# Astronomy | Geophysics homework help

1. Matching: How do astronomers determine the physical characteristics of stars? Match each characteristic of stars with an important technique that astronomers use to determine that characteristic. Refer to Table 18.2 and page 660 in Chapter 19 when answering this question. Each answer will be used once.

How do   Astronomers determine the …

of a   star?

Technique

Surface   temperature

Mass

Diameter

Luminosity

Distance

Techniques for Question 1: Measure the apparent brightness and determine the distance to the star / Measure the Doppler shift / Measure the light curves and Doppler shifts for eclipsing binary stars / Measure the star’s parallax / Measure the peak wavelength of the star’s spectrum and apply Wien’s Law / Measure the period and radial velocity curves for spectroscopic binary stars

2. Matching: (Review Question 4 on page 682 in OSA) Which method would you use to obtain the distance to each of the following? Choose the best answer below:

Method

A. An asteroid crossing Earth’s orbit

B. A star astronomers believe to be no more   than 50 light-years from the Sun

C. A tight group of stars in the Milky Way   Galaxy that includes a significant number of variable stars.

D. A star that is not variable but for which   you can obtain a clearly defined spectrum.

Methods for Question 2: RR Lyrae and/or Cepheid variable stars can be used to determine the distance / Measure the parallax of the object and calculate the distance by triangulation / The information you have is sufficient to allow you to place the star in the correct location on the H-R diagram; this allows you to accurately estimate the object’s luminosity and, using the inverse-square law, its distance / Send a radar beam toward the object and measure the return time

3. (Review Question 5 on page 682 in OSA) What are the luminosity class and spectral type of a star with an effective temperature of 5000 K and a luminosity of 100 Lsun?

A. First, calculate the radius of the star relative to the Sun using the equation L*/Lsun = (R*/Rsun)2 (T*/Tsun)4. The radius of this star is ( 1/100 times / 1/10 times / 1/5.5 times / the same as / 10 times / 13.5 times / 100 times) the radius of the Sun.

B. The luminosity class of this star is ( Ia / Ib / II / III / IV / V / wd ). This indicates that it is a ( Bright Supergiant / Less Luminous Supergiant / Bright Giant / Giant / Subgiant / Main Sequence / White Dwarf ) star. If you need help, refer to page 676 in OSA.

C. The spectral type of this star is ( O / B / A / F / G / K / M ). If you need help, refer to Table 17.2 on page 601 in OSA.

4. What are the spectral type and luminosity class of the star Regulus which has a surface temperature of 10,750 K and a luminosity of 220 Lsun? Regulus is in the constellation Leo and represents the Lion’s Heart.

A. First, calculate the radius of Regulus relative to the Sun using the equation L*/Lsun = (R*/Rsun)2 (T*/Tsun)4. The radius of the star Regulus is ( 1/220 times / 1/20 times / 1/13.5 times / the same as / 4.3 times / 20 times / 220 times) the radius of the Sun.

B. The spectral type of this star is ( O / B / A / F / G / K / M ). If you need help, refer to Table 17.2 on page 601 in OSA.

C. The luminosity class of this star is ( Ia / Ib / II / III / IV / V / wd ). This indicates that it is a ( Bright Supergiant / Less Luminous Supergiant / Bright Giant / Giant / Subgiant / Main Sequence / White Dwarf ) star. This is not easy to interpret using Figure 19.15 in OSA. I recommend that, instead, you determine where Regulus would plot on the H-R diagram we used for questions 7 and 8 on the Chapter 18 homework; this version is easier to interpret because it is contoured in terms of solar diameters.

5. (Thought Question 18 on page 683 in OSA) A G2 star has a luminosity 100 times that of the Sun. What kind of star is it? How does its radius compare to that of the Sun? Refer to Figure 19.15 when answering part A of this question.

A. The luminosity class of this star is ( Ia / Ib / II / III / IV / V / wd ); it is a ( Bright Supergiant / Less Luminous Supergiant / Bright Giant / Giant / Subgiant / Main Sequence / White Dwarf ) star.

B. The radius of this star is ( 1/100 times / 1/10 times / the same as / 10 times / 100 times ) that of the Sun.

6. (Thought Question 19 on page 683 in OSA) A star has a temperature of 10,000 K and a luminosity 10-2 Lsun. What kind of star is it? Refer to Figure 19.15 when answering this question.

The luminosity class of this star is ( Ia / Ib / II / III / IV / V / wd ); it is a ( Bright Supergiant / Less Luminous Supergiant / Bright Giant / Giant / Subgiant / Main Sequence / White Dwarf ) star.

7. (Thought Question 20 on page 683 in OSA) What is the advantage of measuring a parallax distance to a star as compared to our other distance measuring methods?

a. Results from the parallax method can be directly compared to results from measuring the periods of Cepheid variable stars since there are a number of these stars located close to our Solar System.

b. Distances calculated by the parallax method do not rely on any assumptions made about the star; these distances depend only on geometric calculations.

c. As long as a clear spectrum of the star can be obtained, its distance can be calculated using the parallax method.

