Stars Brightness, Luminosity and Stefan’s Law
1. The Sun has an apparent magnitude of -26.7, and Sirius has an apparent magnitude of -1.47. By what factor is the Sun brighter than Sirius in apparent brightness? Note: we define a change of 5 in apparent magnitude to correspond to a factor of 100 in apparent brightness.
2. Sirius is fainter than the Sun in apparent brightness because Sirius lies at a great distance, and the apparent brightness of a star is inversely proportional to the square of the distance at which the star lies. Sirius lies at a distance of 2.64 pc, where 1 pc 206,000 A.U. Is Sirius brighter than the Sun in luminosity, and by what factor is Sirius more luminous than the Sun? Note: the answer is known as the luminosity of Sirius, in solar luminosity.
3. Sirius has a temperature of 9,940 K. By using the Wien’s law, calculate the wavelength at which most radiation is emitted. What form of radiation has this wavelength? 4. The Stefan’s law is a relation between a star’s total amount of energy emitted per unit time and its temperature (radiant flux). The luminosity of a star is proportional to the star’s total amount of energy emitted per unit time, multiplied by the square of the star’s radius. Calculate the radius of Sirius, in solar radii.
Optional Question: Globular Cluster
1. a) If each kilogram of hydrogen in a star is known to release 7x 1014 J and it is known that a star at this stage has used 20% of its hydrogen through fusion to helium, the age of the heaviest star can be worked out from its mass and luminosity. What is the expression for finding this age?
b) Stars in a globular cluster branch (turn off) from the main sequence at about
1 magnitude higher than the Sun, corresponding to the luminosity of about
1027 J/s and a mass of ~ 2 Msun. Comment on the age of the stars in the globular cluster?
A surprise waiting for you! Age of the our known universe is 15billion years