When you sit in your house right now dust falls on flat surfaces because of gravity. This happens in space too. Anything that exists exerts gravity and will pull other things (dust or anything else) towards itself.
There is also one other thing at work too. Electricity. This works the same way that you can rub a balloon and then stick it to yourself. Same thing happens to small dust particles. Any particle that has a charge relative to you will be attracted to you and will stick to you.
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