Stupid question, bowling balls don't fit through the vacuum's hose.

So will the bowling ball gravitationally attract the earth to itself there by reach the earth an infinitesimally small amount?

This argument is deeply flawed when applying classical Newtonian physics. You have two issues:

1. Acceleration of a system is caused by a sum of forces or a net force, not individual forces. To claim that the Earth accelerates differently due to two different forces is an incorrect application of Newton's second law. If you drop a bowling and feather in a vacuum, then both the feather and the bowling ball will be pulling on the Earth simultaneously. The Earth's acceleration would be the same towards both the bowling ball and the feather, because we would consider both the force of the feather on the Earth and the force of the bowling ball on the Earth when calculating the acceleration of the Earth.
2. You present this notion that two different systems can accelerate at 9.81 m/s/s towards Earth according to an observer standing on the surface of Earth; but when you place an observer on either surface of the two systems, Earth is accelerating at a different rate. This is classically impossible. If two systems are accelerating at 9.81 m/s/s towards Earth, then Earth must be accelerating 9.81 m/s/s towards both systems too.

Brian Cox shows ball and feathers falling together in vacuum: https://youtu.be/E43-CfukEgs

But what weighs more:

A ton of bowling balls or a ton of feathers? 🤔

There’s too many words in this meme that’s making me dizzy from all your fancy science leechcraft, wizard.

I reject your reality and substitute my own: the feather falls faster. It’s more streamlined than the bowling ball, and thus it slips through the vacuum much faster and does hit the ground and stay on the ground, I think. The ball will bounce at least once, maybe even three times. On each bounce, parts of it probably break off, which change the weight. Thankfully those broken pieces won’t hurt anyone because they’re sucked up by the vacuum. Thus, rendering your dungeon wizard spells ineffective against me.

Why your spoiler is wrong:

The gravitational force between two objects is G(m1 m2)/r²

G = ~6.67 • 10^-11 Nm²/kg²

m1 = Mass of the earth = ~5.972 • 10^24 kg

m2 = Mass of the second object, I'll use M to refer to this from now on

r = ~6378 • 10^3 m

Fg = 6.67 • 10^-11^ Nm²/kg² • 5.972 • 10^24^ kg • M / (6378 • 10^3 m)² = ~9.81 • M N/kg = 9.81 • M m kg / s² / kg = 9.81 • M m/s² = g • M

Since this is the acceleration that works between both masses, it already includes the mass of an iron ball having a stronger gravitational field than that of a feather.

So yes, they are, in fact, taking the same time to fall.

This would make a good "What if?" for XKCD. In a frictionless vacuum with two spheres the mass of the earth and a bowling ball how far away do they need to start before the force acting on the earth sized mass contributes 1 Planck length to their closure before they come together? And the same question for a sphere with the mass of a feather.

Depends on the color of the feather and the ball.

There's a simple explanation.

If anyone's wondering, I used to be a physicist and gravity was essentially my area of study, OP is right assuming an ideal system, and some of the counter arguments I've seen here are bizarre.

If this wasn't true, then gravity would be a constant acceleration all the time and everything would take the same amount of time to fall towards everything else (assuming constant starting distance).

You can introduce all the technicalities you want about how negligible the difference is between a bowling ball and a feather, and while you'd be right (well actually still wrong, this is an idealised case after all, you can still do the calculation and prove it to be true) you'd be missing the more interesting fact that OP has decided to share with you.

If you do the maths correctly, you should get a=G(m+M)/r^2 for the acceleration between the two, if m is the mass of the bowling ball or feather, you can see why increasing it would result in a larger acceleration. From there it's just a little integration to get the flight time. For the argument where the effect of the bowling ball/feather is negligible, that's apparent by making the approximation m+M≈M, but it is an approximation.

I could probably go ahead and work out what the corrections are under GR but I don't want to and they'd be pretty damn tiny.

But ... Steel is heavier than feathers ...

Reading that spoiler, I hate scientists sometimes.

“In our limited language that tries to describe reality and does so very poorly, how would you describe this situation that would literally never happen?”

Obviously the bowling ball because it's more MASSIVE.

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.

the feather falling toward the earth will also be attracted to the bowling ball (which is on the earth)

doesnt offset, because the feather-ball attraction is not as large as the earth-ball. just wanted to say

uhmmm ackchshickzually, it's the space-time that's falling

This may be a stupid question, but: assuming an object (the bowling ball) is created from materials found on Earth and that it remains within the gravity well of Earth from material procurement stage to the point where it is dropped, wouldn't the acceleration of the Earth towards the object be kind of a null considering the whole timeline of events? I mean, I get the distinction of higher mass objects technically causing the Earth to accelerate towards them faster if we're talking a feather vs a bowling ball that both originated somewhere else before encountering Earth's gravity well in a vacuum, it just seems kind of weird to consider Earth's acceleration towards objects that are originating and staying within its gravity well?

So obviously I ended up in the middle of this bell curve. How would that cause the perception of the ball's acceleration to differ?