Nope. The argument only works if you conjured the bowling ball and feather out of ~~thin air~~ vacuum. https://lemmy.world/comment/13237315 discusses what happens when the objects were lifted off earth.
I didn’t think about that! If the object was taken from earth then indeed the total acceleration between it and earth would be G M_total / r^2, regardless of the mass of the object.
Okay how about now
fixed it sorry
I meant cross-section area, not surface area. Sorry. Edited my comment above.
If your bowling ball is twice as massive, the force between it and earth will be twice as strong. But the ball’s mass will also be twice as large, so the ball’s acceleration will remain the same. This is why g=9.81m/s^2 is the same for every object on earth.
But the earth’s acceleration would not remain the same. The force doubles, but the mass of earth remains constant, so the acceleration of earth doubles.
Here’s a problem for y’all: how heavy does an object have to be to fall 10% faster than g? Just give an approximate answer.
Even in a perfect vacuum the bowling ball still falls faster. See my comment sibling to yours.
Yes, the earth accelerates toward the ball faster than it does toward the feather.
A feather has smaller cross-section area than a bowling ball. But drag acceleration is proportional to the cross-section area divided by the mass (and this quantity is indeed smaller for the bowling ball).
Anyway the hypothetical scenario in this meme is a perfect vacuum. Check my other comments to see why it still works.
Tap for spoiler
The bowling ball isn’t falling to the earth faster. The higher perceived acceleration is due to the earth falling toward the bowling ball.
cross-posted from: https://lemmy.ml/post/19504984
It's all relative
cross-posted from: https://hexbear.net/post/3062545
Important history
I saw a few math memes so I figure these are allowed here
Re your first point: I was imagining doing the two experiments separately. But even if you do them at the same time, as long as you don’t put the two objects right on top of each other, the earth’s acceleration would still be slanted toward the ball, making the ball hit the ground very very slightly sooner.
Re your second point: The object would be accelerating in the direction of earth. The 9.81m/s/s is with respect to an inertial reference frame (say the center of mass frame). The earth is also accelerating in the direction of the object at some acceleration with respect to the inertial reference frame.