So if you put two magnets on a table and they are far enough away from each other they won't go together because the friction can at some distance overcome the magnetic attraction. But out in space all the bits of metal would be attracted to the magnet and have little friction. But of course things in orbit are in general very far apart. But given enough time would something happen? Like imagine if the entire international space station was one big magnet...
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$\begingroup$ How big magnets are you thinking of? A kitchen magnet won't do anything, a six-ton slab of neodymium might be a (mildly) different story. $\endgroup$– John DvorakCommented Feb 19, 2018 at 6:17
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$\begingroup$ How big is the iss? $\endgroup$– user273872Commented Feb 19, 2018 at 6:20
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There is an important conceptual reason that magnets of any strength are very bad at exerting forces over long distances. Magnets are dipoles. Pushing some fussy vector mathematics under the rug, this means that the force on a remote chunk of iron falls off roughly as the seventh power of distance. That is fast. Basically even a strongly magnetic satellite would have to pass within a few ISS radii of your monster ISS magnet to be captured.
If you did want to build a space junk magnet, I suspect it might help to make the monster magnet very long to separate its poles by a long distance.
Your question inspires me to ask another question about your monster ISS magnet, to which I don't know the answer off the top of my head. Would the ISS magnet be influenced in any interesting way by earth's magnetic field (other than swiveling around trying to align its poles with the field direction)? I don't have an intuitive grasp of the scale of the force that would try to pull the ISS into the stronger fields near the poles. Would it be enough to pull the ISS out of a reasonable orbit?
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$\begingroup$ Force only falls off as the fourth power of distance if you have two permanent magnetic dipoles. If you have a permanent magnetic dipole that has to induce a dipole moment in the other, it falls off as the seventh power! $\endgroup$– Chris ♦Commented Feb 19, 2018 at 8:59
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$\begingroup$ Excellent point, editing now. Any thoughts on my follow up question? $\endgroup$ Commented Feb 19, 2018 at 9:02
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$\begingroup$ The force is pretty tiny. Really roughly (assuming we have a $10~\rm T$ coil that measures $100~\rm m$ on every side, and lazily plugging in the radius of the earth rather than including the altitude of the ISS), it comes out to something on the order of hundreds of newtons. Wolfram alpha query. Compare this to the millions of newtons that gravity provides. $\endgroup$– Chris ♦Commented Feb 19, 2018 at 9:31
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$\begingroup$ I am unconvinced that your formula for the magnetic force is relevant so close to the earth, since the earth doesn't look like a distant dipole from low earth orbit. Also the direction of the force will not be straight down, so even a force that is small compared to gravity could be important.I guess it is in a starting place in that the force magnitude is probably within a handful of orders of magnitude of what you got. $\endgroup$ Commented Feb 19, 2018 at 14:00
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$\begingroup$ I think the piece of data we need for a good estimate is the gradient of the earth's magnetic field at some moderate latitude. $\endgroup$ Commented Feb 19, 2018 at 14:02