Deck 12: Characterizing Stars

Question 1

Which of these statements can be used to define stellar parallax?

A) Stellar parallax is the angle taken up by the diameter of a star as seen from Earth.
B) Stellar parallax is the angle subtended by the radius of Earth's orbit as seen from the star.
C) Stellar parallax is the angle subtended by the diameter of Earth's orbit as seen from the star.
D) Stellar parallax is the angle through which a star moves in the sky over the course of 1 year due to the motion of both the star and Earth.

Answer 1

Stellar parallax is the angle subtended by the radius of Earth's orbit as seen from the star.

Question 2

As a person drives along a road, trees in the middle distance seem to shift in position relative to faraway hills. What name is given to this phenomenon?

A) parallax
B) perspective
C) Doppler effect
D) inverse-square law

Answer 2

parallax

Question 3

The motion that is used to change the position of the observer in the most common parallax measurements of distances to relatively nearby stars is the

A) motion of the Sun around the galactic center.
B) change in latitude of the observation point on Earth.
C) motion of Earth in its orbit around the Sun.
D) rotation of Earth on its axis.

Answer 3

motion of Earth in its orbit around the Sun.

Question 4

Aristotle (fourth century B.C.) rejected the idea that Earth moves because he knew stellar parallax motion would result, and he was unable to measure any. About how long after Aristotle was stellar parallax actually measured?

A) two centuries
B) 10 centuries
C) 22 centuries
D) 29 centuries

Question 5

The Sun is about 8000 parsecs from the center of the Milky Way Galaxy, while the Hipparcos satellite measured parallaxes to an accuracy of about 0.01 arcseconds. How far toward the galactic center could astronomers see with Hipparcos (ignoring galactic dust and other obstacles)?

A) all the way to the center
B) about halfway to the center
C) about 1/80 of the way to the center
D) about 1/1000 of the way to the center

Question 6

Which of these properties of a nearby star is determined by a measurement of stellar parallax?

A) spectral type and surface temperature
B) rotation period
C) apparent magnitude
D) distance from Earth

Question 7

The first accurate measurement of stellar parallax was made in

A) the fourth century B.C.
B) 1721.
C) 1838.
D) 1927.

Question 8

Which of these statements BEST characterizes the human study of stellar evolution?

A) The changes in the observable cosmos over a human lifetime are profound.
B) A human lifetime is long enough to witness the evolution of a star through much of its evolutionary history.
C) Astronomers have never witnessed a significant change in any single star.
D) At any moment. Stars can be observed in every phase of evolution.

Question 9

How can astronomers tell that some stars are relatively close to Earth?

A) The stars appear to move periodically back and forth against the background stars because of Earth's movement around the Sun.
B) The stars appear to be extremely bright and must therefore be very close to Earth.
C) The stars are occasionally occulted or eclipsed by the Moon; hence they must be close.
D) The light from these stars shows only a very small redshift caused by the universal expansion of the universe, so they must be close.

Question 10

The MOST accurate stellar parallax measurements for distances to the majority of stars in Earth's neighborhood in the universe have been made by

A) the Hubble Space Telescope.
B) Friedrich Wilhelm Bessel, in 1838; no measurements since then have matched the precision of his measurements.
C) the Gaia satellite.
D) the Very Long Baseline Array of radio telescopes.

Question 11

Who was the first person to measure the parallax of a star successfully?

A) Sir George Airy in England
B) Henry Norris Russell in the United States
C) Tycho Brahe in Denmark
D) Friedrich Wilhelm Bessel in Germany

Question 12

What is parallax?

A) distance to an object, measured in parsecs
B) angle taken up by the size (e.g., diameter) of an object, as seen by an observer
C) shift in angular position of an object as it moves in space
D) apparent shift in position of an object as the observer moves

Question 13

How far away is the nearest star beyond the Sun?

A) about 1/4 ly away
B) about 1/10 ly away
C) about 4 ly away
D) between 1 and 2 ly away

Question 14

The MOST straightforward way to determine the distance to a nearby star involves the measurement of the

A) star's spectrum.
B) ratio of the star's apparent and absolute magnitudes.
C) Zeeman effect of spectral lines in the star's spectrum.
D) star's parallax.

Question 15

Stellar parallax appears because

A) Earth rotates about its own axis.
B) stars move in space.
C) stars have finite size (i.e., they are not really just points of light).
D) Earth moves in space.

Question 16

In what fundamental way do humans (and many other animals) utilize parallax for the measurement of distance?

