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Buzz Bloom
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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:
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.
From http://arxiv.org/pdf/1507.07956v1.pdf
and http://physics.nist.gov/cgi-bin/cuu/Value?bg|search_for=gravity
The calculations:
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.
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 π2 R3 / T2
From http://arxiv.org/pdf/1507.07956v1.pdf
and http://physics.nist.gov/cgi-bin/cuu/Value?bg|search_for=gravity
G = 6.67408 × 10-11 m3 / s2 kg
From http://asa.usno.navy.mil/static/files/2016/Astronomical_Constants_2016.pdf M = 5.9722 × 1024 kg
From http://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.htmlR = 384,400,000 m
andP = 655.728 hrs = 2,360,620.8 s
The calculations:
GM = 3.985894 × 1024 m3 / s2
and4 π2 R3 / T2 = 4.023995 × 1024 m3 / s2
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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