HW 7 - Evan Klein
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School
University of Michigan *
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Course
102
Subject
Astronomy
Date
Jan 9, 2024
Type
Pages
4
Uploaded by DeanMusic10138
Problem 1 Table and Graph:
Table 1: Main sequence Stars
Star Name
Lum. (Sol)
Mass (Sol)
Diam. (Sol)
Lifetime
Sirius
25
2
1.7
Rigil Kent.
1.5
1.1
1.2
Vega
37
2.1
2.3
Procyon
7.7
1.5
2
Achernar
3300
7
10
Altair
10.6
1.8
1.8
Pollux
32
1.9
8
Fomalhaut
17.7
2.1
1.8
Regulus
150
3.5
3.2
Castor
30
2.2
2.3
Elnath
70
4.5
5.5
Miaplacidus
210
3
5.7
Alnair
380
4
3.6
Alioth
108
3
3.7
Kaus Aust.
375
5
7
Alkaid
700
6
1.8
Menkalinan
48
2.4
2.8
Alhena
160
2.8
4.4
Peacock
2100
5
4.4
Problem 2:
L = 1.78*M^3.66
The equation shows that mass and luminosity are exponentially proportional and that when we
raise mass to the 3.66 power and multiply by 1.78, we get a pretty accurate estimate of
luminosity.
Alpha in this equation = 3.66 which is similar to the expected 3.5 exponent.
I think that the dataset I used had a very clear correlation and that it would be hard for this
obvious correlation to yield a vastly different exponent than what is expected.
Problem 3:
Beta = -2.66
T = M^-2.66
T = 5.62*M^-2.66
Beta = 2.66
The expected formula is nearly identical to the actual formula and they have the same
exponent.
Problem 4:
1.
Based on your data and graphs; how does the luminosity of stars vary with their mass?
The luminosity of stars is positively exponentially related to its mass by an exponent of about
3.66. This means that as mass increases, so does luminosity
2.
Also based on your data and graphs; how do the lifetimes of stars vary with their mass?
The lifetimes of stars is inversely exponentially related to the mass of stars with an exponent of
about -2.66. This means that as mass increases, lifetime decreases.
3.
Based on your answers to the previous questions; how do the lifetimes stars vary with
their luminosity? Explain your answer.
Since we know that mass and luminosity are positively correlated, and mass and lifetime are
negatively correlated, when luminosity increases, lifetime decreases.
Problem 5:
1.
More massive main sequence stars are _____ than less massive ones.
A. more luminous (brighter).
B. less luminous (dimmer).
C. [there is no correlation
2.
More massive main sequence stars have ______ hydrogen fuel to burn than less
massive ones.
A. more
B. less
C. [there is no correlation]
3.
More massive main sequence stars live _____ lives than less massive ones.
A. longer
B. shorter
C. [there is no correlation]
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4.
More luminous (brighter) main sequence stars live _____ lives than less luminous
(dimmer) ones.
A. longer
B. shorter
C. [there is no correlation]
5.
The reason(s) for the answers to questions 3 and 4 is (are)
A. that more massive stars last longer because they have more hydrogen fuel to
burn.
B. that more massive stars have more fuel, but because they are hotter and
brighter they burn it more quickly.
C. [neither of the above-there is no correlation]