. Since a revolution for Mercury lasts 87.9691 days, that would be 0.00117674687 arcseconds per day. A century lasts 36,525 days, so that would be 42.98 arcseconds per century.

Quoted:"It's a bit late for me to do this tonight, but I'll try to do so tomorrow when I get the chance (assuming no one else does it first).."  That is what I want to know. But please show us how Dr. Einstein did it, outwitting the whole astronomical societies for 5o years !!!.. jsaldea   Feb. 17, 2019

I don't know exactly how he went about deriving the precession equation, unfortunately. All I know is that he used relativity to do it.

And also show how it works, ie how it changes the 1/RR relationship, or how it drags the frame, or something (ie something mechanical)(ie not an equation).

Unfortunately, I don't really understand it myself. I've seen different explanations online, one implying that it's because massive objects can't reach the speed of light (perhaps meaning that planets always orbit at least slightly more slowly than Newtonian equations predict, with the difference becoming larger the closer the planet is to its star). Another said that it had to do with the fact that the space that the planet travels through is curved.

[evan_au]

I am also thinking that the 1/RR is not as critical as one might think, i think that we would have a functioning solar system if gravity was a 1/R thing, ie we would have orbits.

It is true that if you have a 2-body system (eg Earth and Sun), that you could have a stable circular orbit.

However, it is the precise interconversion of kinetic energy and gravitational potential energy that makes stable elliptical orbits possible. If the strength of gravity was as extreme as 1/R, the Earth's orbit would not be an ellipse - but Kepler worked out observationally that the orbit is an ellipse. And Newton worked out mathematically that this demands that gravity is an inverse-square law.

The solar system with multiple planets is only stable because gravity is an inverse square law - the tugs of other planets transfer angular momentum back and forth between the planets (energy is conserved) - but conservation of energy does not occur if gravity is not an inverse square law.

There are people who think that gravity might differ slightly from 1/R²: For example 1/R^2.0000001, and we may not have noticed that deviation.

But NASA would have - they measured the Sun's gravitational tug on the Pioneer spacecraft, and if gravity had differed from an inverse square law even a tiny bit, some NASA scientist would have a Nobel Prize by now.

I have tinkered with planetary simulators on the web that allowed you to tweak the law of gravity - but unfortunately I can't find one at present

also show how it works, ie how it changes the 1/RR relationship, or how it drags the frame, or something (ie something mechanical)(ie not an equation).

My qualitative understanding of the precession is this:
- Mercury has an exactly elliptical orbit (from the viewpoint of someone on Mercury)
- However, from the viewpoint of someone far from Mercury (eg Earth or Alpha Centauri), when Mercury is closest to the Sun, time slows down for any residents of Mercury
- This means that Mercury travels very slightly further around the Sun before swinging outward to the more distant parts of its orbit.
- This means that the point on Mercury's orbit which is closest to the Sun (perihelion) moves very slowly relative to the distant stars, when measured from year to year.
- This effect is rather subtle to pick up in a single year with an optical telescope, but easy when you look over a period of a century or more
- And is easy to detect when you have a space probe orbiting Mercury which returns very accurate distance measurements to Earth (as the Messenger space probe did from 2011-2015)
See: https://en.wikipedia.org/wiki/MESSENGER

[mad aetherist]

I am also thinking that the 1/RR is not as critical as one might think, i think that we would have a functioning solar system if gravity was a 1/R thing, ie we would have orbits.

It is true that if you have a 2-body system (eg Earth and Sun), that you could have a stable circular orbit.
However, it is the precise interconversion of kinetic energy and gravitational potential energy that makes stable elliptical orbits possible. If the strength of gravity was as extreme as 1/R, the Earth's orbit would not be an ellipse - but Kepler worked out observationally that the orbit is an ellipse. And Newton worked out mathematically that this demands that gravity is an inverse-square law.

Hmmm -- i am thinking that the conservation & interconversion of kinetic & potential energy would work ok for any sort of 1/R^** gravity.  But of course such orbits would not be elliptical (altho that stuff is over my head).

The solar system with multiple planets is only stable because gravity is an inverse square law - the tugs of other planets transfer angular momentum back and forth between the planets (energy is conserved) - but conservation of energy does not occur if gravity is not an inverse square law.

No i am still thinking that conservation is ok under any regime.
But i can see that a 1/R must be very unstable. But anyhow in the end it would be stable but praps with only one planet remaining (praps a big fat one), praps with lots of dust spreading all throo the system.   If only dust remained then praps the  dust would take on the form of lots of spiral arms, & the Sun would play the role of a blackhole.

There are people who think that gravity might differ slightly from 1/R²: For example 1/R^2.0000001, and we may not have noticed that deviation.

But NASA would have - they measured the Sun's gravitational tug on the Pioneer spacecraft, and if gravity had differed from an inverse square law even a tiny bit, some NASA scientist would have a Nobel Prize by now.

I wonder about that. NASA dont know G to better than say 0.3%, & NASA dont know the mass of Mercury to better than say 0.3%, but they know Gm for Mercury to say 0.0000001%.  But praps even so despite this apparently fatal ignorance praps u are correct that NASA would nonetheless see anything straying from 2.0000000.

I have tinkered with planetary simulators on the web that allowed you to tweak the law of gravity - but unfortunately I can't find one at present

Yes i would be good to see how say Earth might orbit under some funny 1/R^**.

[mad aetherist]

also show how it works, ie how it changes the 1/RR relationship, or how it drags the frame, or something (ie something mechanical)(ie not an equation).

