Question

The Sun is about 10.0 billion times brighter than the next brightest star, Sirius (as seen from Earth). How far would we have to be from the Sun for the Sun to be as bright as Sirius?

We would have to be ___× 10 5th AU or _____light-years away from the Sun.

Answer 1

The sun is 10⁹ times brighter than Sirius, which has an apparent magnitude of -1.4. The apparent magnitude of the Sun is -26.7, while its absolute magnitude is 4.83. For the Sun to have a brightness as such as Sirius, it would have to have an apparent magnitude of-1.4. We can calculate the distance using the absolute and apparent magnitudes.

The distance of a star can be calculated if its absolute and apparent magnitudes are known,using the formula as shown below:

d = 10x10^(m-M)/5

where m and M are the apparent and absolute magnitudes respectively.

Thus,

d = 10x10^{(-1.4-4.83)/5}

d = 171.69pc

Thus, the Sun would have to be at a distance of 171.69 parsecs to appear as bright as Sirius.