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Velcro, or maybe Van Der Waals force, or maybe whatever the hell makes gauge blocks stick to each other.
I like the gauge block notion. A (quick) search says that it's a combination of surface tension from the oils they're coated in, suction (gone for us), and the super flat surfaces slightly exchanging electrons and bonding in close proximity.
I'm a fan of the surface tension angle as the "rocket of suction cups", since it's got that "non-binding force" element, where welding or glue feels different, and Velcro feels like a tangle.
It's "pull-y" where suction is "push-y".
Now the question is would surface tension grab something in a vacuum the way it does outside of one. I know you'd have water sublimate off, so it's questionable to me.
In space you have to worry about your materials cold welding, so that might affect how we go about replacing the suction cups.
If it's metal, just rub a bit of it against another piece of metal and it will cold weld/fuse to it.
This only works on "virgin" metal iirc - if it's been exposed to Earth's atmosphere, it won't work. If you shave off some from the surface I believe it works again.
Like I said- "rub it". The oxidized layer on metal is very, very, thin. It doesn't take much at all to get rid of it.
I didn't realize that the layer was thin enough to rub away with minimal friction. I'd learned about this years ago so I could be misremembering things, but the source I read made it out as if it wasn't a major concern with space exploration because it took substantial effort to cold weld things that had been exposed to air.
Actually, it's believed that some of the failures in early satellites was due to cold welding.
Neat, the more ya know!
Wasn't velrco actually invented by a NASA scientist?
Nvm, just a myth, I guess.