Question

a. If the Sun subtends a solid angle Ω on the sky, and the flux from the Sun just above the Earth’s atmosphere, integrated over all wavelengths, is f(d¯), show that the flux at the Solar photosphere is πf(d¯)/Ω.

b. The angular diameter of the Sun is 0.57 degree. Calculate the solid angle subtended by the Sun, in steradians.

Answer 1

A) The formula for the  flux at the Solar photosphere is proven to be; F⊙ = [f(d⊙)π]/Ω

B) The solid angle subtended by the Sun, in steradians is; 7.8 × 10⁻⁵ steradians.

Wavelength of Light of Sun

A) First of all, if we assume that the Sun emits isotopically at a luminosity (L⊙) , the flux at a given distance R from the sun would be f(d) = L⊙/ (4πd^2)

The ratio of flux at the solar photosphere to the flux at the Earth’s atmosphere would be: F⊙/{f(d⊙)} = (R⊙)^2 / (d⊙)^2

Now if we think of this relationship of the flux and the earth as a conical pattern, we'll deduce that the solid angle subtended by the sun at Earth’s surface to be;

Ω = π[(R⊙)²/(d⊙)²]

Combining this with the ratio earlier gotten, well arrive at;

F⊙ = [f(d⊙)π]/Ω

B) Now let's express the radius of the sun (R) in terms of its angular diameter (2α) and this gives;

R⊙ ≈ αd⊙

Now combining this with the equation for Ω earlier, we get;

Ω ≈ πα^2

So,Ω = π((0.57/2π) /180)^2 = 7.8 × 10⁻⁵ steradians.

Read more about wavelength of sun's light at; https://brainly.com/question/15531840