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In Wikipedia section about the Perihelion precession of Mercury, we have the follwing table titled "Sources of the precession of perihelion for Mercury":

Amount (arcsec/Julian century) Cause
532.3035 Gravitational tugs of other solar bodies
0.0286 Oblateness of the Sun (quadrupole moment)
42.9799 Gravitoelectric effects (Schwarzschild-like), a General Relativity effect
−0.0020 Lense–Thirring precession
575.31 Total predicted (*)
574.10±0.65 Observed

Two things caught my eyes which I failed (maybe I was misunderstanding/reading the text) to find explanation for in the text:

  1. It seems that there is still gap between the prediction to the observed precession of at least 0.5 arcsec per century (575.31 - 574.75). Why is that? it it observation issue, if so:
  2. What does the ± account for? is it different values between the centuries or rather observation resolution?

As far as I understand, resolution of 0.5arcs can be easily distinguishable today (say even 0.05 arcsec in 10 years) - so there appear to be a gap between the prediction and observation - a theory gap? Or does it stems from the the uncertainty of accuracy of the Mercury-Sun distance which is to such an extent to cause 0.5arcs sec movement in aphelion in 100 years? or something else?


(*) A more detailed reference to the prediction (from which the figure was taken from Wikipedia) with uncertainties can be found at Park, Ryan S.; et al. (2017). "Precession of Mercury's Perihelion from Ranging to the MESSENGER Spacecraft". The Astronomical Journal. 153 (3): 121. enter image description here

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  • $\begingroup$ Do your sources also give error estimates for the (absoute) contribution of each effect? I expect that these might add up to the observed difference (especially as it is in arcseconds / century) $\endgroup$ May 3 at 9:09
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    $\begingroup$ @planetmaker, I have added the source. it is 0.0015 per century. apparently not enough. Wikipedia also has reference to the observed figure, but unfortunately it seems I don't have access to this paper. $\endgroup$
    – d_e
    May 3 at 9:46
  • $\begingroup$ There doesn't actually look like a discrepancy to me, because the difference is less than 2 sigmas, well below the threshold (5 sigma) to claim a discrepancy. $\endgroup$
    – Allure
    May 3 at 10:25
  • $\begingroup$ The abstract of Park et al. says the precession of Mercury is measured to be 575.3100 +/- 0.0015 arcsec/cy. This is then used to estimate the uncertain theoretical parameters (quadrupole moment, post-Newtonian parameters). $\endgroup$
    – ProfRob
    May 3 at 12:03

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Though Wikipedia writes: "The total observed precession of Mercury is 574.10″±0.65 per century[12] relative to the inertial ICRF", its source is from Clemence, G. M. (1947). "The Relativity Effect in Planetary Motions". Reviews of Modern Physics. Which is quite old article.

The figure of 575.31, on the other hand, is from much recent article (Park, Ryan S.; et al. (2017). "Precession of Mercury's Perihelion from Ranging to the MESSENGER Spacecraft". The Astronomical Journal. 153 (3): 121.). This paper, to the extent I understand, basically shows a match between the prediction (with improved breakdown of the causes) and the observation (emph. mine):

Conclusion: We have processed the MESSENGER ranging data as a part of JPL’s planetary ephemeris development process... . We also estimate the total precession rate of Mercury’s perihelion of (575.3100 ± .0015)″/century that corresponds to our solution and provide estimated contributions and uncertainties due to various perturbing effects.

Moreover, Older version of this Wikipedia article shows this table instead:

enter image description here

In this table there is match between predication and observation, as - if I understand - appears in Clemence, G. M. (1947).

So with the recent 2017 data, an edit was made on Wikipedia page, but it only modified the causes and not the observed figure and thus causing this mismatch (though, as Allure points out in a comment, is only about 2 sigmas; and hence still works; but again the sentence from Wikipedia above is somewhat misleading because it gives the impression that 574.10″±0.65 is a much recent value - hence I was somewhat surprised by this ±0.65 to be high for modern value and did not fully understood what it means. Now it is clear.) . For what I was able to gather from other sources the observed figure of the precession is indeed 575 arcsec per century.

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