A planet orbits 1 AU from a star that is 2 times as massive as our Sun. How does the star's luminosity compare?LSunIf the star has the same radius as our Sun, what is the temperature of the star compared to the Sun?т.TsunIf Earth's average temperature is 287 K and the Sun were replaced with this star, how would its average temperature change? (Enter a temperature in K. Assume that Earth temperature is proportional to solar flux.)KNeed Help?Read It

Let, The luminosity of the star = L The luminosity of the Sun = LSun The mass of the star = M The mass of the Sun = MSun The average temperature of the Earth, Tavg = 287 K The average temperature of the Earth when the said star replaces the Sun = T'avg Here, M = 2MSunThe ratio of the luminosities of the star and the Sun is given as, LLSun = MMSun4 Substitute from the given that M = 2MSun LLSun = 2MSunMSun4 Therefore, LLSun = 161 = 16L = 16 LSun Therefore, the luminosity of the star is 16 times the luminosity of the Sun.The expressions for the luminosities of the star and the Sun in terms of their temperatures are given as, L = 4πr2σT 4 LSun = 4πr2σTSun4 Here, r = radius of the star and the Sunσ = Stefan-Boltzmann ConstantT = Temperature of the starTSun = Temperature of the Sun Therefore, LLSun = 4πr2σT 44πr2σTSun4 = TTSun4 Substitute the value of the luminosity ratio from the solution 1 TTSun4 = 16(TTSun) = (16)1/4 = 2T = 2 TSun Therefore, the temperature of the star is twice the temperature of the Sun.The expression for the average temperature of the Earth is given as, Tavg = 287 K = S01-αp4σ14 Here, S0 is the Solar flux at the Earthαp is the albedoσ is the Stefan-Boltzmann constant The relation between the Solar flux and the Luminosity is given as, S0×4πa2 = LSun here, a is the orbital distance of the Earth. Therefore, S0 = LSun4πa2 Similarly for the said star with luminosity L, S = L4πa2 From Solution 1, L = 16 LSun Therefore, S = 16LSun4πa2 = 16 S0 Therefore the temperature at flux S is given as, T'avg = S1-αp4σ14T'avg = 16 S01-αp4σ14T'avg = 1614·S01-αp4σT'avg = 2·Tavg = 2×287 KT'avg = 574 K The change in average temperature, therefore, is ∆T = T'avg-Tavg = 574-287 = 287 K Therefore, the average temperature of the Earth would be 574 K if the Sun is replaced by the star in consideration. That is, the average temperature would change by 287 K.