8. (Thought Question 21 on page 683 in OSA) What is the disadvantage of the parallax method, especially for studying distant parts of the Galaxy? The parallax method can only be used ______.

a. for stars that are relatively close to us in the Milky Way Galaxy.

b. if a clear spectrum of the star can be obtained.

c. if the star of interest is part of a binary system.

d. if the star of interest is a particular type of variable star.

9. (Thought Question 24 on page 683 in OSA) Why would it be easier to measure the characteristics of intrinsically less luminous Cepheids than more luminous ones?

The relationship that pertains specifically to Cepheid variable stars is the ( Hertzsprung-Russell / period-luminosity / mass-luminosity / Stefan-Boltzmann ) relationship. Hence, the most important characteristic that astronomers want to measure for a Cepheid variable star is ( its surface temperature / its Doppler shift / its absorption lines / the period of its light curve ). It would be easier to make this measurement for a less luminous Cepheid because ( it is easier to measure low surface temperatures rather than high surface temperatures / these have a greater Doppler shift / they have stronger absorption lines / the period for less-luminous Cepheids is shorter making it easier to measure).

10. When Henrietta Leavitt discovered the period-luminosity relationship, she used Cepheid variable stars that were all located in the Large Magellanic Cloud (LMC). It was (easier / more difficult ) to compare Cepheids in the LMC rather than those located in the Milky Way Galaxy because they are all ( about the same distance away / located at widely varying distances from Earth ). As a result ( differences in apparent brightness are directly related to differences in intrinsic brightness of these stars / all of these stars have the same Doppler shift / all of these stars have the same proper motion ).

11. (Figuring for Yourself Question 28 on page 684 in OSA) Estimate the minimum and maximum time it takes a radar signal to make the round trip between Earth and Venus, which has a semimajor axis of 0.72 AU. Hint: draw a diagram! See the one-slide PowerPoint titled “Superior and Inferior Conjunctions” if you need help.

The minimum distance between the Earth and Venus (inferior conjunction) is _____ AU. Your answer should be in the format x.xx.

The maximum distance between the Earth and Venus (superior conjunction) is _____ AU. Your answer should be in the format x.xx.

How long does it take a radar signal to make the round trip between the Earth and Venus when Venus is at its minimum distance from Earth (inferior conjunction)? It takes a radar signal ____ minutes and ____ seconds to travel between the Earth and Venus and back when they are at their minimum possible distance apart. Enter a whole number in each blank; the number in the second blank should be less than 60.

How long does it take a radar signal to make the round trip between the Earth and Venus when Venus is at its maximum distance from Earth (superior conjunction)? It takes a radar signal ____ minutes and ____ seconds to travel between the Earth and Venus and back when they are at their maximum possible distance apart. Enter a whole number in each blank; the number in the second blank should be less than 60.

12. (Figuring for Yourself Questions 38 and 39 on page 684 in OSA) The most recently discovered system close to Earth is a pair of brown dwarfs known as Luhman 16. It has a distance of 6.5 light years.

A. How many parsecs is this? _______ parsecs. Round your answer to the nearest whole number.

B. What would the parallax of Luhman 16 be as measured from Earth? The parallax of Luhman 16 is ______ arcseconds. You may enter your answer as a fraction or a decimal number.

13. The star Fomalhaut is 25 light-years from us. What is this distance in parsecs? ____ parsecs; your answer should be in the format x.x. What would be the parallax of Fomalhaut? ______ arcseconds; give your answer in the format x.xx

14. Star A has a parallax of 0.4 seconds of arc, while star B has a parallax of 0.06 seconds of arc. Which star is closer? Star A is ( closer to / farther from ) Earth than Star B.

Star A has a parallax of 0.4 seconds of arc. Star A is ( 0.06 / 0.4 / 1.3 / 2.5 / 5 / 10.6 / 16.7 ) ( parsecs / light-years) from Earth.

Star B has a parallax of 0.06 seconds of arc. Star B is ( 0.06 / 0.4 / 1.3 / 2.5 / 5 / 10.6 / 16.7 ) ( parsecs / light-years) from Earth.

15. The parallax of the star Regulus is 0.042 arcseconds. What is the distance to Regulus in parsecs? ______ parsecs; your answer should be in the format xx.x. What is the distance to Regulus in light-years? ______ light-years; round your answer to the nearest whole number.

16. (Question 40 from A. Frank, 2016, page 103) Two stars are known to have the same luminosity, but one appears one-sixteenth (1/16) as bright as the other. How many more times distant is the dimmer star?

The dimmer star is ____ times more distant than the brighter star. Enter a whole number in the blank.

17. (Question 41 from A. Frank, 2016, page 103) Star A is 9 times as far away as star B. Both appear to have the same brightness. What is the ratio of the luminosity of star A to that of star B?

Star A is ____ times as luminous as star B. Enter a whole number in the blank.

18. (Figuring for Yourself Question 41 on page 684 in OSA) What physical properties are different for an M giant with a luminosity of 1000 Lsun and an M dwarf with a luminosity of 0.5 Lsun? What physical properties are the same? Place “same” or “different” in each blank.

Surface   temperature

Diameter

Luminosity

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