Question

The surface area of a sphere (any sphere) is 4 steradians. This means that the celestial sphere covers 41253 square degrees (3602/T) of the sky. The HUDF image is a square of side length 2.4 arc-minutes, and 10,000 galaxies are estimated within the image. Assuming the cosmological principle, how many billions of galaxies are there in the known universe?

Answer 1

The number of galaxies in the known universe is 257.83 billions.

Step-by-step explanation:

Given that,

Surface area of sphere = 4 steradians

Area of celestial sphere = 41253 degrees²

Side length = 2.4 arc minutes

We know,

`1 arc-minutes = (1)/(60)\ degree`

The area of the HUDF image is

`A=(2.4\ arc\ minutes)^2`

`A=((2.4)/(60))^2=1.6*10^(-3)\ degree^2`

The total number of galaxies in the image is 10000.

The area of celestial sphere is

`A_(c)=41253 degrees^(2)`

We need to calculate the number of galaxies in the known universe

Using formula for the number of galaxies

`N=(A_(c))/(A)*10000`

`N=(41253)/(1.6*10^(-3))*10000`

`N=2.5783*10^(11)`

`N=257.83\ billions`

Hence, The number of galaxies in the known universe is 257.83 billions.