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
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.
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 Cavendish-like 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.
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. :)
That is exactly right. The uncertainty in the Earth's mass is for, all practical purposes, entirely due to the uncertainty in G. Vanadium 50 already asked the key question here. Piling on, one of the key sources of insight into the dimensions and composition of the Earth comes from remote sensing projects such as GRACE. The problem here is that these remote sensing experiments are sensitive only to the product G*M_{e}. What these observations give us insight into is the Earth's standard gravitational parameter, the Earth/Moon mass ratio, and the Sun/(Earth+Moon) mass ratio. They do not give direct insight to the Earth's mass unencumbered with G.