Skeptics did not believe Newton’s theories of gravitation to be true, but his figures proved valid.
The radius of the Earth has been known since ancient times and the distance to the moon has also been calculated.
Therefore Newton could use these numbers in a clever way to calculate both the universal gravitation constant and the mass of the earth.
When he plugged in numbers it showed that they resulted in the period of the moon being 1/13 of a year, which is accurate.
In a similar way you can often times manipulate multiple variables using known data (like using the calculus technique of summing shells to obtain a volume) to obtain solutions.