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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Two major pieces at work:
1) We have radar & telescopes and orbits in space are *very* stable because there’s essentially zero drag. Once we have enough radar hits, we can calculate the true orbital elements with astonishing accuracy.
2) We can make corrective burns to the probe’s trajectory. So if we have *very* good trajectory data on both asteroid and probe, and those are both very predictable (particularly over short durations), then once we’re mostly going in the right direction we can use pretty small corrections to the probe’s trajectory as we get close.
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.
We know the dimensions and distance to it, because we can see it, and measure it over time. If it were bigger and farther away, then it wouldn’t be in the orbit it is.
And once you know distance, speed, and mass, it’s the simple matter of following Newton’s laws of motion to see where it’s going to be at pretty much any time in the future. And then, it’s the less simple matter of building and launching a rocket into interplanetary space.
If you can do the second part of that, you can do the first.
Smart people can stand on the shoulders of other smart people to see further.
The scientific method has transformed humanity in so many ways.
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