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Quiz 6
Physics 55: Introduction to Astronomy
Professor Henry Greenside
Monday, November 14, 2005
This quiz is closed book. You can use a scientific calculator but no other electronic device. If you have any
questions during the quiz, please do not hesitate to ask me.
The following formulas and data may be useful:
b=
σ ≈ 6 × 10−8
m2
L
,
4πd2
watt
,
Kelvin4
L = 4πr2 · σT 4 ,
d=
1 AU ≈ 1.5 × 108 km,
1
.
p
1 pc ≈ 3.3 ly.
True or False Questions (1 point each)
Please circle “T” for true or “F” for false to indicate the truth of the following statements.
1. T / F The distance to Earth of the A2-type supergiant star Deneb, about 2,500 ly, was determined
by parallax.
2. T / F As you move along a horizontal line of an H-R diagram from left to right, the apparent
brightness of a star decreases.
3. T / F As you move along a vertical line from bottom to top of an H-R diagram, a star becomes
bigger.
4. T / F As you move along a diagonal line from bottom left to top right of an H-R diagram, the
lifetime of a star becomes longer.
5. T / F Main sequence stars are more common in the universe than stars that are not on the main
sequence.
6. T / F If two stars of spectral types A and K are identical in size, then the K-type star is more
luminous.
7. T / F If two stars of spectral types A and K are identical in luminosity, then the K-type star has
the bigger radius.
8. T / F If the apparent brightness and spectral type of a main sequence star are measured with a
telescope, then the star’s approximate distance to Earth can be deduced from an H-R diagram.
1
Multiple Choice Questions (4 points each)
Circle the letter that best answers each of the following questions.
1. A star that has a parallax angle of (1/20)” is a distance
(a) 1/20 pc from Earth,
(b) 20 pc from Earth.
(c) 1/20 ly from Earth.
(d) 20 ly from Earth.
(e) some other value.
2. The feature that all stars on the main sequence have in common is
(a) size.
(b) mass.
(c) luminosity.
(d) surface temperature.
(e) age.
(f) membership in the same cluster.
(g) the type of nucleus that is undergoing fusion in the core.
3. All stars are born with about the same composition by mass of about 75% H and 25% He yet the stars
in the sky look quite different. Which two factors primarily determine the appearance of a star?
(a) mass and age.
(b) mass and surface temperature.
(c) apparent brightness and distance from Earth.
(d) apparent brightness and luminosity.
4. Cepheid variable stars are valuable to astronomers because
(a) they have the largest possible luminosity so that they can be seen from great distances.
(b) they explain why Algol varies every few days in apparent brightness.
(c) they have an easily determined luminosity.
(d) they are close enough for their distances to be determined by parallax.
5. The age of a cluster of stars can be determined from
(a) main sequence fitting.
(b) main sequence turnoff.
(c) the number of stars in the cluster.
(d) the radius of the cluster.
(e) pulsating variable stars in the cluster.
6. In astronomy, a “standard candle” is
(a) The apparent brightness of a standard wax candle one meter away.
2
(b) Any bright object that can be seen at a great distance.
(c) Any bright object whose apparent brightness can be determined.
(d) Any bright object whose luminosity can be determined without a measurement of the object’s
apparent brightness.
Open Questions
1. (6 points) Because of an intrinsic physical effect called the diffraction of light that blurs an image
whenever light passes through a narrow opening like the pupil of an eye, a person with keen vision can
only distinguish two points of light when they lie at least an angle of 1’ (one arcminute) apart; if two
points of light are closer than about this angle, a person sees only a single blurred point of light. Given
that Jupiter has an approximate circular orbit of radius 5.2 AU about the Sun and that Earth has an
approximate circular orbit of 1.0 AU about the Sun, determine by a calculation whether a person with
keen vision on Earth could see Jupiter’s biggest moon Ganymede as distinct from Jupiter, given that
Ganymede orbits Jupiter at a distance of 1.1 × 106 km from Jupiter.
Hints: Use the formula
180 s
in degrees,
π d
that relates the spatial distance s between two objects to the angle α (this is a lower case Greek alpha)
in degrees that separates the objects as measured from Earth, and to the distance d of the two objects
from Earth. Also take into account that a person will have his or her best chance of distinguishing
Ganymede from Jupiter when Jupiter is closest to Earth.
α=
3
2. Draw below a schematic picture of a Hertzsprung-Russell diagram and indicate on your diagram the
following features:
(a) (1 points) The quantity whose values are associated with the horizontal axis.
(b) (1 points) The numerical values on the left and right sides of the horizontal axis, i,e, the numerical
range of the horizontal axis.
(c) (1 points) The quantity whose values are associated with the vertical axis.
(d) (1 points) The numerical values associated with the top and bottom of the vertical axis, i.e., the
numerical range of the vertical axis.
(e) (3 points) Put a letter S where the Sun lies on this diagram and indicate the numerical values
of its horizontal and vertical coordinates on your plot.
(f) (2 points) Put a capital M where the most massive main sequence stars lie on this diagram and
indicate the approximate value of this maximum mass in terms of the mass of the Sun.
(g) (2 points) Put a lower case m where the least massive main sequence stars lie on this diagram,
and indicate what is the approximate value of the smallest stellar mass in terms of the mass of
the Sun. (Make sure your lower case and upper case m’s are easily distinguished).
(h) (1 points) Put a label SG where supergiant stars are found on this diagram.
(i) (1 points) Put a label WD where white dwarfs are found on this diagram.
(j) (2 points) Put an upper case R where the stars of biggest radius are found on the diagram, and
indicate the value of the biggest radius in terms of the radius of the Sun.
(k) (2 points) Put a lower case l where the main sequence stars of the longest lifetime occur, and
indicate the approximate longest lifetime in years.
4
Extra Credit
(5 points) The Dukeades and UNCeades are recently discovered open star clusters near the constellation known as the Triangle. Given the figure below and the fact that the Hyades open cluster is about
150 ly from Earth, what is the approximate distance of all the stars in the UNCeades cluster to Earth?
100
relative apparent brightness
Hyades
UNCeades
10
1
Dukeades
0.1
10,000
6,000
surface temperature (Kelvin)
5