Question

A nearby star with an apparent magnitude of 9.7 and a distance of 2 parsecs has a luminosity of 1/100th of the Sun. What would its luminosity be if it were placed at a distance of 10 parsecs?

Answer 1

Hello,

Solution:

An apparent magnitude of a star measures its brightness.

The brightness of the star is,

The initial distance of the star is,

The initial luminosity of the star is,

Where, Ls is the luminosity of the sun.

The new distance of the star is,

We have to find the new luminosity of the star at the new distance. The brightness of the star remains same.

The expression of the relation between the luminosity, brightness and the distance of the star is

For Initial case,

       ......(1)

For new case,

........(2)

Dividing equation (2) by equation (1) as

Simplify this equation for L2 as

Substituting the given values in it as

The luminosity of the star at new distance is .

Thanking You!