Where would the greatest amount of gravitational force produced between two planets, perse earth and mars as per Newton's universal gravitation? I am thinking at the centre of both planets? what would the answer be with reasoning - thanks in advance!
Well the question you ask is not particularly well defined but I will help with what I have understood of it. If we consider Earth and Mars as isolated systems and you are on either of them, then you would feel the strongest force when you are in the center of mass of both the planet and yourself (i.e. r = 0 for F = GMm/r^2) - the strength of the gravitational field would be infinite. Hence, as more and more systems are added, it is highly possible that you would experience an infinitely powerful gravitational force.
But this is obviously not true, because that would mean every time you dig towards the COM, when you are very close to it you would be obliterated, and hence this infinite strength of gravity a particularly difficult concept to get around. To know a bit more about why you dont get crushed when you are close to the earth's core due to gravity alone (where "you" are resistent to the usual extreme temperatures and pressures) is to look at Shell's theorem. Hope this helps and that I haven't confused you even more
