What if gravity worked differently?

[Zanket]

Anyone know how Galileo explained the fact that a large heavy rock fell at the same rate as a small light rock?

That's in Epstein's book. The large heavy rock comprises pieces each the size of the small light rock, so all must fall at the same rate.

 

[JesseM]

That's in Epstein's book. The large heavy rock comprises pieces each the size of the small light rock, so all must fall at the same rate.

Would this argument give the wrong conclusion when thinking about objects falling through a liquid though? Since the buoyancy force is not proportional to the mass of the object but only to the volume, wouldn't two balls of the same shape and volume but different masses fall through a liquid at different rates?

 

[yogi]

But Jesse - the insight that is revealed is that in a vacuum, Galileo found a very simply explanation that didn't involve the mathematics of combining G with F = ma
I think there is a big lesson to be learned by his logic - its actually quite profound - and it escaped the greatest minds of science since Aristotle who pronounced with certainty that the heavier object would fall faster - and everyone bought into it for nearly 2000 years.

 

[JesseM]

But Jesse - the insight that is revealed is that in a vacuum, Galileo found a very simply explanation that didn't involve the mathematics of combining G with F = ma

But the point is that in Galileo's time no one knew how gravity worked in a vacuum, or even whether space was a true "vacuum" at all. It's logically possible that more massive objects could fall faster than less massive ones, as demonstrated by the fact that they do just that in a fluid, so his thought-experiment, which purports to show that it isn't possible, must be flawed.

 

[Zanket]

Would this argument give the wrong conclusion when thinking about objects falling through a liquid though?

It seems it would. I don't know how Galileo reconciled his argument with that.

 

[yogi]

So does any other explanation - air friction, water friction, whatever, is not involved in Galileo's conception... just as the equating of Inertial force To G force won't give you an accurate measure of the fall time in a liquid.

 

[JesseM]

So does any other explanation - air friction, water friction, whatever, is not involved in Galileo's conception..

That's irrelevant, all that matters is that it's logically possible the gravitational force would pull different masses at different speeds, even without friction from any medium. It doesn't work that way in the real world, but logically there's no reason it couldn't. Instead of the gravitational force on an object being proportional only to its mass, it could be proportional to (mass - volume), for example, in which case there'd be something analogous to the buoyancy term even in the absence of any medium.