Physics, Astronomy & Cosmology / Re: How did scientists measure the mass of the Earth and other planets?« on: 12/10/2018 22:33:50 »
How did scientists measure the mass of the Earth and other planets?This is actually a very good question. It is sort of a chicken/egg problem, which requires an answer to know the answer. To illustrate:
How did Newton know he'd got his maths right?
Using F = GmM/r2 you can calculate the force on a falling object of mass m in terms of M, the mass of the earth, and G, which we assume to be a universal constant.That doesn’t work. We’re trying to compute at least a rough G and M here. We don’t know either of them yet. We do know force F is 9.8 newtons for a 1KG mass. We can assume we know r. We therefore know the product of G and M, but not either separately.
As F = ma, we can measure the acceleration of a falling object or the period of a pendulum to get a value for F/mF=ma works (F 9.8 = 1 (mass) * 9.8 m/sec acceleration), but that doesn’t yield either mass of Earth M nor G, which are the two things we’re trying to determine here.
The pendulum thing is a function of acceleration (9., not of the mass of Earth. Put a pendulum in a rocket accelerating at that rate and it will have the same period as here on Earth. It tells you nothing about the mass of the Earth under you.
So the way to do it is to find an object with known mass and something detectably orbiting it at a known radius. Then G can be determined, and mass of Earth along with it. Is that how it was done??? What object possibly fits that description?