A Sirius Matter

Classical Mechanics Level 3

Find the luminosity of the Sun, expressed as a fraction of the luminosity of the star Sirius.

You may use the following information:

Radius of Sirius = 1.711 Solar Radii

*solar radii is the radius of the Sun

Temperature of Sirius = 9940K

Temperature of Sun = 5778K

Stefan-Boltzmann Law = $L=a\sigma { T }^{ 4 }$

where a is area, $\sigma$ is the Stefan-Boltzmann constant and T is temperature.

Leave your answer to 3 decimal places.

The answer is 0.039.

1 solution

Nicole Tay
Jan 28, 2016

Using the Stefan-Boltzmann Law, we can conclude that the Luminosity, L of a star is proportional to its area multiplied by its temperature to the power of 4.

Hence, $\frac { { L }_{ sun } }{ { L }_{ sirius } } =\frac { 1\times \pi \times { 5778 }^{ 4 } }{ { 1.711 {^2} }\times \pi \times { 9940 }^{ 4 } }$

which gives 0.039, rounded to 3 decimal places.

Note that the question asks for a ratio, and hence we can make use of the proportion in the Stefan-Boltzmann Law to solve without using the constant sigma.

I think it should be 1.711^2 in your solution instead of 1.711

Prince Loomba - 5 years, 4 months ago

oh yes, sorry about that, will edit. Thank you :) The answer does not change though.

Nicole Tay - 5 years, 4 months ago

A Sirius Matter

The answer is 0.039.

1 solution

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