how we manage to calculate the location/speed/size of an asteroid with enough precision to slam a space probe into it?

Question

How do we ever manage to connect a small space probe with a small asteroid at large speeds and distances? Like how do we know it’s a small asteroid at distance X versus a slightly larger asteroid at distance Y, etc?

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Answer 1

Smart people can stand on the shoulders of other smart people to see further.

The scientific method has transformed humanity in so many ways.