<p>The general relativistic contribution to the <a href="https://en.wikipedia.org/wiki/Tests_of_general_relativity#Perihelion_precession_of_Mercury" rel="nofollow noreferrer">precession of Mercury's orbit</a> is 43 arc seconds per century. Since a complete circle has <span class="math-container">$360 \times 60 \times 60 = 1296000$</span> arc seconds, this means it will take approximately 30140 centuries (about 3 million years) for there to be one extra full precession cycle due to GR effects.</p>

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2021-06-29T19:40:41.727Z
So when Newton had lived 3 million years he could have realized he made a mistske?
Deschele Schilder
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2021-06-29T20:02:30.063Z
So if you divide 1296000 by 43 you get about 30 000. Then multiply by 100 and you get  3000 000 days. About 10 000 years.
Deschele Schilder
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2021-06-29T20:06:29.307Z
@DescheleSchilder it's 43 arc seconds *per century*, so it's 30,000 *centuries* (as I noted in my answer). Which is about 3 million years.
Peter Erwin
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2021-06-29T20:09:49.960Z
I accept again!
Deschele Schilder
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2021-06-29T22:01:38.303Z
Does an extra single full precession cycle imply an extra single rotation?
Connor Garcia
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2021-06-29T22:18:45.770Z
@ConnorGarcia Yes, one rotation of the long axis of the orbit.
Peter Erwin
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2021-06-30T05:15:47.187Z
FWIW, using that figure from Wikipedia, the total precession period is 225,750 ± 250 years.
PM 2Ring
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2021-06-30T08:01:26.823Z
@PM2Ring Good point; I’ve updated the link to point to the Wiki article instead.
Peter Erwin
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2021-06-30T08:38:07.807Z
@PeterErwin Dòesnt it take about    
  225 000 years then for an extra rotation? Or is Wikipedia wrong?
Deschele Schilder
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2021-06-30T13:43:00.467Z
@Deschele That Wikipedia data comes directly from [Park, Ryan S.; et al. (2017). "Precession of Mercury's Perihelion from Ranging to the MESSENGER Spacecraft". The Astronomical Journal](https://doi.org/10.3847%2F1538-3881%2Faa5be2). So it's probably pretty good. ;) Newtonian gravity gives Mercury one precession cycle per ~243,460 years. General relativity speeds up the precession, so we get one *extra* precession cycle per 3 million years, giving the total observed precession cycle that I mentioned previously.
PM 2Ring
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2021-06-29T19:37:13.400Z
2021-06-30T08:00:02.140Z
2021-06-30T08:00:02.140Z
Peter Erwin
<p>It is well known that Mercury orbits slightly differently from a pure Newtonian orbit. Every year a slight deviation is found.</p>
<p>Now if we observe a lot of these orbits then Mercury should at one point have rotated an extra round around its axis. Has Mercury already made enough voyages around the Sun for this to become apparent?</p>
<p>Is this simply 360 degrees divided by 43 seconds? It takes about 80 days for Mercury to make one rotation so you have to multiply it by this number.</p>
<p>Is the extra rotation observed (or part of it)?</p>

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2021-06-29T19:20:15.273Z
Why do you think Mercury's 3:2 tide-locking would be to its theoretical Newtonian orbit, instead of its actual orbit?
notovny
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2021-06-29T19:27:33.873Z
@notovny Why is that?
Deschele Schilder
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2021-06-30T04:23:48.493Z
*"Mercury should at one point have rotated an extra round around its axis."* We (normally) measure the perihelion precession of a planet's orbit relative to the stars, not relative to the planet's rotation on its axis.
PM 2Ring
CC BY-SA 4.0
2021-06-30T04:43:22.567Z
@PM2Ring  If Newton had lived 3 million years and knew the rotatiòn and orbit time exactly ( by a wonder measuring device and absolute calculus ability) would he notice a difference after say a million years, between prediction and observatio? Or does the defìnitio of the rotation (as normally used) prohibit this?
Deschele Schilder
CC BY-SA 4.0
2021-06-30T05:00:49.977Z
Sorry @Deschele, I don't get the point of that question. The anomaly in Mercury's precession was observed over 160 years ago, we didn't have to wait a million years to notice it.
PM 2Ring
CC BY-SA 4.0
2021-06-30T05:03:25.547Z
BTW, we have (at least) 3 different rotations involved in this question: Mercury's rotation on its axis (1 Mercury day), its revolution around the Sun (1 Mercury year), and the rotation of the major axis of its orbit (the apsidal precession). So when you use the word "rotation" you have to make sure that it's clear which rotation you mean.
PM 2Ring
CC BY-SA 4.0
2021-06-30T05:31:23.060Z
@PM2Ring Its more complicated than at first sight!
Deschele Schilder
CC BY-SA 4.0
2021-06-30T05:52:37.803Z
Yes, it is! There are also two other types of precession. See [here](https://en.wikipedia.org/wiki/Precession#Astronomy). I get dizzy if I try to visualise the combined effect of all of these different rotations. :)
PM 2Ring
CC BY-SA 4.0
2021-06-30T06:05:18.893Z
@PM2Ring All these rotations... Dazzling...;)
Deschele Schilder
CC BY-SA 4.0
2021-06-30T08:47:11.407Z
@PM2Ring I see what you mean by a previous comment. The divergent behavior was indeed already seen by looking at the orbit. But looking at the rotation only you dont have to take other planets into consideration. What would Newton have concluded if he could see the extra rotation (if if if...)?
Deschele Schilder
<orbit><rotation><general-relativity><mercury>
When will Mercury have rotated an extra round around its axis?
Deschele Schilder
# When will Mercury have rotated an extra round around its axis?

