Question

Alpha Centauri B is a star that is about the same size as the Sun. Why does it appear much smaller and dimmer than the Sun when seen from Earth?

Answer 1

 To the eye – taken by itself – Alpha Centauri A appears as the fourth-brightest star seen from Earth, just slightly outshone by Arcturus. However, the combined light of Alpha Centauri A and B is slightly greater than Arcturus, so in that sense it appears as the third-brightest star visible in Earth's sky.

Answer 2

Alpha Centauri B appears much smaller and dimmer than Sun, due to its greater distance from earth than Sun's and its lesser temperature than Sun, respectively.

Step-by-step explanation:

Alpha Centauri B has a mass of 0.907 times the mass of Sun. But, its luminosity is less than that of the luminosity of Sun, because its temperature (5260 K) is less than that of the Sun (5778 K).

This, is the reason why Alpha Centauri B appears dimmer than the Sun.

The Sun is at a distance of 0.000015559 light years from earth, while Alpha Centauri B is at much larger distance of 4.37 light years from Earth.

Due, to this reason Alpha Centaurus B appears much smaller than the Sun from Earth.