Question

Barnard's star is a near neighbor of the Sun whose properties we know quite well. It is a type M4V with absolute magnitude 13.22. Suppose that another star of spectral type M4V is observed to have apparent magnitude "8.22." How far away is it?

Answer 1

Answer:

The star is at a distance of 100 parsecs.

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:

$d = 10^{(13.22 - 8.22+ 5)/5}$  

$d = 100 pc$    

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

Key term:

Parsec: Parallax of arc seconds

Answer 2

In this exercise, we have to use distance and logarithm knowledge to find:

The star is at a distance of 100 parsecs.

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

$M-m=5log(d)-5$

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:

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

Then, Applying logarithmic properties it is gotten:

$d=10^{M-m+5)/5$

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:

$d= 10^{(13.22-8.22+5)/5}\\d= 100 pc$

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

See more about distance modulus at brainly.com/question/15178872