Local coordinates are useful to the backyard observer, but it's clear that a more general coordinate system is required if we want to assign a single and unchanging set of coordinates to an object in the sky, so that anyone anywhere may find it at any time.
For this reason, astronomers devised a system called the equatorial coordinate system. These coordinates are fixed for any unmoving object in the sky. Slightly more complicated to understand but very similar to the local coordinate system, the equatorial system uses two numbers, right ascension and declination, to define a position in the sky.