Question

Consider two stars that are identical (same size, temperature and luminosity). Star A is 10 pc away from us and Star B is 20 pc away. How would the apparent brightness of the two stars compare

Answer 1

Answer:

Star A would be brighter than Star B

Explanation:

The apparent brightness of a star as perceived on Earth is dependent on its temperature, size, luminosity and distance from the Earth. Apparent brightness is the visible brightness to the eye at the surface of the Earth, while luminosity is the true brightness at the surface of the star.

A hotter star will radiate more energy per second per meter square of surface area. A larger star will have a greater surface area for radiation of energy, thus increasing the luminosity. For two identical stars, the difference in apparent brightness will be dependent on their distances from Earth.

Brightness and distance from earth have an inverse square relationship.

$brightness$∝$\frac{1}{distance^{2} }$

Assuming the star is a point source of radiation, as distance from the source is increased, the radiation is distributed over a surface proportional to the distance form the source. As distance is further increased, the radiation is distributed over a larger surface area reducing the effective luminosity.

If one star (Star B) is twice as far from the earth as the first (Star A), the brightness of Star B will be $\frac{1}{2^{2} }$ of Star A.

Thus, Star B will appear to be a quarter of the brightness of Star A. Or, Star A will appear to be 4 times as bright as Star B.