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Review of the Relationship between Absolute Magnitude and Luminosity and Practice Problems Review Chapter 11.1.3 Magnitude System in AstronomyNotes for a more complete discussion of the details of this relationship. The Relationship between Absolute Magnitude and Luminosity The relationship between the absolute magnitude of two stars and their luminosities is LStar 1 M Star 2 M Star 1 2.512 LStar 2 LStar 1 M Star 2 M Star1 2.512 LStar 2 Practice Problem 1: Star 1 has an absolute magnitude of -7 and star 2 has an absolute magnitude of 3.5. How many times more luminous is star 1 compared to star 2? Solution: M Star 2 M Star 1 3.5 7 10.5 LStar 1 2.512 M Star 2 M Star 1 2.51210.5 15,856 LStar 2 Answer in a sentence: Star 1 is about 15,856 times more luminous than star 2. LStar 1 M Star 2 M Star1 2.512 LStar 2 Practice Problem 2: Star 1 has an absolute magnitude of 11.5 and star 2 has an absolute magnitude of 4.8. How many times more luminous is star 2 compared to star 1? Solution: M Star 2 M Star 1 4.8 11.5 6.7 LStar 1 2.512 M Star 2 M Star 1 2.512 6.7 0.00209 LStar 2 Answer in a sentence: Star 1 is about 0.00209 times less luminous than star 2 or equivalently star 1 is about 2 thousandths of the luminosity of star 2. LStar 1 M Star 2 M Star1 2.512 LStar 2 Practice Problem 3: Star 1 has an absolute magnitude of 0. How many times more luminous is star 1 compared to the Sun? Note: the absolute magnitude of the Sun is +4.8. Solution: M Sun M Star 1 4.8 0 4.8 LStar 1 2.512 M Sun M Star 1 2.512 4.8 83.2 LSun Answer in a sentence: Star 1 is about 83.2 times more luminous than the Sun. LStar 1 M Star 2 M Star1 2.512 LStar 2 Practice Problem 4: Star 1 has an absolute magnitude of 15. How many times more luminous is star 1 compared to the Sun? Solve this yourself Answer in a sentence: Star 1 is about 8.31×10-5 times the luminosity of the Sun of equivalently 83 millionths the luminosity of the Sun or 12,028 times less luminous than the Sun. LStar 1 2.512 M Star 2 M Star 1 LStar 2 Practice Problem 5: How does the blue star on the HR diagram to the right compare in luminosity to the Sun? (Assume MSun = 5) MSun = 5 and MBlue Star = -3 LBlue Star 2.512 M Sun M Blue Star LSun 2.5125 3 2.5128 1,585 Answer in a sentence: The blue star has a luminosity of about 1,585 times that of the Sun. LStar 1 2.512 M Star 2 M Star1 LStar 2 Practice Problem 6: How does the red star on the HR diagram to the right compare in luminosity to the Sun? (Assume MSun = 5) MSun = 5 and MRed Star = -9 LBlue Star 2.512 M Sun M Blue Star LSun 2.51259 2.512 4 0.0251 Answer in a sentence: The red star has a luminosity of about 0.0251 times that of the Sun or about 2.5% the Sun’s luminosity. LStar 1 2.512 M Star 2 M Star1 LStar 2 Practice Problem 7: How does the red star on the HR diagram to the right compare in luminosity to the Sun? (Assume MSun = 5) Solve this yourself Answer in a sentence: The red star has a luminosity of about 63,130 times that of the Sun.