Finding the magnitude difference between two star

[Benzoate]

Homework Statement

Determine the apparent magnitude difference between sirius and the sun,as seen from the Earth. How much more luminosity is sirius than the Sun ?

Homework Equations

f=sigma*T^4(eff)
m-n=2.5*log(f(m)/f(n))

The Attempt at a Solution

the apparent magnitude difference is m-n, m and n being the apparent magnitudes being the sun and sirius. I probably need the find the flux of each star. the flux=5.67e-8 W/(m^2*K^4)*T^4(eff). 30000 K is the effective temperature of Sirius and T(eff)=5780 K for the sun. f(sirius)/f(sun)=(30000 K)^4/(5780)^4=726 . Therefore, m(sirius)-n(sun)=2.5*log(726)=7.152

 

[anathema]

. The apparent magnitude difference between Sirius and the Sun is approximately 7.15.

To determine the luminosity difference between Sirius and the Sun, we can use the equation L=4*pi*R^2*f, where L is the luminosity, R is the radius, and f is the flux. The radius of Sirius is approximately 1.71 times that of the Sun (based on their respective effective temperatures and using the Stefan-Boltzmann law), so we can calculate the luminosity ratio as:

L(sirius)/L(sun) = (1.71)^2 * (726) = 2195.83

Therefore, Sirius is approximately 2195.83 times more luminous than the Sun. This is expected, as Sirius is known to be one of the brightest stars in the sky.

 

[m2003]

. This means that Sirius appears 7.152 magnitudes brighter than the sun from Earth.

To determine the luminosity difference between Sirius and the sun, we can use the formula L=4*pi*R^2*f, where L is the luminosity, R is the radius, and f is the flux. The radius of Sirius is approximately 1.71 times that of the sun, so the luminosity of Sirius is 4*pi*(1.71)^2*726=17274 times that of the sun. This means that Sirius is approximately 17274 times more luminous than the sun.