Expert: Ahmed Salami - 8/13/2004

Question
Q.How did newton prove that the product of the masses of two bodies is directly propotional to the force and the distance between the bodies centers square is inversely propotional to the force. How did he also prove that the force applied is from the center of the body(mathematically and not experimentally)?

Answer
Hi vinod,
Concerning how he proved that that the force is at the centre, thats a bit long and you can find it in a good text.
I can't really explain what Newton actually did concerning massses but he definitely found out that the force increased as the mass did, so it was a good conclusion to consider the product. He must have performed some experiments with different masses and made the conclusion, so i don't think its really about mathematics.
As for the distance concerned, he also found out it decreased with increasing force.
Now, to tell you what i personally feel about the square in the distance. I guess he knew that the distance could be measured from anyone of the bodies and we could have negative values using a coordinate system, so squaring i guess was a good technique.
Of course i haven't said much, but i know that mathematics was only a tool to bring the findings on paper, not a direct player in the game.
I hope you would find this little talk helpful. Of course, gravitation is closely related to electrostatics. Try going over the proof of coulomb's law and you would find it really similar.
I'm always here on this and other things.
Good luck.
Regards.