system
Given the following post, respond as if you're commenting on Reddit:
human
How was Newton's gravity equation derived if we didn't know the specific quantities involved? How could you check your math with the evidence to verify it's correct? (Such as the masses of planetary objects or the distance between them?) Said another way, how did we compute the masses of planets?

In Newton's equation for the force of gravity, he derived
F = GmM/r^2
and then that has been used to calculate, say, the masses of the planets in our solar system as well as the sun. What i don't understand is how that was able to be accomplished considering you need all of the values except for one in order to solve the equation (for a specific value).

So, for example, if I want to know the mass of the moon, I need to already know the mass of Earth, its distance to the moon, the gravitational constant as well as the force of gravity between the two! Which quantities became known first in order to figure out these things??
gpt
Newton actually didn't know the masses of the objects in the solar systems, because astronomically you can only measure GM, and he didn't know the value of G. Only like a hundred years later did someone manage to measure the gravity between two big lead balls of known mass and determine G from that; this experiment was known as "weighing the Earth" because it allowed people to find out the mass of the Earth.

What Newton did was to figure out that in general, an attraction that goes like 1/r^(2) produces elliptical orbits with the Sun at the focus. Since Kepler had already figured out that the orbits are elliptical (using Tycho Brahe's data), this gave Newton confidence that his law was right, even if he didn't know all the numbers.