6.67 x 10<sup>-11</sup>?
I think newton got it the same way as how planck got his constant.. using some strange technique.
Here's how they do it. They draw a paper with numbers 0, 1 , 2 , 3 , 4 , 5 all the way til 9. They then hold a pen, close their eye, and just move the pen / inkpen all the way through the page. The numbers that were crossed by the line were then taken.
Einstein must have gone through many 0s, and got a surprisingly small number. Because of this "phenomena", he thinks the number is special. It turns out it fits with all the motion equations.
Im not sure about planck, but this is a rumor i heard from a very trustworthy person.