Chapter 15 Homework

Which of the following must be true if we are to infer (calculate) a star's luminosity directly from the inverse square law for light?

- We have measured the star's apparent brightness - We have measured the star's distance. - No interstellar gas or dust absorbs or scatters light between us and the star.

You should now see that the reason the mass of the star in Part A must be inferred is that the star has no known orbiting objects, which means we cannot apply Newton's version of Kepler's third law. Which of the following must be true if the star's inferred mass is to be accurate?

- We have measured the star's spectral type - We have determined that the star is a main-sequence star

Approximately what is the parallax angle of a star that is 20 light-years away?

0.16 arcsecond.

About what is Rigel's surface temperature?

10,000 K

Rigel's luminosity is about _____ times the Sun's luminosity.

100,000

Suppose there was a star with a parallax angle of 1 arcsecond. How far away would it be?

3.26 light-years

Suppose that a star had a parallax angle of exactly 1 arcsecond. Approximately how far away would it be, in light-years?

3.3 light-years.

A star with a parallax angle of 0.0001 arcsecond is _______ away from us.

32,600 light-years

A star with a parallax angle of 0.1 arcsecond is _______ away from us.

32.6 light-years

A star with a parallax angle of 0.01 arcsecond is ______ away from us.

326 light-years

A star with a parallax angle of 0.001 arcsecond is _______ away from us.

3260 light-years

Rigel's radius is about _____ times the Sun's radius.

80

Five stars are shown on the following H-R diagrams. Rank the stars based on their luminosity from highest to lowest; notice that these are the same five stars shown in Part D. If two (or more) stars have the same luminosity, drag one star on top of the other(s).

All overlap

Star A is identical to Star B, but Star A is twice as far from us as Star B. Therefore, ______________.

Both stars have the same luminosity, but the apparent brightness of Star B is four times that of star A.

Listed following are several fictitious stars with their luminosities given in terms of the Sun's luminosity (LSunLSun) and their distances from Earth given in light-years (lyly). Rank the stars based on how bright each would appear in the sky as seen from Earth, from brightest to dimmest. If two (or more) stars have the same brightness in the sky, show this equality by dragging one star on top of the other(s)

Brightest: - Nismo - Shelby and Ferdinand - Enzo - Lotus

Listed following is the same set of fictitious stars given in Part A. Rank the stars based on how bright each would appear in the sky as seen from Jupiter, from brightest to dimmest.

Brightest: - Nismo - Shelby and Ferdinand - Enzo - Lotus

Assuming that we can measure the apparent brightness of a star, what does the inverse square law for light allow us to do?

Calculate the star's luminosity if we know its distance, or calculate its distance if we know its luminosity.

The sketch shows groups of stars on the H-R diagram, labeled (a) through (e); note that (a) represents the entire main sequence, while (c) and (d) represent only small parts of the main sequence. Which group represents stars that are cool and dim?

D

The sketch shows groups of stars on the H-R diagram, labeled (a) through (e); note that (a) represents the entire main sequence, while (c) and (d) represent only small parts of the main sequence. Which group represents stars with the longest main-sequence lifetimes?

D

The following figure shows how four identical stars appear in the night sky seen from Earth. The shading is used to indicate how bright (white) or dim (dark gray) the star would appear in the sky from Earth. Rank the stars based on their distance from Earth, from farthest to closest.

Dark gray, light gray, gray, white.

The sketch shows groups of stars on the H-R diagram, labeled (a) through (e); note that (a) represents the entire main sequence, while (c) and (d) represent only small parts of the main sequence. Which group represents stars of the largest radii?

E

Suppose our Sun were suddenly replaced by a supergiant star. Which of the following would be true?

Earth would be inside the supergiant.

What is the cause of stellar parallax?

Earth's orbit around the Sun.

Which of the following makes it possible for us to observe stellar parallax (from Earth)?

Earth's orbit around the Sun.

Five stars are shown on the following H-R diagrams; notice that these are the same five stars shown in Part F. Rank the stars based on their luminosity from highest to lowest. If two (or more) stars have the same luminosity, drag one star on top of the other(s).

Highest Luminosity - Upper right and upper left - Middle - Bottom right and Bottom left

Five stars are shown on the following H-R diagrams. Rank the stars based on their surface temperature from highest to lowest. If two (or more) stars have the same surface temperature, drag one star on top of the other(s).

Highest Temperature - Upper left and Bottom Left - Middle - Upper right and bottom right

Consider the four stars shown following. Rank the stars based on their surface temperature from highest to lowest.

Highest Temperature - a blue white dwarf star - sun - an orange main-sequence star - a red supergiant star

Five stars are shown on the following H-R diagrams. Rank the stars based on their surface temperature from highest to lowest. If two (or more) stars have the same surface temperature, drag one star on top of the other(s).

Highest temperature - O - B - A - G - H

Which of the following is a valid way of demonstrating parallax for yourself?

Hold up your hand in front of your face, and alternately close your left and right eyes.

You learned about the general concept of parallax in Chapter 2, and the video offers a review of the basic ideas. To check your understanding of the concept, which of the following is a valid way of demonstrating parallax for yourself?

Hold your hand up in front of your face, and alternately close your left and right eyes.

We found that mass must be inferred for the star described in Part A. However, we can measure a star's mass directly if __________.

It is a member of an eclipsing binary system.

According to the inverse square law of light, how will the apparent brightness of an object change if its distance to us triples?

