Once lightly landed on an asteroid, the sent load's robotic collection would probe deep under the surface, gaining a sample it would do simple analysis of. A rod would be sufficiently anchored there to become a simple tower. The communications cube would be fixed (very lightweight here) at the tower top. It would beam to Earth initial orbit and asteroid surface details.
Included in each such load would be a good Universal Time clock. Times taken for signals to reach other places having UT time clocks let them compute the asteroid's distance. (It takes 2.56s for light to pass across Luna's orbit, 499s (8.31min) for light from Sol to pass by Earth.) The distance computed for the asteroid's beamed signal to reach the other place would be sent back, to then get better confirmed by a new UT time being returned at light speed, sent some specified amount of time after the UT time recently sent from the asteroid.
The asteroid's Solar system position could be further computed by using the viewing angles found by its communications cube to be best centered on Sol, planets, and also a few distinct bright stars. Repeatedly finding its own position would then let it keep computing and refining its orbit details. Also this would let it report any orbit change (from any knock or very slight deflection by a close slowly passing asteroid). All this would let it send good freshly updated orbit details and location information etc. back to any remote sender requesting this.
Achieving this for lots of asteroids could cost centuries. There were so many asteroids to find the orbits of, including billions under 100m size, smaller than a sports field park, which could be badly devastating if ever one fell toward any Earth town.
Since the current investors group starting this could afford doing so, why not? Such a project might otherwise have ultimately been done by others in the future, likely by similar efficient low cost robotic methods.
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