Astronomy Assignment – The Stars

 

Reading           Chapter 17

 

 

Objectives/HW

 

       The student will be able to:

HW:

1

Define and apply stellar parallax and the unit of the parsec.

1 – 3

2

Relate parallax and the parsec to skinny triangles and other units such as meters and light years.

3

Define and describe proper motion.

4 – 6

4

Describe and apply methods by which the velocity of a star through space may be determined by including both radial and transverse velocity.

5

Describe direct and indirect methods used to determine the size of a star and classify stars as giants, supergiants, or dwarfs.

7 – 8

6

State and apply the relation between luminosity, radius, and temperature.

7

State and apply the relation between luminosity, distance, and energy flux.

9 – 16

8

Define and contrast the concepts: absolute magnitude, intrinsic brightness, luminosity, and apparent magnitude, apparent brightness, energy flux.

9

Explain and apply the magnitude scale of brightness.

10

Describe and apply the relation between a stars color and its temperature.

17

11

Define, describe, and apply color index and explain its application in photometry and its relationship to blackbody radiation and Wein’s Law.

12

State in order of temperature the stellar spectral classes and list characteristics and examples of each.

18

13

Describe and define the Hertzsprung-Russell diagram in terms of each axis.

19 – 23

14

Plot a star’s coordinates on the H-R diagram.

15

Explain and illustrate how the H-R diagram is used to help classify and understand different types of stars such as main sequence stars, red giants, blue giants, supergiants, red dwarfs, and white dwarfs.

16

Define, describe, and give examples of the stellar luminosity classes.

24 – 25

17

Describe and apply the method of spectroscopic parallax and explain the importance of luminosity class to this method.

 

18

Describe and explain methods for determining a star’s mass and relate to the different types of binary-star systems:  visual binary, spectroscopic binary, and eclipsing binary.

26

19

Describe and explain the significance of a star’s mass in determining its location on the H-R diagram and in determining the lifetime of the star.

27

20

Describe properties and significance of open clusters and globular clusters.

 

 

Reminder:  Write out conceptual answers in complete sentences.  You must show work to get credit for numerical problems.  You will still get credit even if you get the wrong answer so long as you make a reasonable attempt to work the problem.

1.      Determine the distance to the star Zubenelgenubi (Alpha Librae) based on its parallax of 0.0435″.  Give your answer in both parsecs and light years.

2.      The star Zubeneschamali (Beta Librae) is 1.75 x 1018m away from Earth.  (a) Convert this distance to light years and parsecs.  (b) Calculate the parallactic angle.

3.      At a distance of 590 pc the star iota1 Scorpii has a parallax of about 1.7 mas.  Stars at this distance (or greater) have parallactic angles that are straining the limits of detection and measurement.  Suppose an astronomical observatory could be built on Mars, which is 1.52 A.U. from the Sun – this would extend the reach of the parallax method.  (a) What would be the parallax of iota1 Scorpii as observed from Mars?  (b) At what maximum distance would a star have a parallax of 1.7 mas as observed from Mars?

4.      Answer the following for the Twenty Brightest Stars (see appendix in your book or table given in class).  Find the columns: proper motion, transverse velocity, and radial velocity. 
(a) Which star listed is approaching our Sun most rapidly?  At what rate?  (b) Which star is receding (moving away) from our Sun most rapidly?  At what rate?  (c) Which star is moving through space (in any direction) at the greatest velocity?  At what rate?

5.      Consulting the same table, compare Procyon and Betelgeuse.  Although the two stars have similar values for transverse velocity, Procyon has a much greater proper motion.  Explain!

6.      A certain star in Canis Major has a transverse velocity of 16.8 km/s and a blueshift of 0.0000183.  (For low values (less than 0.05) the amount of redshift or blueshift is the ratio v/c where c = speed of light, 300,000 km/s – see pp. 650 – 651.)  The distance from the Sun to this star is 2.64 pc.  (a) Determine the star’s proper motion in arc seconds per year.  (b) Determine its radial velocity in km/s and describe the direction as approaching or receding. 
(c) Determine the true velocity of the star through space.  Can you identify this star?

7.      Use proportions and the relation from pp. 450 – p. 451.  (a) Determine the luminosity of a star having three times the radius of the Sun and a surface temperature twice that of the Sun?  (b) A certain star has the same surface temperature as the Sun and yet it is 100 times more luminous.  What is its radius, in solar units?  (c) Another star has the same luminosity as the Sun and yet its temperature is 20,000 K.  What is its radius, in solar units?  (d) Yet another star has a temperature three times that of the Sun and a luminosity 64 times greater than the solar value.  What is its radius, in solar units?

8.      Besides the technique used in the previous problem describe at least two other methods that astronomers can use to determine the diameter of stars.

9.      The Sun’s luminosity is 3.85 x 1026 Watts.  At the Earth’s distance, the energy flux from the Sun is 1370 W/m2.  Determine the solar energy flux at the following distances:  (a) at Jupiter’s distance 5.20 A.U., (b) at Mercury’s distance of 0.39 A.U., and (c) at Pluto’s distance of 39.5 A.U.

