On an asteroid for producing big telescopes, the initial starting Solar light to electricity converting film would first be used to begin refining all needed to expand its starting robotic refining & construction equipment. Formed early would be an expanded Solar light converting surface film to gain more useful electricity to begin accomplishing more tasks quicker.
Robotically form 2 high towers at the rotation axis opposite poles. Out from their tops lightly hang new made Solar energy collecting wide films (at under 1% Earth surface weights). Gradually turn their facing direction once each orbit "year" to stay always best facing Sol. Now much more electricity is gained for use at any time, for anywhere all around the asteroid.
A very wide not too curved mirror permits high resolution more magnified views, able to then study not just stars, but also sometimes even view not too small planets not too dimly far from a star. Or making a more curved mirror provides a wider area view, to see more all at once (but less magnified). Another telescope can also be made on the opposite face of the asteroid to then permit viewing from here anywhere all around the universe.
While the first telescope mirror gets perfectly formed, the asteroid's daily (and yearly) rotation can start being slowly halted by a strong ion jet up on a high tower at its equator. (While doing so, any past tilt of the old daily rotation axis relative to the orbit axis can slowly be also reduced.)
Finally, unlike on Earth, there'll nicely become no need for motors constantly turning telescopes to compensate against Earth's daily rotation. So after aiming perfectly at some star, a telescope can conveniently stay quietly virtually perfectly aimed motionless as long as wanted.
In space, electricity converted from Solar light will let a telescope's computer control use and facing directions, then continually save microgridded images data to be beamed encoded to Earth astronomers. Up at the 2 opposite axis tower tops put microgridded communications cubes to send images to Earth or to any settlements. These will receive future requests for many wanted telescope views.
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