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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Physics in space is highly predictable. The only forces in play are gravity and the thrusters of the probe. So once the location and velocity of an object are known, you can throw a few equations at it to figure out just how much thrust you need for your probe to intercept the asteroid.
As to figuring out how large and where something is in space, it involves taking multiple measurements from different locations. By having at least a couple different angles from observation telescopes to the object, the difference between the two images can be used to calculate the distance to an object. By taking enough pictures over time, scientists can calculate both the distance and velocity of an object simply by tracking the position change over time.
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