Question

Our Sun is a G2V star with absolute magnitude 4.8. Suppose that a star of spectral type G2V is observed to have apparent magnitude -0.2. How far away is it? A 1 parsec. B 5 parsecs. C 10 parsecs. D 100 parsecs. E 1000 parsecs.

Answer 1

Option D

The star is at a distance of 100 parsecs.

Step-by-step explanation:

The distance can be determined by means of the distance modulus:

`M - m = 5log(d) - 5` (1)

Where M is the absolute magnitude, m is the apparent magnitude and d is the distance in units of parsec.

Therefore, d can be isolated from equation 1

`log(d) = (M - m + 5)/5`

Then, Applying logarithmic properties it is gotten:

`d = 10^((M - m + 5)/5)` (2)

The absolute magnitude is the intrinsic brightness of a star, while the apparent magnitude is the apparent brightness that a star will appear to have as is seen from the Earth.

Since both have the same spectral type is absolute magnitude will be the same.

Finally, equation 2 can be used:

`d = 10^((4.8 - (-0.2)+ 5)/5)`

`d = 100 pc`

Hence, the star is at a distance of 100 parsecs.

Key term:

Parsec: Parallax of arc seconds