The surface temperature of a star can be determined by analyzing its wavelength emissions through a method known as spectral analysis. This technique involves studying the intensity of light emitted by the star at different wavelengths, which provides insights into its temperature and other physical properties. Here's how this process works:

1. Emission Spectrum: Every star emits light across a range of wavelengths, which, when combined, forms its emission spectrum. The emission spectrum of a star is unique and carries information about its temperature and composition.

2. Wien's Displacement Law: According to Wien's Displacement Law, the wavelength of maximum emission (λmax) from an object is inversely proportional to its temperature. This means that hotter objects emit light at shorter wavelengths, while cooler objects emit light at longer wavelengths.

3. Blackbody Radiation: Stars can be approximated as blackbody radiators, which means that they emit radiation according to the laws of blackbody radiation. A blackbody is an ideal emitter and absorber of electromagnetic radiation.

4. Planck's Law: Planck's Law describes the intensity of radiation emitted by a blackbody at different wavelengths and temperatures. It establishes a relationship between the wavelength and the intensity of radiation.

5. Curve Fitting: The emission spectrum of a star is compared with the theoretical emission spectrum predicted by Planck's Law. By fitting a blackbody curve to the observed emission spectrum, astronomers can determine the temperature at which the star radiates most of its energy.

6. Effective Temperature: The temperature derived from this analysis is known as the effective temperature. It represents the temperature of a blackbody that would emit the same total amount of radiation as the star over all wavelengths.

7. Color and Temperature: Different surface temperatures of stars correspond to different colors. For instance, hotter stars appear blue or white, while cooler stars appear orange or red.

By analyzing the wavelength emissions of a star and comparing them with theoretical models, astronomers can determine its surface temperature. This technique provides valuable insights into the physical properties and characteristics of stars and allows scientists to study and categorize different types of stars based on their surface temperatures and other spectral features.