why do two objects fall same rate in a vacuum

[trevor borocz johnson]

Google searching why do two objects fall at the same rate in a vacuum, I found this:

 

"The mass, size, and shape of the object are not a factor in describing the motion of the object. So allobjects, regardless of size or shape or weight, free fallwith the same acceleration. In a vacuum, a beach ballfalls at the same rate as an airliner."

 

But isn't it more true that the three objects: the earth, a feather, and a cannonball, would all move toward each other in ratio to there size? So if you replace the earth with say a brick, and you put each thing at the corner of an equilateral triangle, the three objects wouldn't meet in the middle, the feather would move the most and the brick second but all three would move towards each other. Same thing with the earth, except the earth is so big it appears that the two objects fall and land at the same time, while in reality all three objects move towards each other.

[+and-then]

This one shook me a little... if you fire a bullet from a perfectly level (with the earth's surface in your location) barrel and simultaneously drop another bullet from the height of the muzzle, both will strike the round at the same time.  One may be a half-mile farther away, but they'll strike the ground at the same time.

[ChrLzs]

So, Trevor, you are quoting something you found on the Interwebz, that was simplistically worded.  And you didn't cite the reference so we cannot check the surrounding text.....

 

Sigh.

Anyway, here's a Yotube video - that's what this thread needs!!!!1111!!!!!:

 

[trevor borocz johnson]

19 hours ago, ChrLzs said:

And you didn't cite the reference

https://www.grc.nasa.gov/www/k-12/airplane/ffall.html

[Timothy]

@trevor borocz johnson, they just use the word ‘fall’ as relative to Earth. 

Yes it is just gravity doing its thang. Take away friction and that’s what happens.

Equal and opposite reaction type stuff, super basic physics.

[trevor borocz johnson]

 

[sepulchrave]

On 1/8/2018 at 2:08 PM, trevor borocz johnson said:

Google searching why do two objects fall at the same rate in a vacuum, I found this:

 

"The mass, size, and shape of the object are not a factor in describing the motion of the object. So allobjects, regardless of size or shape or weight, free fallwith the same acceleration. In a vacuum, a beach ballfalls at the same rate as an airliner."

 

But isn't it more true that the three objects: the earth, a feather, and a cannonball, would all move toward each other in ratio to there size? So if you replace the earth with say a brick, and you put each thing at the corner of an equilateral triangle, the three objects wouldn't meet in the middle, the feather would move the most and the brick second but all three would move towards each other. Same thing with the earth, except the earth is so big it appears that the two objects fall and land at the same time, while in reality all three objects move towards each other.

The quote is correct. So is your post.

Considering a "feather + Earth" system and a "cannonball + Earth" system, both the feather and the cannonball fall with the same acceleration, as mentioned in the post. In a gravitational system, the acceleration of an object is related only to the masses of the other objects, not to its own mass^[1].

Of course you are also correct; the Earth is also attracted to the other object so in the "cannonball + Earth" system, the cannonball hits the Earth slightly sooner than the feather would in the "feather + Earth" system. See the wiki on free-fall time, note how it depends on the combined mass (m₁+m₂).

_________________________

1. Of course this assumes that the weak equivalence principle is correct, i.e. that inertial mass is the same as gravitational mass. Experimentally they are equivalent to 1 part in 10¹² or less, so it seems pretty safe to conclude that they are identically equal.

[trevor borocz johnson]

3 hours ago, sepulchrave said:

Of course you are also correct; the Earth is also attracted to the other object so in the "cannonball + Earth" system, the cannonball hits the Earth slightly sooner than the feather would in the "feather + Earth" system. See the wiki on free-fall time, note how it depends on the combined mass (m₁+m₂).

 so the larger the two objects the faster they accelerate towards each other. Nice one I never thought of it like that, makes good sense though.