## Assume All Stars Have Same Absolute Magnitudes

Exercise 4.1 The total magnitude of a triple star is 0.0. Two of its components have magnitudes 1.0 and 2.0. What is the magnitude of the third component?

Exercise 4.2 The absolute magnitude of a star in the Andromeda galaxy (distance 690 kpc) is M = 5. It explodes as a supernova, becoming one billion (109) times brighter. What is its apparent magnitude?

Exercise 4.3 Assume that all stars have the same absolute magnitude and stars are evenly distributed in space. Let N(m) be the number of stars brighter than m magnitudes. Find the ratio N(m +1)/N(m).

 Altitude Zenith distance Air mass Magnitude 50° 40° 1.31 0.90 35° 55° 1.74 0.98 25° 65° 2.37 1.07 20° 70° 2.92 1.17

By plotting the observations as in the following figure, we can determine the extinction coefficient k and the magnitude m0 outside the atmosphere. This can be done graphically (as here) or using a least-squares fit.

Extrapolation to the air mass X = 0 gives m0 = 0.68. The slope of the line gives k = 0.17.

Exercise 4.4 The V magnitude of a star is 15.1, B — V = 1.6, and absolute magnitude MV = 1.3. The extinction in the direction of the star in the visual band is aV = 1 mag kpc-1. What is the intrinsic colour of the star?

Exercise 4.5 Stars are observed through a triple window. Each surface reflects away 15% of the incident light.

a) What is the magnitude of Regulus (MV = 1.36) seen through the window?

b) What is the optical thickness of the window?

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