system
Given the following post, respond as if you're commenting on Reddit:
human
Is it technically inaccurate to say that objects different mass fall at the same rate in a frictionless environment? (i.e. bowling ball vs feather on the moon)

I'm not quite sure how to articulate this, however this is something that has troubled me for sometime now. Why is it that a feather and a bowling ball would fall at the same rate on the moons surface? Considering that all objects of mass in a system have gravitational effects on all other objects, wouldn't the bowling ball, having a higher mass than the feather, have a greater gravitational pull on the moon thus causing the bowling ball to impact first?
gpt
Yes, that's exactly right. However, this effect depends on pulling the moon toward the falling object, and because the moon is so much heavier, it doesn't move much. So the difference in falling times for the ball and feather, while nonzero, is very small, and so we observe approximately simultaneous impacts.

It might be interesting to try and calculate the time difference, if you have the math background.

Edit: To people saying that the bowling ball and feather do indeed fall at exactly the same rate, because F = ma: you are missing the point the OP is making. Consider that for a falling mass near the surface of a planet, we know that the mass of the planet affects the rate of acceleration of a falling object. But the laws of physics make no distinction between the planet and the object! So the mass of the object must have some impact on the falling rate (albeit a very small one). As bluebiscuit says,

> Considering that all objects of mass in a system have gravitational effects on all other objects, wouldn't the bowling ball, having a higher mass than the feather, **have a greater gravitational pull on the moon** thus causing the bowling ball to impact first? 

Emphasis mine. The answer is yes.