Stars come in all different brightnesses and distances, which makes the sky very

Question

Stars come in all different brightnesses and distances, which makes the sky very complicated in appearance. Two quantities determine how bright a star will appear in the sky. The first is its distance, and the second is the brilliance or ‘luminosity’ of the star, measured in watts. If you take a 100-watt light bulb and place it 10 meters away from you, the amount of light you see will look the same as a 1-watt light bulb only 1 meter away. For stars, the apparent brightness or ‘magnitude’ of a star depends on its distance and its luminosity, also called its absolute magnitude. What you see in the sky is the apparent brightness of a star. The actual amount of light produced by the surface of the star is its absolute magnitude. A simple equation, basic to all astronomy, relates the star’s distance in parsecs, D, apparent magnitude, m, and absolute magnitude, M as follows: M = m + 5 - 5log(D)

Problem 1 – The star Sirius has an apparent magnitude of m = -1.5, while Polaris has an apparent magnitude of m = +2.3. If the absolute magnitude of Sirius is M = +1.4 and Polaris is M = -4.6, what are the distances to these two stars?

Problem 2 – An astronomer determined the distance to the red supergiant Betelgeuse as 200 parsecs. If its apparent magnitude is m = +0.8, what is the absolute magnitude of this star?

Problem 3 – As seen in the sky, Regulus and Deneb have exactly the same apparent magnitudes of m = +1.3. If the distance to Deneb is 500 parsecs, and the absolute magnitude of Regulus is 1/9 that of Deneb, what is the distance to Regulus?

Explanation / Answer

1.For Sirius the equation will be, 1.4=-1.5+5-5log(D)

Or, -2.1=-5log(D)

So, D =antilog(2.1/5)

D = -0.37 parsec

For Polaris the equation is, -4.6=2.3+5-5log(D)

Or, -11.9=-5log(D)

So, D=antilog(11.9/5)

D=0.37 parsec

The appearence of the negative sign in the first result indicates the fact that both the stars will appear at diametrically opposite positions with respect to the observer.

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