Answer:
B(A)100=B(B), the star A is 100 times fainter than star B.
Explanation:
Brightness of the star is defined by the formula,
[tex]B=\frac{L}{4\pi d^{2}}[/tex]
Here, L is the luminosity and d is the distance.
For star A, the distance is 10d. The brightness of star A.
[tex]B(A)=\frac{L}{4\pi (10d)^{2}}[/tex]
For star B, the distance is d. The brightness of star B.
[tex]B(B)=\frac{L}{4\pi d^{2}}[/tex]
Now according to the question luminosity of two stars is equal.
Therefore,
[tex]B(A){4\pi (10d)^{2}}=B(B){4\pi (d)^{2}}\\B(A)100=B(B)[/tex]
So, star B is 100 times brighter than star A.
Therefore the star A is 100 times fainter than star B.
