Astronomy is based nearly entirely upon earthly observations of radiation emitted from other sources. Astronomers study visible light, but they also study other portions of the electromagnetic spectrum.
Neutron stars [local]sometimes emit pulses of radio waves which serve as the means by which they are detected. They are then called pulsars. A special class of stars called x-ray binary stars (a normal star paired with a collapsed star) are detected by emitting x-rays. Infrared radiation [local] detects cool stars, or stars hidden behind interstellar dust.
In fact, where ever one looks at the sky, there is microwave background radiation, which astrophysicists interpret in terms of the origin of the universe.