Star Luminosity????

Question

a) If 2 stars, A if luminosity 9000 and B of luminosity 90 (both relative to the sun) apear equally bright from Earth, how mych further away is A than B(in relative terms)??

b)Star A is twice as bright as Star B, but B is twice as faw away as A. Which has greater luminosity, and by what ratio?

c)If two stars, A and B, are the same distance away, but B is 20 times more luminous than A, how much brighter will B appear than A?

Answer 1

All these are solved by the inverse square law.

a) Since A is 100 times as bright as B, it must be 10 times farther away (10x10=100) to appear the same brightness.
b) Moving twice the distance reduces apparent brightness by a factor of 4. I think the question is worded incorrectly, I suspect they meant to say that A (the brighter) is twice as far away. If that's the case, it would appear half as bright.
c) At the same distance, there is no difference from the inverse square law. So B would appear 20 times more luminous.

Answer 2

luminosity has nothing to do with how nearby they are. Luminosity is an intrinsic property of the star. What you probably mean, is the apparent magnitude, the further a star, the less bright it is, it's also a logarithmic scale. if you have a high luminosity star and a star with low luminosity, and the bright star or high luminosity is farther away than the low luminosity star, it is possible that they have the same apparent magnitude.

Answer 3

Remember that luminosity varys as 1/r² so in (a) the two stars will appear to be the same luminosity if a is 10 times as far away as B.

You solve the rest of them using the same logic.

HTH

Doug

Answer 4

a) 10 times
b) A appears brighter
c) B will appear 20 times brighter