## Astr 2100 Descriptive Astronomy Fall 2017 - Assignment 10 due Monday November 20th 2017

#### Assignment

Finding the distances using stellar parallax
1. Star A, with a parallax angle of 0.1 arc seconds d = 1/A = 1/0.2 = 10 pc
2. Star B, with a parallax angle of 0.012 arc seconds d = 1/A = 1/0.012 = 83.3 pc
3. Look up the parallax angle for the star Arcturus, and use that to find its distance (in pc).
1. A = 0.08883 arc seconds (88.83 milliarcseconds)
2. d = 1/A = 1/0.08883 = 11.3 pc

Absolute and relative magnitudes

Star Absolute Magnitude (M) Relative Magnitude (m)
Deneb
-6.93
1.25
Capella
-0.54
0.05
Polaris
1.86
1.95
Aldebaran
-0.7
0.85
Zuben El Genubi
3.34
5.15
The table to the right shows the magnitudes of five stars.
1. Which one is the brightest in reality (most luminous)? Deneb, it has the most neagtive absolute magnitude
2. Which one is the least luminous? Zuben El Genubi, it has the most positive absolute magnitude
3. Which one appears brightest to us? Capella, it has the least neagtive absolute magnitude
4. Which one appears dimmest to us? Zuben El Genubi, it has the most positive relative magnitude

Finding the distance using the distance modulus

1. Star C is 450 pc from us. To us it appears to have a relative magnitude of 5.5. What is its absolute magnitude?
1. M - m = 5 - 5 log10(d)
2. M - 5.5 = 5 - 5 log10(450) = -8.26
3. M = -8.26 + 5.5 = -2.8
2. Look up the distance and relative magnitude of the star Spica. From that information calculate its absolute magnitude.
1. m = 0.97, d = 77 pc
2. M - m = 5 - 5 log10(d)
3. M - 0.97 = 5 - 5 log10(77) = -4.43
4. M = -4.43 + 0.97 = -3.5
3. Star D has a relative magnitude of 4.9 and an absolute magnitude of -3.1. How far is it from us?
1. 5 - 5 log10(d) = M - m
2. 5 - 5 log10(d) = M - m = -3.1 - 4.9 = -8
3. 5 log10(d) = 5 - (-8) = 13
4. log10(d) = 13/5 = 2.6
5. d = 102.6 = 398 pc
4. Star E has a relative magnitude of 1.8 and an absolute magnitude of 3.7. How far is it from us?
1. 5 - 5 log10(d) = M - m
2. 5 - 5 log10(d) = M - m = 3.7 - 1.8 = 1.9
3. 5 log10(d) = 5 - 1.9 = 3.1
4. log10(d) = 3.1/5 = 0.62
5. d = 100.62 = 4.2 pc

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