Its apparent brightness will decrease by a factor of 9

Compared to a main-sequence star with a short lifetime, a main-sequence star with a long lifetime is __________.

Less luminous, cooler, smaller, and less massive

The three bins represent three important properties of stars. Drag the items that we must measure in order to determine each property into the appropriate bin.

Luminosity - distance - apparent brightness Surface Temperature - color or spectral Mass - orbital period in binary system - orbital distance in binary system

All stars are born with the same basic composition, yet stars can look quite different from one another. Which two factors primarily determine the characteristics of a star?

Mass and stage of life.

Based on its location on the HR diagram, what can we say about Rigel's mass and lifetime?

Nothing, because it is not on the main sequence.

Consider a relatively nearby, single star, that is, a star that is not a member of a binary system and has no known orbiting planets. Listed below are a few properties of this star. Classify each property as either something that we can observe or measure directly (with the aid of a telescope and instruments such as cameras or spectrographs) or something that we must infer indirectly (and hence is correct only if all of our assumptions are correct).

Observe Directly - color - parallax angle - apparent brightness - spectral type Infer Indirectly - luminosity - radius - mass - surface temperature

To calculate the masses of stars in a binary system, we must measure their _____.

Orbital period and average orbital distance.

How would stellar parallax observed from Uranus differ from the stellar parallax we observe from earth?

Parallax from Uranus/Parallax from Earth = 19.

Listed following is a set of statements describing individual stars or characteristics of stars. Match these to the appropriate object category.

Red Giant or Supergiant Stars - Very cool but very luminous - Found in the upper right of the H-R diagram Main-Sequence Stars - the majority of stars in our galaxy - the Sun, for example - the hottest and most luminous stars White Dwarfs - not much larger in radius than Earth - very hot but very dim

The more distant a star, the __________.

Smaller its parallax angle.

Compared to a nearer star, a more distant star will have a _______.

Smaller parallax angle.

From Part A, you know that surface temperature is a stellar property that we infer indirectly. What must we measure directly so that we can infer a star's surface temperature?

Spectral type

What do we mean by a star's spectral type, and how is spectral type related to surface temperature and color.

Spectral types are a way of classifying stars according to their color or what spectral lines we see in their light. The spectral types run OBAFGKM, where O stars are the hottest and M are the coolest. Hotter stars look bluer to us, and cooler stars look redder.

A star's color is related to its surface temperature because _____.

Stars emit thermal radiation.

Which of the following statements comparing open and globular star clusters is true?

Stars in open clusters are relatively young, while stars in globular clusters are very old.

Before we can use parallax to measure the distance to a nearby star, we first need to know __________.

The Earth-Sun distance

The choices below each describe the appearance of an H-R diagram for a different star cluster. Which cluster is the youngest?

The diagram shows main-sequence stars of every spectral type except O, along with a few giants and supergiants.

Why do some of the bright stars (such as the one indicated by the arrow) in this photo have cross-shaped spikes over them?

The spikes are an artifact of photography through a telescope.

Five stars are shown on the following H-R diagrams. Rank the stars based on their surface temperature from highest to lowest. If two (or more) stars have the same surface temperature, drag one star on top of the other(s).

They all overlap.

What is the common trait of all main-sequence stars?

They generate energy through hydrogen fusion in their core.

The GAIA spacecraft is capable of measuring parallax angles as small as about 0.00002 arcsecond (20 microarcseconds). Based on this fact, GAIA should in principle be able to measure the distances of stars located __________.

Throughout the Milky Way Galaxy, but not in the Andromeda galaxy or other more distant galaxies.

The position of a star along the main sequence tells you both its mass and its hydrogen-burning lifetime. Label the indicated blanks on the main sequence with the approximate lifetimes of stars at those positions.

Top - Down - 10 million year lifetime - 10 billion year lifetime - 100 billion year lifetime

The diagonal lines on the H-R diagram represent lines along which all stars would have the same radius. Label the three white lines with the correct values for the radii of stars that fall on them.

Top - Down - 1000 solar radii - 1 - solar radius - 1 Earth radius

Use the labels to identify what kinds of stars inhabit each region of the the H-R diagram.

Top - Down - Supergiants - Main sequence - Red giants - Main sequence - White Dwarfs

Would it be easier or more difficult to measure stellar distances?

Uranus has the greater orbital distance than Earth. Therefore, parallaxes obtained from the Uranus would be greater, and it would be easier to measure stellar distances.

The figure shows a standard Hertzsprung-Russell (H-R) diagram. Label the horizontal and vertical axes using the two blanks nearest the center of each axis, and label the extremes on the two axes using the blanks on the ends of the axes

Y-Axis: Bottom up - fainter - luminosity - brighter X-Axis: Left to Right - hotter - surface temperature - colder

This photo shows an object located in the halo of our Milky Way galaxy. What kind of object is it?

a globular cluster of stars

Compared to a high-luminosity main-sequence star, stars in the upper right of the H-R diagram are __________.

cooler and larger in radius

Five stars are shown on the following H-R diagrams; notice that these are the same five stars shown in Part B. Rank the stars based on their luminosity from highest to lowest. If two (or more) stars have the same luminosity, drag one star on top of the other(s).

highest luminosity - 10,000 - 100 - 1 - .01 - .001

Compared to a low-luminosity main-sequence star, stars in the lower left of the H-R diagram are __________.

hotter and smaller in radius