Suppose Star A is three times as luminous as Star B If these

Suppose Star A is three times as luminous as Star B. If these stars are both 500 light-years away from Earth, how will their apparent brightness compare? How will the apparent brightness of these stars compare if Star A is twice as far away as Star B?

Solution

Brightness is inversely proportional to d^2 where d is the distance
B= L/(4*pi*d^2)

a) when distance of both the stars are 500 light years
B1/B2= (L1/L2)* (d2/d1)^2
B1/B2= (3)* (500/500)^2
= 3
B1 = 3*B2
Answer: Brightness of A is 3 times that of B

b)

a) when distance of both the stars are 500 light years
B1/B2= (L1/L2)* (d2/d1)^2
B1/B2= (3)* (1/2)^2
= 3/4
B1 = 3/4*B2
Answer: Brightness of A is 0.75 times that of B