Timeline for Newtonian contribution to perihelion precession of Mercury
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
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| Mar 3, 2022 at 21:17 | comment | added | Thomas | @PG1995 The only way to have a smaller velocity in the orbit would be to reduced the mass (i.e. the gravitational attraction) of the Sun. In this case, yes, the precession per orbit would be larger (it is actually proportional to the ratio of the mass of the disturbing planet to that of the Sun). The orbital period would go up though with the inverse square root of the Sun (Kepler's third law), so in a given time interval the precession would be proportional to the inverse square root of the Sun's mass. The velocity in turn would be proportional to the square root of the Sun's mass. | |
| Mar 2, 2022 at 21:37 | comment | added | PG1995 | @Thomas Thanks you! "If the velocity of the planet in its orbit is small enough, it could only make a couple of orbits in 100 years." Yes, less orbital speed means less number of orbits in 100 years. But lesser speed also means that the the planet would be spending more time under the influence of influencing planet. In other words, influencing planet could impose its pull to precess the planet in a dominant direction for longer period for each full orbit. Honestly, now I think that increasing orbital speed or making it less would not affect the precession. | |
| Mar 1, 2022 at 21:11 | comment | added | Thomas | @PG1995 Just think about it: the precession rate is measured per time interval. If the velocity of the planet in its orbit is small enough, it could only make a couple of orbits in 100 years. The precession for this would be even too small to measure. In any case, the velocity in a given orbit is fixed by Kepler laws. You can not just change it. | |
| Mar 1, 2022 at 8:28 | comment | added | Thomas | @PG1995 You would be correct with regard to Q1 if you would track Mercury's orbit continuously. As it is, only the position at perihelion is tracked, so that averages over the wobb;le of Mercury's orbit and you won't see it in this plot. You only see the wobble due to the disturbing planets, even if you zoom in closely As for Q2, you are right, the webpage is referring to the disturbing planet, but the precessing orbit definitely precesses faster for closer orbits (i,.e. higher velocities) as well, evem much more so than for the disturbing planet. | |
| Feb 28, 2022 at 22:31 | history | edited | Thomas | CC BY-SA 4.0 |
Added explanation
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| Feb 28, 2022 at 21:48 | comment | added | PG1995 | @Thomas So, what I was saying in case of Q1 was correct? Regarding Q2, but in the linked webpage they only change the speed of influencing planet which is Venus. They didn't change speed for Mercury. I still think that if Venus speed is kept constant and Mercury's orbital speed is lowered, the precession would increase. If Mercury's speed is increased, the precession will decrease. Could you please clarify this? | |
| Feb 28, 2022 at 21:37 | comment | added | Thomas | @PG1995 Q2: No, it is the other way around. The precession is faster for planets closer to the sun i.e. planets that are faster (see also the link to that website I gave in my answer, where the effect of changing planet velocity is shown) | |
| Feb 28, 2022 at 21:32 | comment | added | Thomas | @PG1995 Q1: The curves are strictly speaking not continuous. They consist of points showing the location of the perihelion angle. Each point contains the integrated effect of a whole Mercury orbit, so by definition the orbit wobble of Mercury is averaged out here already | |
| Feb 28, 2022 at 21:17 | comment | added | Thomas | @ProfRob I added units to the graphs. As for the sign change of the effect: the precession angle changes sign when the disturbing potential force changes sign. If the disturbing outer planet is in opposition the resultant force pulls Mercury outward (away from the sun), but in conjunction it pulls Mercury towards the Sun. In the latter case, the distance is greater though, so the force is smaller. So the net effect will still be an increasing precession angle (consistent with the fact that on average the planet position is a ring which will result in an average net outward force) | |
| Feb 28, 2022 at 20:53 | history | edited | Thomas | CC BY-SA 4.0 |
Added units to graphs
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| Feb 28, 2022 at 20:46 | history | edited | Thomas | CC BY-SA 4.0 |
Added units to graph
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| Feb 28, 2022 at 7:48 | vote | accept | PG1995 | ||
| Feb 28, 2022 at 6:21 | comment | added | PG1995 | Mercury is pulled in positive direction though the shown curve is going in negative direction. At point B, Mercury is pulled in negative direction while dominant portion of precession is headed toward positive direction. Do I make sense? i.sstatic.net/fgZ0a.png Q2 If Mercury's orbital speed becomes too low while keeping the orbital speed of influencing planet the same, I think the magnitude of precession would increase. But if the Mercury's speed is increased, the magnitude of precession would decrease. Do I have it right? | |
| Feb 28, 2022 at 6:20 | comment | added | PG1995 | @Thomas Q1: In the following image which has been taken from your linked webpage, they are showing, for Neptune, a smooth sine wave with period of 165 years (orbital period of Neptune). I think in reality, there will be small oscillations superimposed on that smooth curve. Mercury completes its revolution in 88 days compared to 165 years revolution of Neptune and hence there will come a short period of time when Mercury is in such a position in its orbit that Neptune starts giving it precession in opposite direction which doesn't last for long. For example, in the image at point A, Cont'd | |
| Feb 28, 2022 at 5:59 | comment | added | ProfRob | Could you put units on the graphs? It was my answer that I have deleted since it was incorrect in the sense that I did not think the perturbations could reverse in sign, even instantaneously. | |
| Feb 27, 2022 at 8:44 | comment | added | Thomas | @PG1995 Yes, I saw and read this other answer as well. It must have been removed by the author. | |
| Feb 27, 2022 at 2:00 | comment | added | PG1995 | Thank you for the help! Just curious, I remember that yesterday I saw another answer to my question mentioning something about gravitational potential. I checked it on my phone and couldn't even read it carefully. Wonder where it went?! | |
| Feb 26, 2022 at 17:19 | history | answered | Thomas | CC BY-SA 4.0 |
