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Hello I need some help understanding Newtons universal gravitation. I read on a site that an objects Force on earth is its mass x gravity(on earth) hence MG (like F=MA). Then they say using newtons inverse square law that the same object at a distance of the moon would have the force(g) MG/distance to moon² and so it would be that much weaker.

Now with the universal gravitation between two masses we know F=GxM1xM2/R²

my questions are how did newton come to this conclusion?, what is the inverse square law?, and why are the two masses multiplied not added? I'm a little confused about this the only answer I can come up with is:

say we have the first equation they talked about F=MG (g for gravity on earth) if we substitute G with its components M x Gravitational constant we get two seperate masses mass 1 for the object and mass 2 for the earth and we also get G (grav. const.) so thats our GxM1xM2, now divide that by the square of the distance between them and we get the answer. Is that even close? can anyone answer where this equation comes from?