The mechanism is unknown, but the movement is visible.
Answer the OP.
I'm not sure what the question in the OP is. Asteroids are discovered by different astronomers, and not the same astronomers, because finding asteroids is like finding a needles in a haystack. It's a giant where's waldo game, and not everyone will find all the same asteroids.
Asteroids stand out from the stars because they are moving at a slightly different speed around the celestial system. Astronomers use photo-telescopes which take pictures of small thumb-sized sections of the sky every night at the same time for weeks on end, and then compare the images for a change of star configuration.