Question

(A) Using the inverse square law for light, determine the apparent brightness of the Sun in our sky.

I got 1350 W/m² and it was correct.

(B) Using the inverse square law for light, determine the apparent brightness our Sun would have if it were at a distance of 12 billion light-years.

(C) From your answers to parts A and B, estimate how many stars like the Sun would need to exist at a distance of 12 billion light-years for their total apparent brightness to equal that of our Sun.

(D) Compare your answer to part C with the estimate of the total number of stars in our observable universe. Use your answer to explain why the night sky is much darker than the daytime sky. How much larger would the total number of stars need to be for "night" to be as bright as day?

Answer 1

A)

The Luminosity of the sun is given by

R_s is the radius of Sun = 6.96*10⁸ m

is Stephan Boltzmann's constant = 5.67 *10^-8 Wm^-2 K^-4

T is surface temperature of Sun = 5778 K

Apparent brightness of the Sun in our sky given by

d is the distance between Sun and earth = 1.496*10¹¹ m

B)

If the distance is 12 billion light years = 12*9.46*10²⁴ = 1.135*10²⁶ m

C)

No. of stars needed (N)

D)

Number of stars visible in the night sky around 5000

Thus since there is such difference between night and day sky.