Quote:
Originally Posted by Robh
I am inclined to Alex's view here. That two bodies do not in fact fall with the same acceleration. Consider this case (mind games)...
The Earth is "dropped" into the Sun, it falls into the Sun in a manner largely dependent on the mass of the Sun. One zapped Earth.
A star of 100 solar masses is "dropped" into the Sun. The Sun accelerates towards the large star in a manner more dependent on the large star's mass. One zapped Sun.
Now consider some maths.
F = GMm/r^2 is the force between two bodies mass M and m.
What is the acceleration of m towards M?
F = ma1 = GMm/r^2
a1 = GM/r^2
However, there is also an acceleration of M towards m.
F = Ma2 = GMm/r^2
a2 = Gm/r^2
Does this not mean the combined acceleration is in fact
a1+a2 = GM/r^2+Gm/r^2 = G(M+m)/r^2
For a small body m, the acceleration would approximate to GM/r^2 without measurable difference. However, for larger bodies e.g. m = M the acceleration will increase substantially.
Regards, Rob.
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The forces on the two bodies are equivalent. Newton's third law in action.
Regards
Steven