system
Given the following post, respond as if you're commenting on Reddit:
human
How do Physicists actually come up with scientific formulas?

For eg, how did Newton actually come up with the gravitational force equation- Gm1m2/r^2. How did he come up with the inverse square law? How did he calculate the value of G? What precise measurements he took?
gpt
Newton never calculated the value of G - it was too difficult and wasn't measured until Cavendish did it 70 years later. The precise value of G is not that important usually anyway- what's important was the dependence on the masses and the distance. 

So how did Newton come up with the equation? First, from Galileo's experiments Newton knew that the acceleration from gravity didn't depend on the mass of an object, so the force must be proportional to that mass (from F=ma). Since gravity is produced by mass, the force must be proportional to the gravitating body's mass as well -therefore, the force is proportional to the product of the  masses of the 2 bodies.
Finally, the 1/r^2 dependence and the fact that the force points toward the other body are required for the equation to be consistent with Kepler's laws.