I recently saw How the Universe Works, and was impressed by the video of astronaut Don Pettit’s sugar-and-salt experiment. (6 minutes into the show. Put sugar and salt in a plastic bag, and watch as the grains visibly gravitate toward each other in zero-G.) I’m trying to express this process with math, but the numbers I’m coming up with are way too big. Here’s the formula I derived:(adsbygoogle = window.adsbygoogle || []).push({});

Assuming two masses (m) separated by some distance (d) in zero-G conditions, how long does it take for the two masses to meet halfway?

First I take the distance equation and solve for time: [itex] t = \sqrt{2d/a} [/itex]

Now I modify this equation to take into account the fact that each mass only has to move half of [itex]d[/itex]: [itex] t = \sqrt{d/a} [/itex]

Now I use the G-force equation to derive each mass’ acceleration: [itex] a = F/m = Gm^2/d^2 / m = Gm/d^2 [/itex]

Now I plug the second equation into the first: [itex] t = \sqrt{d/ (Gm/d^2)} [/itex] [itex] = \sqrt{d^3/ Gm} [/itex]

Being extremely liberal, I’ll assume each grain is 1 gram and the two are separated by 10 cm. The equation says it takes them 34 hours to drift together, but that's way too long. The video isn’t time-lapse, and it clearly takes only moments for gravity to pull the grains together.

I suspect that I need to do some integration, but I have no practice defining integrals. Obviously acceleration is the variable that has to be integrated, but with respect to what? I’m not sure I can even do set up the proper integration without going back a few steps. Anyway, help is appreciated!

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# Theorizing a Zero-G Experiment

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