What do you call the study of stars and planets?

Astronomy. Astrology is the other thing, and for most of history they were the same profession - Kepler cast horoscopes for a living while working out that the planets move in ellipses, and considered it a distasteful necessity that paid for the real work.

It is the oldest science by a wide margin, because the sky was the only reliable clock and calendar available. Knowing when to plant, when the river would flood and when the rains were due all came from watching the sky, and monuments like Stonehenge and Newgrange are alignment instruments as much as anything else.

For nearly all of that history it was done with the naked eye, and done extremely well - Tycho Brahe measured planetary positions to about an arcminute without a telescope, and it was the precision of those measurements that let Kepler prove the orbits were not circles. Galileo pointed a telescope at the sky in 1609 and the field has spent four centuries since discovering that most of what is out there is invisible to the human eye anyway: radio, infrared, X-rays, and a great deal of matter that emits nothing at all.