Final answer:
The Sun appears brighter than Alpha Centauri to an observer on Earth because it is much closer, despite both stars having nearly the same luminosity. Apparent brightness is influenced by a star's distance from Earth, and since the Sun is our closest star, it is the brightest in our sky.
Step-by-step explanation:
The stars Alpha Centauri and the Sun have nearly the same luminosity, but the Sun will appear brighter to us due to its proximity. Alpha Centauri, while similar in total energy emission, is much farther away from Earth. Therefore, the correct answer is B. The Sun appears brighter to us than Alpha Centauri does.
Luminosity is an intrinsic property of a star, indicating the amount of light it emits from its surface. However, the apparent brightness of a star to an observer on Earth depends on both its luminosity and its distance from Earth. The Sun, which is about 93 million miles away from Earth, is much closer than Alpha Centauri, which lies about 4.37 light-years from Earth. This vast difference in distance makes the Sun appear much brighter to us than Alpha Centauri.