Then you send the telescopes closer to the areas your searching. I thought I mentioned that?
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So you are saying sending out telescopes into space to continually search for all the asteroids is pointless? Please elaborate.
Well, the point is to look for Near Earth Objects, isn't it. There isn't a place better suited for that than Earth's orbit, by definition. And Earth itself is the most convenient platform to operate scopes on in the general vicinity of Earth's orbit.
Only if you have enough telescopes in operation to catch any object that approaches Earth to within detection range, then it might make any sense to send more scopes to other places. Worse for the space cadet, those ground based scopes will catch >>90% of all larger NEOs within a few years.
It might even be more effective to simply extend that earth-based program instead of sending probes randomly around the solar system for finding those last 1%, 0.1%, 0.01%, ... you have missed so far. As someone already mentioned, space is awfully spacious
Space telecopes tend to be kinda expensive, especially if you want to have them above LEO. The additional observation time compared to earth-bound scopes can't compensate for that.
Space telecopes make sense for things you can't do (well) with an atmosphere above you, chasing NEOs isn't one of them.
Somehow I have the impression you think a telecope can instantaneously detect any asteroid closer than x million km.
No, it has to integrate each image for many minutes or even hours, with each image the ballpark size of a degree angular diameter. Do it twice at the very least for each spot of sky remotely close to the ecliptic.
If something is found, then there has to be several follow-up observations to get a good fix on the orbital elements.
All the time moving with several km/s relative to the asteroids it's looking for, which can be detected only within a finite distance.
For optical/infrared telecopes telescopes the apparent brightness of an asteroid drops roughly with the square of the distance. For your deep space radio dish, it drops with the distance to the power of 4. And it takes something like the Arecibo dish and a close approach to earth to observe an asteroid with radar.
Of course you can try to solve the detection problem with brute force, and send a bazillion of probes. But it gets ridicoulously expensive for anything significantly better than what can be achieved from earth.
And no, you cant self-assembly high precision telescopes by from asteroids.