Final answer:
Stars with the same apparent brightness can have different luminosity due to their varying distances from Earth. Closer stars appear brighter as their light spreads out less before reaching us. By knowing a star's luminosity, astronomers can calculate its distance and apparent brightness correctly.
Step-by-step explanation:
Two stars with the same apparent brightness may differ in luminosity due to their distances from Earth. Imagine a dark room with identical bulbs spread out; bulbs closer to you appear brighter, while those farther away seem dimmer. Luminosity indicates a star's true energy output, while apparent brightness is how much light from the star actually reaches an observer on Earth. If two stars have equal luminosity but are at different distances, the closer one will appear brighter because its light has less space to spread out before reaching us.
For instance, if Star A and Star B have identical luminosities but Star A is 20 light-years away and Star B is 40 light-years away, Star A will appear brighter. The apparent brightness drops with the square of the distance, so Star B will look four times fainter than Star A. Astronomers have developed systems to determine a star's luminosity, which allows them to calculate the star's distance and understand its apparent brightness.