Final answer:
Astronomers measure the surface temperature of stars by constructing power curves that indicate energy emission at various wavelengths, with the peak correlating to the star's temperature as per Wien's law.
Step-by-step explanation:
Astronomers have developed methods to measure the surface temperature of stars with precision. One effective method is by analyzing the amount of energy that a star emits at each wavelength and constructing a power curve. The peak of this power curve, according to Wien's law, directly corresponds to the temperature of the star. The Sun, for example, has an average surface temperature of about 5800 K. Infrared observation poses additional challenges due to Earth's heat emission, which must be accounted for when measuring distant cosmic sources. Advanced projects like the Gaia survey are now enabling astronomers to gather vast amounts of data on star characteristics and distances with improved efficiency.