Quick intuition boost for the non-believers: How do things look like if you’re standing on the surface of the bowling ball? Are feather and earth falling towards you at the same speed, or is there a difference?
Comment on your mom falls significantly faster than g
Sasha@lemmy.blahaj.zone 2 weeks ago
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 in this system 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.
barsoap@lemm.ee 2 weeks ago
Simulation6@sopuli.xyz 2 weeks ago
Physics books always say to assume the objects are points in doing calculations. Does the fact that the ball is thicker then the feather make a difference?
Sasha@lemmy.blahaj.zone 2 weeks ago
Possibly?
A bowling ball is more dense than a feather (I assume) and that’s probably going to matter more than just the size. Things get messy when you start considering the actual mass distributions, and honestly the easiest way to do any calculations like that is to just break each object up into tiny point like masses that are all rigidly connected, and then calculate all the forces between all of those points on a computer.
I full expect it just won’t matter as much as the difference in massed.
BB84@mander.xyz 2 weeks ago
For the bowling ball, Newton’s shell theorem applies, right?
Sasha@lemmy.blahaj.zone 2 weeks ago
Yeah it would fair point, I’ll be honest I haven’t touched Newtonian gravity in a long time now so is forgotten that was a thing.
There’s a similar phenomenon in general relativity, but it doesn’t apply when you’ve got multiple sources because it’s non-linear.