Python 3 - 192 bytes

def f(N):
 import math as m;c=lambda x,y:"🟨"if x*x+y*y<N*N/64 else"🟥"if abs(round(m.atan2(y,x)/m.pi*16))%2 else"🟧"
 for y in range(N):print(''.join([c(x-N/2,y-N/2)for x in range(N)]))

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Explanation

Prints a simple 2-D grid, with a function defining the color of the cell: $$ color(x, y) = \text{Yellow, if } x^2 + y^2 < \left(\frac{N}{8}\right)^2$$ Then the angle is obtained with math.atan2, and the circle is divided in 32 sections: $$N = \left[\alpha \cdot \frac {2\pi} {32} \right]$$ N being the number of the corresponding section. When N is even, the returned color is orange, when N is odd, it returns red.

JavaScript (ES6), 124 bytes

f=(w,y=x=w)=>y?[...`🟧🟨🟥
`][x--?(X=x-~-w/2)*X+(Y=y+~w/2)*Y<w*w/64?1:Math.atan(X/Y)*10.19+33&2:(y--,x=w,3)]+f(w,y):""

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Method

For each coordinates \$(x,y) \in [0\dots w-1]^2\$, we compute:

$$X=x-\frac{w}{2}+\frac{1}{2}$$ $$Y=y-\frac{w}{2}+\frac{1}{2}$$

and then convert \$(X,Y)\$ to polar coordinates \$(r,\phi)\$:

$$r=\sqrt{X^2+Y^2}$$ $$\phi=\arctan(X/Y)$$

The test for the sun is:

$$r<\frac{w}{8} \iff X^2+Y^2<\frac{w^2}{64}$$

The color of each ray is obtained by testing the parity of:

$$\left\lfloor \phi\times \frac{16}{\pi}+\frac{1}{2}\right\rfloor\approx\lfloor\phi\times 5.09+0.5\rfloor$$

In the JS implementation, we actually multiply by \$32/\pi\approx 10.19\$, add \$33\$^(*) and test the 2nd least significant bit.

_{(*) Because the sign of % in JS is the sign of the dividend and because we use a bitwise AND for our test, we need to add a large enough constant to force a positive result.}

Ruby, 106 bytes

->n{(1..n*m=n+1).map{|i|z=i%m-m/2+(i/m-n/2)*1i
i%m<1?$/:z.abs>n/8?'🟥🟧'[(z.arg*5.1-0.5)%2]:?🟨}*""}

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A function accepting an integer and returning a newline separated string

Commented code

->n{(1..n*m=n+1).map{|i|    #Output n rows of m=n+1 characters by iterating through i from 1 to n*m
z=i%m-m/2+(i/m-n/2)*1i      #Convert the x and y coordinates into a complex number z, with origin at the centre.
i%m<1?$/:                   #For the last character in each row output newline.
 z.abs>n/8?                  #If absolute value of z > n/8
  '🟥🟧'[(z.arg*5.1-0.5)%2]: #Output red or orange depending on angle
  ?🟨                        #Else output yellow for centre (the ? marks a character literal)
  }*""                     #Close iteration bracket. Convert array into string by concatenating
}                          #Return string

Charcoal, 61 52 bytes

ＮθＥθ⭆Ｅθ⁻⁺ι×λＩ1j×⊘⊖θＩ1+1j⎇‹×⁸↔λθ🟨§🟧🟥№ＩＸλ¹⁶(-

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ＮθＥθ⭆Ｅθ⁻⁺ι×λＩ1j×⊘⊖θＩ1+1j

Input N and calculate the complex numbers for an N×N grid with the origin at its centre.

⎇‹×⁸↔λθ🟨§🟧🟥№ＩＸλ¹⁶(-

Calculate the appropriate emoji for each element.