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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)?

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  • $\begingroup$ Why do you think Mercury's 3:2 tide-locking would be to its theoretical Newtonian orbit, instead of its actual orbit? $\endgroup$
    – notovny
    Jun 29 at 19:20
  • $\begingroup$ @notovny Why is that? $\endgroup$ Jun 29 at 19:27
  • $\begingroup$ "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. $\endgroup$
    – PM 2Ring
    Jun 30 at 4:23
  • $\begingroup$ @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? $\endgroup$ Jun 30 at 4:43
  • $\begingroup$ 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. $\endgroup$
    – PM 2Ring
    Jun 30 at 5:00
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The general relativistic contribution to the precession of Mercury's orbit 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.

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  • $\begingroup$ So when Newton had lived 3 million years he could have realized he made a mistske? $\endgroup$ Jun 29 at 19:40
  • $\begingroup$ 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. $\endgroup$ Jun 29 at 20:02
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    $\begingroup$ @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. $\endgroup$ Jun 29 at 20:06
  • $\begingroup$ I accept again! $\endgroup$ Jun 29 at 20:09
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    $\begingroup$ @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. 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. $\endgroup$
    – PM 2Ring
    Jun 30 at 13:43

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