Final answer:
To identify stars in the same life cycle stage as the Sun, one must look for G2 main-sequence stars with similar properties such as mass, luminosity, and spectrum, while making sure they are not giants or supergiants with subtly different spectrums.
Step-by-step explanation:
To identify two stars that are at the same life cycle stage as the Sun, we must look for stars that are in the main-sequence phase of their evolution. According to stellar evolution theories and observations, stars spend approximately 90% of their lives on the main sequence, where they fuse hydrogen into helium to produce energy. The Sun, a G2 main-sequence star, is approximately 4.5 billion years old. Therefore, to find similar stars, you would look for G2 stars with similar characteristics in the H-R diagram which indicates the stellar evolution stages of various stars. On average, these stars should have similar mass, luminosity, and spectral type as the Sun.
A distant G2 star with a spectrum and color matching those of the Sun could be considered at the same life stage. However, careful analysis is needed to ensure that the star is not a giant or supergiant, which might have subtle differences in its spectrum.