I have been working on some calculations about the history of our Moon's orbit, and I have found an inconsistency with respect published value for the following four constants:(adsbygoogle = window.adsbygoogle || []).push({});

G = Universal Gravitational Constant

M = Earth's Mass

R = Moon's orbit semi-major axis

P = Moon's orbit sidereal period

From https://en.wikipedia.org/wiki/Standard_gravitational_parameter

and https://en.wikipedia.org/wiki/Elliptic_orbit

There are two different ways to calculate a value for μ.

μ = GM = 4 π^{2}R^{3}/ T^{2}

From http://arxiv.org/pdf/1507.07956v1.pdf

and http://physics.nist.gov/cgi-bin/cuu/Value?bg|search_for=gravity

G = 6.67408 × 10From http://asa.usno.navy.mil/static/files/2016/Astronomical_Constants_2016.pdf [Broken]^{-11}m^{3}/ s^{2}kg

M = 5.9722 × 10From http://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html^{24}kg

R = 384,400,000 mand

P = 655.728 hrs = 2,360,620.8 s

The calculations:

GM = 3.985894 × 10and^{24}m^{3}/ s^{2}

4 π^{2}R^{3}/ T^{2}= 4.023995 × 10^{24}m^{3}/ s^{2}

The difference between these two calculations shows an approximate error percentage of 1%. Does anyone have any explanation about why this error percentage is so large given the precision of the published values?

Can someone suggestion about how I can find relatively recent published values which will result in a better match between the two different calculations of μ?

ADDED

I just had the thought that I should adjust the value for R to be the average of the distances of the moon at apogee and perigee from the center of mass of the Earth and Moon.

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# I Inconsistencies re Astronomical constants

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