Final answer:
The luminosity of a star can be determined by measuring the peak wavelength in the stellar spectra, which relates to the star's temperature and thus its luminosity. The Doppler shift and line broadening are used to assess a star's rotation and radial velocity.
Step-by-step explanation:
The luminosity of a star can be determined by measuring the peak wavelength in the stellar spectra. When we look at the light a star emits, we can analyze various aspects such as the Doppler shift to determine stellar motion. The peak wavelength of the spectral emission or absorption lines can give us information on the temperature and hence, the luminosity of a star. This is because the wavelength at which a star's spectrum peaks corresponds directly to its temperature through Wien's displacement law, and a star's temperature is related to its luminosity.
In the context of stellar rotation and radial velocity, the Doppler effect causes the spectral lines to broaden or change position depending on whether parts of the star are moving towards or away from us. This broadening, also known as line broadening, indicates the speed of the star's rotation. Moreover, if a star is moving towards or away from us, its spectral lines will shift towards the blue or red end of the spectrum, respectively. This shift, called the Doppler shift, reveals the radial velocity of the star. Reliable measurements of a star's luminosity, rotation, and motion are crucial for understanding its properties and the dynamics of the Universe.