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I'am looking two references:

  1. Williams George E. 1998. Precambrian tidal and glacial clastic deposits: implications for Precambrian Earth-Moon dynamics and palaeoclimate. Sedimentary Geology 120 (1998) 55-74.

(copy partly below) On page 62:

"Table 1. Palaeotidal and palaeorotational values for Neoproterozoic clastic tidal rhythmites and modern values.

Lunar day / synodic month. Modern 28.53"

  1. Espenal Fred, NASA's GSFC. Eclipses and the Moon's Orbit. NATIONAL AERONAUTICS AND SPACE ADMINISTRATION. https://eclipse.gsfc.nasa.gov/SEhelp/moonorbit.html

(copy partly below 27.9.2024)

"4.3 Anomalistic Month. ... In comparison, the longest anomalistic months take place when the difference in longitude passes through 0 degree or 180 degree. The line of apsides is then directed towards or away from the Sun. The maximum duration of the anomalistic month is then about 28.5 days (1.0 day longer than the mean 27.55455 days). The Earth-Sun distance also influences the anomalistic month by causing greater extremes near perihelion. This currently occurs in early January each year."

Q. Is this longest anomalistic month, 1.0 day longer than the mean (27.55455 days), also always 1.0 day longer than the mean (now not 27.55455 days) on GEOLOGIC TIME SCALE?

Best Regards, Hannu Poropudas

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  • $\begingroup$ The Moon's orbit was smaller half a billion years ago. It was probably also more eccentric. And the day length was shorter, too. $\endgroup$
    – PM 2Ring
    Commented Sep 27 at 8:54
  • $\begingroup$ Ref. 3. Williams G E 2000. Geological constraints on the precambrian history of Earth's rotation and the Moon's orbit. Reviews of Geophysics, 38, 1/February 2000 pages 37-59. on page 50 Table 1. Paleotidal and Paleorotational Values for Precambrian Cyclic Rhythmites and Modern Values: (Lunar days + 1 day ) per synodic month = Solar days per synodic month ? at points 2450 Ma, 900 Ma and 620 Ma ago ??? $\endgroup$
    – Hannu Poropudas
    Commented Sep 28 at 7:28
  • $\begingroup$ Runcorn's formula: 1/T - 1/T' = 1/Y, Y=365.2422 days, T=length of sideral month, T'=length of the month recorded by marine life (=synodic month). No formula for length of lunar month. $\endgroup$
    – Hannu Poropudas
    Commented Sep 30 at 9:02
  • $\begingroup$ The term "lunar month" is ambiguous. There are several types of lunar month. Chapront-Touzé and Chapront give formulae for the changes in the lengths of the various lunar months, but those formulae are only valid for timespans of centuries, maybe a few millenia, not the huge timespans you're asking about. $\endgroup$
    – PM 2Ring
    Commented Sep 30 at 9:32
  • $\begingroup$ Ref. 4. Runcorn S. K. 1970. Paleogeophysics. 518 pages, pp. 17-23, page 21. Second Runcorn's formula: 1/t - 1/t' = 1/Y, t= length of sideral day, t'= length of the day recorded by marine life (=solar day), Y=length of the year (=tropical year, this is assumed to be constant = 365.2422 days = not changed significantly). S = T'/t' = niumber of days in month recorded in paleontological specimens. $\endgroup$
    – Hannu Poropudas
    Commented Oct 1 at 7:50

1 Answer 1

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Is this longest anomalistic month, 1.0 day longer than the mean?

No. Espanak should have written "about 1.0 days" rather than "1.0 days". Then again, he did use the word "about" just before that. That this is not exact even over a 2008 to 2010 as can be seen in image below.

Plot of length of anomalistic month for 2008-2010 (plus some additional curves on the same plot)
Source: Eclipses and the Moon's Orbit.
Fred Espanak grants permission to use images generated by him at https://www.eclipsewise.com with caveats. One his that he wants credit. This image was created by Fred Espanak.

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