### Question --- Two stars are observed to have the same color and brightness. One of them is a giant at a greater distance than the other, which is a main sequence star. How could these be distinguished from spectroscopic measurements? ### Answer --- If two stars are observed have the same color (surface temperature, $T_{\rm eff}$) and the same brightness ([[Magnitude#Apparent Magnitude|apparent magnitude]]), then we cannot distinguish them through the [[Spectral Classes#Harvard Spectral Classification Scheme|Harvard Spectral Classification Scheme]] alone - regardless of their distance away from the observer. Because of this, we would classify the luminous, distant star (giant) and dim, nearby star (MS) as the same type of object. ![[hr29.png|align:center|400]] To distinguish further, we need to know the luminosity. Therefore, enter the [[Luminosity Classes#Morgan-Keenan Luminosity Classification Scheme|Morgan-Keenan Luminosity Classification Scheme]]. By getting estimates for the radius of the star from the spectral line broadening and knowing the temperature, we can estimate the luminosity ($L = 4 \pi R^{2} \sigma T^{4}$). ![[Luminosity Classes#Morgan-Keenan Luminosity Classification Scheme]]