Easy physics puzzles

I just realized it's 10^-18 and 10^-17 ,,,, -18 &-17 , not 18 & 17. Sorry

yes I think it is never really explained that if the 'falling' objects are really massive , everything changes
So it makes sense that the effect on even small objects is there even if tiny, it actually is a little unsettling to me to think the 'inertia' perfectly cancelled it all out

Quote: aceside

Don’s consideration is very thorough; however, Earth is not a perfect sphere, so gravity at North Pole is very different from that at the Equator. Moreover, gravity is a field, so the equations you use are just a good approximation.
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Don's more massive ball still reaches the ground first (by a tiny fraction of a second) no matter where on Earth he stands. Einstein's general theory of relativity also has no relevance and no effect on the solution to this puzzle.

"gravity at North Pole is very different from that at the Equator" The accuracy of that statement would be improved by omitting the word "very".

I have climbed to the summit of Cotopaxi (almost 20,000 ft above sea level) in Ecuador (on the equator) and I can assure you that the weight of my backpack was not noticeably lighter than it was at home in Tennessee.

I guess Don overstretched this problem. I haven’t checked if his calculation is correct or not, but the gravitational acceleration on Earth is approximately 9.81 m/s^2. It’s dangerous to question this number.

Quote: odiousgambit

10^17 vs 10^18 is an order of magnitude so how is that "not by much"?...... and are you saying Galileo was wrong?
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"Not by much" in absolute terms.

Technically, Galileo was wrong, although in real world experiments, you have to take not only things like air resistance into account, but also, is the distance that each object falling the same? Put a grain of sand on the ground directly underneath the lighter object, and it will get to the ground first. Also, if the objects aren't the same shape, the centers of mass aren't the same distance from the center of Earth. In the general sense, Galileo was correct - as far as can be observed, two objects of different sizes will fall at the same velocity.

Here's a bonus problem that I have not worked out yet; again assuming the only forces are gravity between Earth and the objects, from how high would they have to be dropped before the heavier one lands one microsecond (0.000001 second) before the other? The problem here is, as the balls drop, r in the equation changes, so it's probably not a straightforward integral.