Use the radius-luminosity-temperature relation to calculate the radius of a red supergiant with temperature 3000 K and total luminosity 10000 times that of the Sun.

The radius of the red supergiant is .

Explanation:

The radiant power 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 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 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 for the Sun.  

The following expression can be used to find the luminosity of the star:

Finally, equation 4 can be used.

Hence, the radius of the red supergiant is .

i had this question and the answer was 3.15 miles.

martina travels from school to her mom's office. from there, she walks to school. after school, she walks to the library and then to a friends house before finally ending back at home. find martina's total distance traveled.

a) 0 miles  

b) 0.4 miles  

c) 1 mile  

d) 3.15 miles