10.  Two stars are observed to have the same apparent brightness in the night sky.  It is determined that star A has a luminosity of 0.5 solar units and star B has a luminosity of 4.5 solar units.  Which star is more distant, and how much farther away is it than the other?

11.  The brightest object in the sky is the Sun at magnitude –27.  The dimmest objects visible in the night sky are stars with magnitude 6.  By what factor is the Sun’s light brighter than the dimmest star’s light in terms of energy flux?

12.  Suppose star C and star D have equal luminosities and that Star C has an apparent magnitude of 0 and star D has an apparent magnitude of 5.  (a) Which star appears brighter and by how much?  (b) Which star is farther away and by how much?

13.  Calculate the distance in parsecs to the Sun based on its absolute magnitude of 4.83 and its apparent magnitude of –26.7.  If you convert to AU do you get the expected result?

14.  Determine the distance to each star based on its absolute and apparent magnitudes.
(a) iota1 Scorpii:  M = -5.85, m = 3.03
(b) Kepler-22:  M = 5.27, m = 11.664

15.  The star Deneb has an absolute magnitude of –8.38 compared to the Sun’s absolute magnitude which is 4.83.  Which star is intrinsically brighter and by what factor?

16.  The stars Spica and Antares have nearly equal magnitudes at about 1.0.  Spica is 77 pc away and Antares is 170 pc away.  Which star is more luminous and by what factor?

17.  Use Table 17.1 on p. 448 or https://en.wikipedia.org/wiki/Color_index.  For each of the following stars determine its approximate temperature and color.  (a) The star Alnilam in Orion has magnitude 1.553 when viewed through a B filter an magnitude 1.692 when viewed through a V filter.  (b) The star SAO 44383 has B magnitude 7.719 and V magnitude 6.014.  (c) The star Beid in Eridanus has B magnitude 4.441 and V magnitude 4.073.

18.  When the spectral classes were first invented they went in order A, B, C, etc.  Now the classes are arranged in order OBAFGKM.  (a) What was the original basis for the alphabetical order of the classes?  (b) What is the current basis for arranging the classes OBAFGKM?

19.  For each of the following regions on the H-R diagram describe its identifying characteristics:  (a) main sequence, (b) blue giants, (c) red giants, (d) white dwarfs, (e) red dwarfs.

20.  Use the H-R diagrams on p. 453 and/or Overlay 1 between pp. 552 and 553 to classify each of the following as one of the above types of stars. 
(a) A star with temperature = 9000 K and luminosity = 0.005 solar units.
(b) A star with temperature = 4000 K and luminosity = 2000 solar units.
(c) A star with temperature = 6000 K and luminosity = 1 solar units.
(d) A star with temperature = 10,000 K and luminosity = 100 solar units.
(e) A star with temperature = 10,000 K and luminosity = 10,000 solar units.

21.  Use the H-R diagrams to answer the following questions in approximate terms.
(a) Determine the luminosity of a type B star on the main sequence.
(b) Determine the size of a type M star on the main sequence.
(c) Find the spectral type and temperature of a main sequence star 1 tenth the Sun’s diameter.
(d) Find spectral type and size of a main sequence star that is 100 times the Sun’s luminosity.
(e) Compare and contrast a type M main sequence star and a type M red giant star.

22.  Why does the H-R diagram constructed using the brightest stars differ so much from the diagram constructed using the nearest stars?

23.  Which stars are most common in the Galaxy?  Why don’t we see many of them in H-R diagrams?

24.  Give the six different luminosity classes and describe stars found in each class.

25.  Compare and contrast a G2V star and a G2II star – differences?  Similarities?

26.  Explain the three different types of binary star systems and how astronomers determine the period of revolution for these systems.

27.  Given that the Sun’s lifetime is about 10 billion years, estimate the life expectance of (a) a 0.2 solar mass, 0.01 solar luminosity red dwarf, (b) a 3 solar mass, 30 solar luminosity main sequence star, (c) a 10 solar mass, 1000 solar luminosity blue giant.

Selected Answers

 

1. 23.0 pc or 75.0 ly

2. a. 56.7 pc or 185 ly

    b. 17.6 mas

3. a. 2.6 mas

    b. 890 pc

4. a. (Hint: all three answers

    b.   begin with the letter A)

    c.

5.

6. a. 1.34″/yr

    b. –5.5 km/s (approaching)

    c. 17.7 km/s

7. a. 144 L⊙

    b. 10 R⊙

    c. 0.084 R⊙

    d. 0.89 R⊙

8.

9. a. 51 W/m2

    b. 9000 W/m2

    c. 0.88 W/m2

10. ? is 3 × more distant than ?

11. Sun’s flux is 16 trillion times greater

12. a. ? appears 100 × brighter

      b. ? is 10 × more distant

13. 4.94 × 10–6 pc (yes, = 1.02 AU)

14. a. 597 pc

      b. 190 pc

15. ? is 190,000 × brighter

16. ? is 4.9 × brighter than ?

17. a.

      b.

      c.

18. a.

      b.

19. a.

      b.

      c.

      d.

      e.

20. a.

      b.

      c.

      d.

      e.

21. a.

      b.

      c.

      d.

      e.

22.

23.

24.

25.

26.

27. a. 200 billion years

      b. 1 billion years

      c. 100 million years