) Diameter of a star: Assume that the temperature of the Sun is 5800K and the temperature of Sirius A is 10,000K. If the luminosity of Sirius A is 23 times that of the Sun, calculate the radius of Sirius A relative to the Sun. Sirius A is times the size of the Sun. Your answer should be a number in the format (x. x).

Sirius A is 1.608 times the size of the Sun.

Explanation:

The radiant flux establishes how much energy an observer or a detector can get from a luminous source per unit time and per unit surface area.

 (1)

Where is the radiant power received from the source, L is its intrinsic luminosity and r is the distance.

The Stefan-Boltzmann law is defined as:

 (2)

Where is the radiant power, is the Stefan-Boltzmann constant and T is the temperature.

Then, equation 2 can be replaced in equation 1

(3)

Notice that L is the energy emitted per second by the source.

Therefore, r can be isolated from equation 3.

 (4)

The luminosity of the Sun can be estimated isolating L from equation 3.

but, and

To find the luminosity of Sirius A, the following can be used:

Finally, equation 4 can be used to determine the radius of Sirius A.

So, Sirius A has a radius of

Hence, Sirius A is 1.608 times the size of the Sun.

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