Question

The star Betelgeuse has a temperature only half that of the Sun but has 100,000 times the luminosity of the Sun. Using only this information, calculate the radius of the Betelgeuse in terms of the Sun's.

Answer 1

R/R_s = (T_s/T)²(L/L_s)^1/2

^{where R,T and L are radius temperature and luminosity of the Betelgeuse respectively}  and

^{R_{​​​​​s}, T_{​​​​​​s} and L_{​​​​​​s} are radius temperature and luminosity of the sun respectively}

^{R/Rs = 2² × 100000^1/2}

^{R = (4 ×316.23) Rs = 1264.92 R}​​​​​​s