The star Vega has an apparent visual magnitude of 0.03, and the star HR 4374 has an apparent visual magnitude of 4.87. It has been determined that both stars are at the same distance from Earth. What does this information tell us about the two stars? (A) Vega must be closer to Earth than HR 4374. (B) Vega must be farther from Earth than HR 4374. (C) Vega must produce less energy than HR 4374. (D) Vega must produce more energy than HR 4374. (E) Vega will appear fainter to us than HR 4374.

(D) Vega must produce more energy than HR 4374.

Explanation:

The apparent visual magnitude is defined as the luminosity of a star seen from earth. The Greek astronomer Hipparcos was the first who invent a numerical scale to describe how bright a star appear to be in the sky to the naked eye, so he gave an apparent magnitude of 6 to the faintest star in the sky and an apparent magnitude of 1 to the brigthest one. Since the arrive of the telescope era this range was expanded to negative numbers for the most luminous one.

The human eye has a logaritmical response to the luminosity of stars, so as an example, if one star has an apparent magnitude of 6 and another one has an apparent magnitude of 1, the second one will be 100 times brigther than the first one. In the other hand, for a star that has apparent magnitude of 1 it will appear to be 2.512 times brigther than a star with apparent magnitude of 2.

The apparent magnitude of a star can variate as a consecuence of the distance from earth or for its energy production.

With all these facts clear enough described above, it is easier to conclude that as the two star are at the same distance the apparent visual magnitude will depend in the energy production. In the case of Vega it has an apparent visual magnitude of 0.03, while HR 4374 has an apparent visual magnitude of 4.87. According with the scale stablished for Hipparcos, Vega will be more luminous than HR 4374. This means that Vega produce more energy than HR 4374.