Mass spectrometry, classical physics, radio spectrum wizardry, and a whole lot of signals theory
Also, don't you mean stellar spectroscopy? Mass spectrometry is when you fire ions through an electric field to determine their mass-to-charge ratio. Doesn't seem even a little bit applicable to far-away objects.
Think about our knowledge of the Earth rotating around the sun vs. the sun rotating around the Earth, or flat Earth vs a spheroid Earth, our models increase in accuracy as their testability increases in tandem.