this post was submitted on 03 Nov 2024
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Science Memes

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ur dada so buff he falls significantly faster than g (mander.xyz)
submitted 2 weeks ago* (last edited 2 weeks ago) by [email protected] to c/[email protected]
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Tap for spoilerThe bowling ball isn’t falling to the earth faster. The higher perceived acceleration is due to the earth falling toward the bowling ball.

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[–] [email protected] 23 points 2 weeks ago* (last edited 2 weeks ago) (1 children)

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.

[–] [email protected] 3 points 2 weeks ago* (last edited 2 weeks ago)

I actually thought the answer might be never, but a quick back of the envelope calculation suggests you can do this by dropping a ~1kg bowling ball from a height of 10^-11^m. (Above the surface of the earth ofc)

This is an extremely rough calculation, I'm basically just looking at how big a bunch of numbers are and pushing all that through some approximate formulae. I could easily be off by a few orders of magnitude and frankly I didn't take care to check I was even doing any of it correctly.

10^-11^m seems wrong, and it probably is. But that's still 1,000,000,000,000,000,000,000,000 times further than the earth moves in this situation. Which hey, fun What If style fact for you: that's about the same ratio of 1kg to the mass of the Earth at ~10^24^kg.

That makes perfect sense because the approximations I made are linear in mass, so the distance ratio should be given by the mass ratio.