Stellar Masses and Distances Worksheet
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Chaffey College *
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Subject
Astronomy
Date
Dec 6, 2023
Type
docx
Pages
4
Uploaded by MateMongoose804
Stellar Masses and Distances Worksheet
Name Leah Walker
Please answer in complete sentences and show all calculations in detail.
Part 1:
For stars on the main sequence, luminosity (expressed in units of the Sun’s luminosity, L
⊙
) varies as the fourth
power of the mass (in units of the Sun’s mass, M
⊙
)
L
M
4
If a main sequence star has a mass of 3 M
⊙
, how much more luminous will it be compared to the Sun?
L = (3
M
⊙
)^4 = 52
If two main sequence stars differ in mass by a factor of 2, by how much would they differ in luminosity?
L2/L1 = (M2/M1)^4
L2/L1 = (2)^4 = 16
In a binary star system, each star orbits the common center of mass (barycenter). Newton’s reformulation of
Kepler’s third law can be used to determine the combined mass of the stars if we know the semi-major axis of
the orbit and the orbital period. For the mutually orbiting stars, the orbital period (P) is the period with which
they go around each other and the semi-major axis happens to be the separation distance between the stars,
which we can call (d), so that the equation can be written as,
d
3
= (M
1
+M
2
)P
2
where
d
is in astronomical units (AU),
P
is in years (yr) and the mass is in solar mass units (M
⊙
).
A distant star and its companion are separated by about 11 AU and have an orbital period of about 27 years.
Calculate the combined mass of the system.
d
3
= (M
1
+M
2
)P
2
11
3
= (M
1
+M
2
)27
2
What other information would you need to determine the individual masses?
Click or tap here to enter text.
Part 2:
Refer to the following figure to answer the questions below.
A star of spectral class G is found to have a luminosity of 10,000 L
⊙
. What kind of star is it?
Super giant
What are the spectral type and luminosity class of a star with an effective temperature of 3000 K and a
luminosity of 10
-2
L
⊙
?
(Hint: for spectral class and temperature range, see Table 17.2 in your textbook)
O Blue > 30,000 Neutral and ionized helium lines, weak hydrogen lines
Part 3:
Your textbook defines a
parsec
(pc) as “the distance at which we have a parallax of one arcsecond”, so that we
have 1 parsec = 206,265 AU = 3.26 light-year. The distance (
D
) to a star in parsecs can then be calculated from,
D
=
1
p
where
p
is its parallax in arcseconds.
If you determine a certain star to have a parallax of 0.5 arcsecond, what would be the distance to that star in
parsecs?
D
=
1
p
=
d
=
1
.5
=
2
Part 4:
You make observations of the brightness of a cepheid variable over several weeks and obtain the following light
curve:
What is the average brightness (apparent magnitude) for this star?
3.6
What is the pulsation period for the star?
3 days
Briefly describe the steps involved in finding the distance to this star, assuming you have a working period-
luminosity relation.
1.
Measure the period of pulsation of the star
: Stars go through a cycle of brightening and shrinking, and
the time it takes to complete one cycle is called the period of pulsation.
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2.
Use the period-luminosity relation to calculate the mean luminosity
: To determine the distance of a
star, you can compare its brightness with its luminosity using the inverse square law of light. C =
(calibration distance) × Sqrt [ (calibration brightness)/ (apparent brightness)]
3.
Compare the luminosity to the mean apparent brightness and calculate a distance
: If we know the
luminosity of a star and its apparent brightness, we can calculate how far away it is.