Answer to Question #50856 in Astronomy | Astrophysics for Nayan Jyoti Das

Question

The average temperature of the interior of a sun-like star is of the order 108 K. Estimate the mass of the star in terms of the solar mass if it has a radius of order 1010 cm.

Answer 1

Given
T = 108 K
Radius = 1010 cm
We must find mass of the star.
Solution use the next formula
L = Lsun*(R/Rsun).^2 * (T/Tsun).^4
Mass star = L.^(1/4)
Matlab script
Tstar = 108; % K
Tsun = 5778; %K
Rsun =695500*1000*100 ; %in cm
Rstar=1010; % cm
% Using formulas L/Lsun = (R/Rsun).^2 * (T/Tsun).^2
l = (Rstar/Rsun).^2 * (Tstar/Tsun).^4
Mass_star = l.^0.25
Matlab Output
Mass_star = 2.2525e-06 * Mass Sun