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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 :

Answer:

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

Explanation:

Given that,

Surface area of sphere = 4 steradians

Area of  celestial sphere = 41253 degrees²

Side length  = 2.4 arc minutes

We know,

[tex]1 arc-minutes = \dfrac{1}{60}\ degree[/tex]

The area of the HUDF image is

[tex]A=(2.4\ arc\ minutes)^2[/tex]

[tex]A=(\dfrac{2.4}{60})^2=1.6\times10^{-3}\ degree^2[/tex]

The total number of galaxies in the image is 10000.

The area of  celestial sphere is

[tex]A_{c}=41253 degrees^{2}[/tex]

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

Using formula for  the number of galaxies

[tex]N=\dfrac{A_{c}}{A}\times10000[/tex]

[tex]N=\dfrac{41253}{1.6\times10^{-3}}\times10000[/tex]

[tex]N=2.5783\times10^{11}[/tex]

[tex]N=257.83\ billions[/tex]

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

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