(Asked by: username_0 on 2021-06-29)

It is well known that Mercury orbits slightly differently from a pure Newtonian orbit. Every year a slight deviation is found.

Now if we observe a lot of these orbits then Mercury should at one point have rotated an extra round around its axis. Has Mercury already made enough voyages around the Sun for this to become apparent?

Is this simply 360 degrees divided by 43 seconds? It takes about 80 days for Mercury to make one rotation so you have to multiply it by this number.

Is the extra rotation observed (or part of it)?

**Tags:** orbit, rotation, general-relativity, mercury
> **Comments:**
> **username_1**: Why do you think Mercury's 3:2 tide-locking would be to its theoretical Newtonian orbit, instead of its actual orbit?  
> **username_0**: @notovny Why is that?  
> **username_2**: *"Mercury should at one point have rotated an extra round around its axis."* We (normally) measure the perihelion precession of a planet's orbit relative to the stars, not relative to the planet's rotation on its axis.  
> **username_0**: @PM2Ring  If Newton had lived 3 million years and knew the rotatiòn and orbit time exactly ( by a wonder measuring device and absolute calculus ability) would he notice a difference after say a million years, between prediction and observatio? Or does the defìnitio of the rotation (as normally used) prohibit this?  
> **username_2**: Sorry @Deschele, I don't get the point of that question. The anomaly in Mercury's precession was observed over 160 years ago, we didn't have to wait a million years to notice it.  
> **username_2**: BTW, we have (at least) 3 different rotations involved in this question: Mercury's rotation on its axis (1 Mercury day), its revolution around the Sun (1 Mercury year), and the rotation of the major axis of its orbit (the apsidal precession). So when you use the word "rotation" you have to make sure that it's clear which rotation you mean.  
> **username_0**: @PM2Ring Its more complicated than at first sight!  
> **username_2**: Yes, it is! There are also two other types of precession. See [here](https://en.wikipedia.org/wiki/Precession#Astronomy). I get dizzy if I try to visualise the combined effect of all of these different rotations. :)  
> **username_0**: @PM2Ring All these rotations... Dazzling...;)  
> **username_0**: @PM2Ring I see what you mean by a previous comment. The divergent behavior was indeed already seen by looking at the orbit. But looking at the rotation only you dont have to take other planets into consideration. What would Newton have concluded if he could see the extra rotation (if if if...)?  

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## 1 answers

### Answer by username_3 on 2021-06-29. Score: 3 | Accepted answer

The general relativistic contribution to the [precession of Mercury's orbit](https://en.wikipedia.org/wiki/Tests_of_general_relativity#Perihelion_precession_of_Mercury) is 43 arc seconds per century. Since a complete circle has $360 \times 60 \times 60 = 1296000$ arc seconds, this means it will take approximately 30140 centuries (about 3 million years) for there to be one extra full precession cycle due to GR effects.

> **Comments:**
> **username_0**: So when Newton had lived 3 million years he could have realized he made a mistske?  
> **username_0**: So if you divide 1296000 by 43 you get about 30 000. Then multiply by 100 and you get  3000 000 days. About 10 000 years.  
> **username_3**: @DescheleSchilder it's 43 arc seconds *per century*, so it's 30,000 *centuries* (as I noted in my answer). Which is about 3 million years.  
> **username_0**: I accept again!  
> **username_4**: Does an extra single full precession cycle imply an extra single rotation?  
> **username_3**: @ConnorGarcia Yes, one rotation of the long axis of the orbit.  
> **username_2**: FWIW, using that figure from Wikipedia, the total precession period is 225,750 ± 250 years.  
> **username_3**: @PM2Ring Good point; I’ve updated the link to point to the Wiki article instead.  
> **username_0**: @PeterErwin Dòesnt it take about       225 000 years then for an extra rotation? Or is Wikipedia wrong?  
> **username_2**: @Deschele That Wikipedia data comes directly from [Park, Ryan S.; et al. (2017). "Precession of Mercury's Perihelion from Ranging to the MESSENGER Spacecraft". The Astronomical Journal](https://doi.org/10.3847%2F1538-3881%2Faa5be2). So it's probably pretty good. ;) Newtonian gravity gives Mercury one precession cycle per ~243,460 years. General relativity speeds up the precession, so we get one *extra* precession cycle per 3 million years, giving the total observed precession cycle that I mentioned previously.  

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