B How Has the Calculation of Solar System Body SGPs Evolved Over Time?

[GregM]

TL;DR Summary

history of standard gravity parameter measurements

does anyone have a good reference on the history of calculating the standard gravity parameters of solar system bodies? My guess is a rough estimate of Jupiter's SGP can be gained from observing the motion of its moons, in which case the first estimates could have been made soon after Newtonian theory had made SGPs pertinent to astronomy. Or maybe the estimates were already there in an rearrangement in the numbers gained from Galilean observations around 1610.

 

[Drakkith]

It's likely that scientists first determined the gravitational constant and then used that to determine the mass of the Sun, Moon, and planets. From those two values you can get the SGP by multiplying them together. As far as I am aware, the first semi-accurate measurement to determine the gravitational constant (actually the density of the Earth, from which you can get the constant) was the Schiehallion experiment of 1774. This found the density of the Earth to be about 4500 kg/m³, about 20% off from the modern value of 5515 kg/m³.

Jupiter's mass was calculated at various times afterward. Here is George Biddell Airy's article from 1833 in the Memoirs of the Royal Astronomical Society, Vol. 6, p.83 in which he determines the mass of Jupiter by observing the orbit of its 4th satellite. He seems somewhat aghast that various measurements had differed widely up to that point and that no one had lately tried to reconcile them properly. I'm not actually certain what value he obtained, as he states it in a way I've never seen before. Something about a logarithm of the mass.

 

[Vanadium 50]

GM is known far better for the planets than G or M. (Indeed, M is essentially unknown directly - it's actually (GM)/G )

 

[Drakkith]

GM is known far better for the planets than G or M. (Indeed, M is essentially unknown directly - it's actually (GM)/G )

Ah I wasn't aware of this. A little more reading of the wiki article gives me this:
Thus only the product of G and M is needed to predict the motion of the smaller body. Conversely, measurements of the smaller body's orbit only provide information on the product, μ, not G and M separately. The gravitational constant, G, is difficult to measure with high accuracy,[12] while orbits, at least in the solar system, can be measured with great precision and used to determine μ with similar precision.

Very interesting.