Question

The star Sirius has a parallax angle of 0.379 arcseconds and its brightness is 8.8 x 10^-11 that of the Sun (b Sirius=8.8 x 10^-11bSun). The wavelength of maximum emission of Sirius is 241.7 nm.

a) What is Sirius luminosity in terms of solar luminosity?

b) And what is Sirius luminosity in Watts? (Assume that the Sun's luminosity is 3.8 x 10^26W)

c) What is Sirius surface temperature?

d) Use the information above to compute Sirius radius.

Answer 1

parallax angle = 0.379 arcseconds

d = 1/P = 1/0.379 = 2.63 P.C

brightness is 8.8 X 10^-11

Sun's luminosity is 3.8 X 10²⁶ W

birghtness b = L / 4 X 3.14 X d²

b = 3.8 X 10²⁶ / 4 X 3.14 X 1.49 X 10¹¹

b = 1362 W/m²  

luminiisity of Sirius L = b X 4 X 3.14 X d²

L = 1 X 10²⁸ W

we have _m T = b

T = 2.9 X 10^-3 / 241.7 X 10^-9

T = 11998.3 K

R² = 1 X 10²⁸ / 5.67 X 10^-8 X 4 X 3.14 X 11998.3⁴

R = 8.23 X 10⁸ m

T_Sirius / T_Sun = ( 1 X 10²⁸ X R_sun² / 3.8 X 10²⁶ X 1.7² X R_sun² )^1/4  

T_Sirius / T_Sun = ( 1 X 10²⁸/ 3.8 X 10²⁶ X 1.7²)^1/4   

T_Sirius / T_Sun = 1.737  

T_Sirius = 1.737 X T_sun

T = 10074 K