My qualitative understanding of the precession is this:
- Mercury has an exactly elliptical orbit (from the viewpoint of someone on Mercury)
- However, from the viewpoint of someone far from Mercury (eg Earth or Alpha Centauri), when Mercury is closest to the Sun, time slows down for any residents of Mercury
- This means that Mercury travels very slightly further around the Sun before swinging outward to the more distant parts of its orbit.
- This means that the point on Mercury's orbit which is closest to the Sun (perihelion) moves very slowly relative to the distant stars, when measured from year to year.

But i am thinking that that ticking dilation effect must be symmetrical, ie it applies equally on approach & then on departure, & then ditto in the 2nd half of the orbit. And if symmetrical then the ellipse might not be an ellipse but (whatever it is) there aint no precession.

My own theory-explanation is that the 43 arcsec is a secondary precession due to the primary 532.3 arcsec.  I have come up with say 4 possible effects potentially giving a precession, but all of them fail because when looked into in detail i could see that they all suffer symmetry.  But my primary-precession-makes-secondary-precession effect is not symmetrical, hencely it works. And it aint  relativistic (not important)(just saying).

This effect is rather subtle to pick up in a single year with an optical telescope, but easy when you look over a period of a century or more
- And is easy to detect when you have a space probe orbiting Mercury which returns very accurate distance measurements to Earth (as the Messenger space probe did from 2011-2015)
See: https://en.wikipedia.org/wiki/MESSENGER

Yes there might be an observation-reading showing XX arcsec of precession, & everyone might agree on that number, & the number might be true & accurate, but, it is another question altogether as to what is the root cause of that number.

But i have seen graphs showing how the precession varies so much from year to year that a simple annual analysis can suggest an advance of anywhere tween say zero arcsec to 200 arcsec per century.  Hencely a measured advance of 0.43 arcsec in any one year can only be a lucky coincidence.

[jsaldea12 (OP)]

The astronomical equation is for those who want to master in astronomiy, hard to understand and it beclouds HOW Dr. Einstein solved the anomalous precession of Mercury and all other planets. There, that is the clue. But the astronomical equation can translated into simple high school math  equation and will disclosed how  creative Dr. Enstein solved it. jsaldea12  Feb. 17, 2019aswefv

[Kryptid]

hard to understand

It's just algebra. How is that hard to understand?

But the astronomical equation can translated into simple high school math  equation

Please tell me how you would make it any simpler than it already is.

[Bored chemist]

Can we just kill off this thread?
"Do you know how Dr. Einstein solved the anomalous precession of Mercury?"
Like this
https://sites.math.washington.edu/~morrow/papers/Genrel.pdf

Strictly speaking, that's not Einstein's actual work but its a nice clear summary of the classical, and relativistic solutions and it shows that the predicted disparity is pretty close to the observed value.

Relativity works.

[mad aetherist]

The importance of the Mercury perihelion explanation appears in a completely different light if one considers the perihelion motion that occurs in the case of all of the planets of the solar system, these being of different
magnitudes and, in the case of Venus, even negative, i.e. a retreating perihelion. These are values that the GTR cannot explain.

[Bored chemist]

These are values that the GTR cannot explain.

Even in the case of mercury, the relativistic part of the precession isn't very big.
"For Mercury, the perihelion precession rate due to general relativistic effects is 43″ (arcseconds) per century. By comparison, the precession due to perturbations from the other planets in the Solar System is 532″ per century, whereas the oblateness of the Sun (quadrupole moment) causes a negligible contribution of 0.025″ per century"
From
https://en.wikipedia.org/wiki/Apsidal_precession

So, obviously GR isn't going to explain everything.

[mad aetherist]

These are values that the GTR cannot explain.

Even in the case of mercury, the relativistic part of the precession isn't very big.
"For Mercury, the perihelion precession rate due to general relativistic effects is 43″ (arcseconds) per century. By comparison, the precession due to perturbations from the other planets in the Solar System is 532″ per century, whereas the oblateness of the Sun (quadrupole moment) causes a negligible contribution of 0.025″ per century"
Fromhttps://en.wikipedia.org/wiki/Apsidal_precession
So, obviously GR isn't going to explain everything.

When u fraudulently work backwards to make a nonsense equation spit out a desired number then it wont work in any other case, ie every other case, eg Venus.

Re GR not explaining everything, it duznt explain anything. Where is the explanation of the mechanics, ie of the cause.

[Bored chemist]

When u fraudulently work backwards to make a nonsense equation

If that was what they were doing then they could simply make up some other nonsense.
And then the data would all fit beautifully.
But it doesn't.
And that's because they don't.

Didn't you realise that your own observations contradict your assertion?

[jsaldea12 (OP)]

Mad aetherist is not far how Dr. Einstein solved the anomalous precession of Mercury. re-worked backward, Thus do show us the simple math equation that is easy to understand. That equation is right..  jsaldea  Feb. 17, 2019

[Kryptid]

Thus do show us the simple math equation that is easy to understand. That equation is right.

And again, I ask, how would you make the equation I posted any simpler than it already is?

[Bored chemist]

There is no equation in your referred article..

Yes there is
 and, as these things go, it's fairly simple.

[mad aetherist]

When u fraudulently work backwards to make a nonsense equation

If that was what they were doing then they could simply make up some other nonsense.
And then the data would all fit beautifully. But it doesn't. And that's because they don't. Didn't you realise that your own observations contradict your assertion?

Who are they? -- Alby & ??.
How does data for precessions of Venus & for Mars fit perfectly??
What observations of mine??