A) The eyes focus back and forth continuously, and the brain interprets the focusing in terms of distance to the object viewed.
B) The eye can measure the time taken for light to travel from an object, and the brain interprets this information in terms of distance to the object viewed.
C) Humans are always moving their heads slightly from side to side, and the brain compares the angles from each of these positions to obtain the distance to the object viewed.
D) Human eyes are mounted horizontally about 10 cm apart, and the brain interprets the relative look angles of their eyes in terms of distance to the object viewed.

Question 17

Parallax of a nearby star is used to estimate its

A) surface temperature.
B) distance from Earth.
C) apparent magnitude.
D) physical size or diameter.

Question 18

Stellar parallax is the

A) inferred change in the distance to a star as its light is dimmed by passing through an interstellar cloud.
B) apparent shift seen in the position of a nearby star against more distant stars as Earth orbits the Sun.
C) difference between the apparent and absolute magnitudes of a star.
D) circular or elliptical motion of a star in a binary system as the two stars orbit each other.

Question 19

How far away is the nearest star beyond the Sun, in parsecs?

A) between 1 and 2 pc
B) about 12 pc
C) about 4 pc
D) between 1/2 and 1 pc

Question 20

How many stars (other than the Sun) have an angle of parallax greater than 1 second of arc?

A) about a hundred
B) Millions
C) None
D) only one

Question 21

The star Proxima Centauri has a parallax of 0.77 arcsec (the largest parallax known). How far is this star system from the Sun in light-years? (Careful with units!)

A) 4.24 ly
B) 0.41 ly
C) 1.33 ly
D) 0.75 ly

Question 22

Suppose astronomers want to measure the distance to a star in astronomical units. They would use the equation d (au) = x/parallax angle (arcsec). What is x?

A) 3.26
B) 360
C) 206,265
D) 3.0 × 10⁸

Question 23

How many eleventh magnitude stars are required to equal the brightness of one first magnitude?

A) 10
B) 100
C) 1000
D) 10,000

Question 24

How far out into space can distances be determined using telescopes on Earth if stellar parallax values no smaller than 0.01 arcsec can be measured?

A) 10 pc
B) 100 pc
C) 500 pc
D) 2000 pc

Question 25

The Hipparcos satellite could measure stars up to approximately 150 pc away. What was the smallest parallax angle it could measure?

A) 150 arcsec
B) 1/150 arcsec
C) 1/150 degrees
D) 1/75 arcsec

Question 26

Apparent magnitude is a measure of a star's

A) intrinsic brightness (actual light output).
B) size (diameter).
C) temperature.
D) brightness, as seen from Earth.

Question 27

How much can astronomers learn about a star from a measurement of its apparent magnitude?

A) intrinsic brightness (the total light actually emitted by the star)
B) brightness the star would appear to have if it were exactly 10 pc from Earth
C) brightness of the star as it appears in Earth's sky
D) total output of electromagnetic energy emitted at all wavelengths from the star

Question 28

A star is 80 pc from the Sun. Its apparent motion against the background sky, that is, its stellar parallax, as a result of Earth's motion through 1 au is

A) 0.0125 arcsecond.
B) 0.0125 arcminute.
C) 0.0125 radian or 0.72 $\degree$ .
D) 80 arcseconds.

Question 29

The Hipparcos satellite was able to measure parallax for stars out to about 150 pc. This distance includes roughly 2.5 million stars. What is the average number of stars in 1 cubic parsec?

A) 5.1 × 10^-3
B) 0.18
C) 5.65
D) 8.84

Question 30

Sirius, in Canis Major (the large hunting dog of Orion), is the brightest star in the northern hemisphere winter night sky. It has a parallax angle of 0.38 arcseconds. The brightest star in Orion's other hunting dog, Canis Minor, is Procyon, with a parallax angle of 0.29 arcseconds. Vega, in Lyra (the Lyre [Harp]), is the brightest star in the northern summer night sky. It has a parallax angle of 0.13 seconds of arc. Which of these stars is farthest away?

A) Sirius
B) Procyon
C) Vega
D) The answer to the question cannot be determined from this information alone.

Question 31

The Hipparcos satellite was able to measure parallax for stars out to about 150 pc. This distance includes roughly 2.5 million stars. The new Gaia satellite should be able to measure the parallax of roughly a billion stars. Assuming the density of stars is approximately constant, what distance would this correspond to? (Hint: The volume of a sphere is proportional to the cube of the radius.)

