
#1
Nov1208, 08:53 PM

P: 20

Hi,
Is it true that the standard gravitational parameter of an object (G*M) is more accurately known than the the gravitational constant (G)? If so, why? Any references would be much appreciated. Thanks, San 



#2
Nov1208, 09:04 PM

Mentor
P: 14,456

Yes, its true. We can measure the standard gravitational parameter of some object by observing other objects orbits about the object in question. With hundreds of years of observing planets in orbit about the Sun, we have the standard gravitational parameter for the Sun nailed down extremely well (11 significant digits). We know the standard gravitational parameter for the Earth to 9 or 10 significant digits. While we can measure G*M very precisely, untangling G (or M) from G*M is a much harder task. We only know G to 4 or 5 significant digits.




#3
Nov1208, 11:12 PM

P: 2,265

i think what this also means (and i dunno which is cause and effect) is that we don't know the mass of the earth precisely. i know it's true that G*M is known to 10 digits and that G only to 5 (by measurement with a Cavendishlike experiment) but i find it unexpected that knowing the dimensions and composition of the Earth well, of the mutual orbit of these (unequal) twin planets around their common center of gravity, that with years of astronomical observation of the Moon, that we wouldn't have gotten that more precisely.




#4
Nov1308, 01:26 AM

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P: 15,601

standard gravitational parameter
Why do you think we know the composition of the earth well? (Better than 10 parts per million, which is what 5 digits of accuracy means) Most of it is underground. :)




#5
Nov1308, 07:26 AM

Mentor
P: 14,456




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