Astronomy 106

Luminosity, Radius and Temperature

20. Luminosity, Radius and Temperature
    

    The luminosity (brightness) L, radius R, and temperature T of a star are related by the formula:

    

    However, we can simplify the formula when comparing two stars by taking ratios. If we denote the luminosity, radius and temperature of the sun by , , and , respectively, we can set up a ratio:

    

    Example:
    

    If another star has the same radius as the Sun, but a temperature twice that of the sun, how many times more luminous is this star? Here we do not need any absolute measures of temperature or luminosity, only ratios. The ratio () = 2 and the ratio () = 1. Thus () = = 16. The second star is 16 times as bright as the Sun.