A) 35 pc
B) 167 pc
C) 350 pc
D) 20 kpc

Question 32

The European Space Agency recently launched the Gaia mission, which will measure parallax angles down to 10^-5 arcseconds. What distance does this correspond to?

A) 10^-5 pc
B) 10⁵ light-years
C) 10 kpc
D) 100 kpc

Question 33

If astronomers measure the parallax of a star against the background stars and conclude that the star has a parallax of 0.004 arcsec, how far is the star from Earth?

A) 25 pc or 81.5 ly
B) 250 pc or 815 ly
C) 400 pc or 1300 ly
D) 0.004 pc or 0.013 ly

Question 34

Stellar parallax as small as 0.01 arcsec can be measured using telescopes on Earth. To what distance does this measurement correspond in space?

A) 500 pc
B) 200 pc
C) 0.01 pc
D) 100 pc

Question 35

The semimajor axis of Pluto's orbit is almost 40 au. From its orbit around Earth, the Hipparcos satellite measured stellar parallaxes to an accuracy of about 0.01 arcsecond. Suppose astronomers use this technique to measure parallax from Pluto's orbit (over the course of half a Pluto "year"). What is the maximum distance they could measure?

A) 4 pc
B) 100 pc
C) 4000 pc
D) 8000 pc

Question 36

What is the relationship between stellar parallax (p) measured in seconds of arc and distance (d) measured in parsecs?

A) d = 1/p²
B) d = 1/p
C) d = p
D) d = p²

Question 37

f a nearby star shows a parallax of 0.5 arcsec (when Earth moves through 1 au, by definition), what is its distance from Earth, in light-years?

A) 2 ly
B) 1.83 ly
C) 6.52 ly
D) 3.26 ly

Question 38

A particular star has an angle of parallax of 0.1 arcsec. What is the distance to this star?

A) about 10 ly
B) about 33 ly
C) about 0.1 ly
D) about 3.3 ly

Question 39

A particular star is 20 pc away from Earth. What is the stellar parallax for this star?

A) 6 arcsec
B) 20 arcsec
C) 0.02 arcsec
D) 0.05 arcsec

Question 40

The relative brightness of a star as seen in Earth's sky is called

A) absolute magnitude.
B) apparent magnitude.
C) surface temperature.
D) luminosity.

Question 41

Two stars whose apparent magnitudes differ from each other by 5 magnitudes have a ratio of brightnesses of

A) 25.
B) 10.
C) 100.
D) 2.5.

Question 42

As an observer moves closer to a star, which two of its properties change?

A) luminosity and absolute magnitude
B) luminosity and apparent brightness
C) absolute magnitude and brightness
D) apparent magnitude and brightness

Question 43

When observers look out at the night sky, the number of stars with

A) each magnitude (first, second, etc.) is about the same.
B) smaller magnitude numbers is much larger than the number of stars with larger magnitude numbers.
C) larger magnitude numbers is much larger than the number of stars with smaller magnitude numbers.
D) magnitudes around 3 is larger than either the number with magnitudes around 2 or the number with magnitudes around 4.

Question 44

A star of apparent magnitude +2.1 appears _____ than a star of apparent magnitude -1.2.

A) farther away
B) fainter
C) brighter
D) either brighter or fainter, depending on the distance to the stars,

Question 45

A star of apparent magnitude +5 appears _____ than a star of apparent magnitude +3.

A) fainter
B) farther away
C) brighter
D) either brighter or fainter, depending on the distance to the stars,

Question 46

The modern system of apparent magnitudes uses the star Vega as its basis. In this scheme Vega is defined to have an apparent magnitude of

A) 10.
B) 1.0.
C) 0.0.
D) -1.0.

Question 47

A star of apparent magnitude -2 appears _____ than a star of apparent magnitude -3.

A) fainter
B) brighter
C) farther away
D) either brighter or fainter, depending on the distance to the stars,

Question 48

Which of these stars (each of which is listed with its apparent magnitude) would NOT be visible to the unaided eye on a clear night?

A) tau Ceti; m = +3.49
B) alpha Centauri B; m = +1.34
C) Barnard's star; m = +9.53
D) 61 Cygni A; m = +5.21

Question 49

A star of apparent magnitude +1 appears _____ than a star of apparent magnitude +2.

A) either brighter or fainter, depending on the distance to the stars,
B) farther away
C) brighter
D) fainter

Question 50

The star Alphard has an apparent magnitude of 2.0, and the star Megrez has an apparent magnitude of 3.3. The only thing that can be said with certainty about Alphard is that it is _____ than Megrez.

