Answer:
I = W / 4π R_{s}², P = W / 2π c R_{s}², Io /I_{earth} = 10⁴
Explanation:
The intensity is defined as the ratio between the emitted power and the area of the spherical surface
I = P / A
Since the emitted power is constant and has a value of W for this case, let's look for the area of the sphere on the surface of the sun
A = 4π ²
I = W / 4π R_{s}²
.- The radiation pressure for total absorption is
P = S / c
Where S is the Pointer vector that is equal to the intensity
Let's replace
P = W / 2π c R_{s}²
.- We repeat for r = R_{s}/2
I₂ = W / 4π (R_{s}/ 2)²
I₂ = 4 W / 4π R_{s}²
I₂ = 4 Io
I₀ = W / 4piRs2
We calculate the radiation pressure
P₂ = I₂ / c
P₂ = 4 I₀ / c
P₂ = 4 (W / 4pi c Rs2)
.- the relationship between these magnitudes is
I₂ / I₀ = 4
P₂ / P₀ = 4
Let's calculate the intensity on the surface where the Earth is
r = 1.50 10¹¹ m
= W / 4π r²
Io / I_{earth} = r² /²
Io /I_{earth} = (1.5 10¹¹ / 6.96 10⁸) 2
Io /I_{earth} = 4.6 10⁴
Io /I_{earth} = 10⁴