me said:
Shall I wikki wikki, or will you?
I did and I was wrong and you were right.
This concerned the question of whether more massive and less massive bodies fall towards Earth (say) at the same rate of acceleration. I could have sworn I saw a full and very clear refutation as per my own posts earlier, but either it was wrong or I imagined it, apparently, and everything I've turned up seems to support Galileo and humber...
...except one, which anyway relates to when two bodies are dropped
together, making three bodies with the earth:
http://paias.org/Science/Newton/Newton.htm ...wherupon the lesser mass falls very, very slightly faster, yes, you read that right, the lesser mass. I haven't read the detail yet, but how ironic if true!
However, I meant in the situation of a small mass falling to Earth and a large mass falling towards Earth, separately, without considering them as a triad.
I mistook the force, for m1 and m2 masses at distance r from Earth of mass M, as:
F = G.m1.M/r^2 and
F = G.m2.M/r^2,
like a complete idiot. In fact, I didn't bother with m2 at all. I went on to the acceleration:
a = F/m1 (which is ok, except that I assumed) ...
a = F/m2 in the second case, when of course I should have had F1 and F2 and substituted from the Law of UG above, hence, as you said, they cancel:
For m1,
a1 = F1/m1
= G.m1.M/m1.r^2
= G.M/r^2
Similarly for m2, m2 disappears from the equation,
a2 = G.M/r^2,
a1 = a2 (er, QED,

)
Not only that, but where I had before calculated the acceleration of Earth towards m1 as F/M, again it should have dawned on me that the object mass didn't appear in the equation at all, and hence the Earth would accelerate towards everything at the same rate! It should, of course, be
A1 = F1/M
= G.m1.M/M.r^2
= G.m1/r^2 ... and, in the case of m2
A2 = G.m2/r^2
Whatever we consider the object, its mass cancels out. The acceleration of it depends entirely on the other mass.
I notice you physics experts (sorry, humber, although you won that one, I'm not considering you an expert without further evidence) sat there and let me perpetrate that heresy and make a complete twit of myself into the bargain!
Right, let's see that triad situation...any thoughts anyone on whether the
lesser mass falls fastest?
