Download Review of the Principles of Stellar Parallax and Practice Problems

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
 2.5125 3 
 2.5128 
 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
 2.51259 
 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.