For example, like if an asteroid was projected to pass Earth but not until 20 years from now, how do we calculate this? How is that even possible to know?
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There are a couple of different ways. If you are talking about an asteroid the easiest thing is to just waatch it from multiple different points in space, which allows you to figure out its velocity even if it does happen to be coming directly for us. Although in your example it would be more a case of plotting the orbit that the object is taken, since 20 years means it is almost certainly going to go around the sun several times.
If you are talking about a star thousands or even millions of light years away, you can still determine whether it is moving towards us or away from us by using what is known as red shift or blue shift.
When an object is moving towards us any radiation it emits gets compressed, and if it is moving away then that radiation gets stretched. This results in the color of the star changing blue if it is coming towards us or red if it is going away.
And we can know what color the star is supposed to be by looking at the hydrogen emission lines. These are kind of like fingerprint lines in a star’s emission spectrum that always occur on very specific wavelengths. So if we see those lines and they are more red than they should be, then we know the star is moving away from us.
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