A) brighter, as seen in Earth's sky
B) more luminous
C) fainter, as seen in Earth's sky
D) closer to Earth

Question 51

Two of the brightest stars in Orion are Betelgeuse (apparent magnitude = 0.45) and Rigel (apparent magnitude = 0.15). From this information, one can determine

A) that Betelgeuse is brighter than Rigel.
B) that Betelgeuse is bigger than Rigel.
C) that Betelgeuse is farther away than Rigel.
D) None of these are correct.

Question 52

A star that has an apparent magnitude of 0 would

A) be fainter than Spica (alpha Virginis), which has an apparent magnitude of +1.0.
B) be brighter than Deneb (alpha Cygni), which has an apparent magnitude of +1.2.
C) have infinite brightness since 1/0 = infinity.
D) not be emitting any light and therefore could not be seen from Earth.

Question 53

Which of these stars (each of which is listed with its apparent magnitude) looks brightest when viewed from Earth?

A) tau Ceti; m = +3.49
B) alpha Centauri B; m = +1.34
C) Barnard's star; m = +9.53
D) 61 Cygni A; m = +5.21

Question 54

The ancient Greek astronomer Hipparchus introduced the magnitude scale on which he called the brightest stars "first magnitude". Today, the brightest star in the night sky is Sirius, with a magnitude of -1.4, considerably brighter than first magnitude. Why the discrepancy?

A) Sirius was formed since the era in which Hipparchus lived.
B) Sirius existed during Hipparchus's lifetime, but it has obviously brightened considerably since then.
C) Hipparchus had poor eyesight and made many classification errors.
D) After using modern scientific instruments to measure the actual energy output of stars, astronomers modified the magnitude scale of Hipparchus.

Question 55

Some stars are variable, with many properties that change over time. The statement that the apparent magnitude of a variable star has INCREASED indicates that its

A) brightness has increased.
B) surface temperature has decreased.
C) brightness has decreased.
D) surface temperature has increased.

Question 56

What is the ratio of the brightnesses of two stars if their apparent magnitudes differ by +1?

A) about 2.5
B) 100
C) 2, by definition
D) 10

Question 57

A star of apparent magnitude +4.7 appears _____ than a star of apparent magnitude +4.8.

A) brighter
B) either brighter or fainter, depending on the distance to the stars,
C) farther away
D) fainter

Question 58

A star of apparent magnitude +3.5 appears _____ than a star of apparent magnitude +3.3.

A) farther away
B) fainter
C) either brighter or fainter, depending on the distance to the stars,
D) brighter

Question 59

If an observer looks out at a clear night sky with the unaided eye, the faintest stars the observer can see have magnitudes around

A) -6
B) 0
C) +6
D) +12

Question 60

A star of apparent magnitude -1.5 appears _____ than a star of apparent magnitude +2.0.

A) farther away
B) fainter
C) brighter
D) either brighter or fainter, depending on the distance to the stars,

Question 61

Vega is often used as the star to define an apparent magnitude of 0. Actually, the standard for 0 magnitude is the average of a group of stars including Vega. But the averaging must be done with care. If one takes the combined brightness of one 0.1-magnitude star and one -0.1-magnitude star and divides this brightness by two, the equivalent brightness is

A) one 0-magnitude star.
B) one star with a magnitude less than 0.
C) one star with a magnitude greater than 0.
D) two 0-magnitude stars.

Question 62

How many times brighter does the Sun appear from Earth than it does from Neptune, which has an orbital radius of approximately 30 au?

A) 30
B) 30 × 2.512 = 75.4
C) (30)² = 900
D) 4 $\pi$ (30)² = 1130

Question 63

Suppose that two identical stars (they have the same total light output) are located so that star A is at a distance of 5 pc, and star B is at a distance of 25 pc from Earth. How will star B appear, compared with star A?

A) Star B will be 1/5 as bright as star A.
B) Star B will be 1/25 as bright as star A.
C) Star B will be 1/2.2 as bright as star A.
D) Star B will be 1/20 as bright as star A.

Question 64

If star A has an apparent magnitude of +5 and star B has an apparent magnitude of +10, then

A) star A is twice as bright as star B.
B) star B is twice as bright as star A.
C) star A is 100 times as bright as star B.
D) star B is 100 times as bright as star A.

Question 65

How many times brighter than a magnitude +4.0 star is a magnitude +3.0 star?

A) 100 times brighter
B) twice as bright
C) a factor of 4/3, or 1.333 times, brighter
D) 2.512 times brighter

Question 66

Suppose the distance between an observer and a lightbulb is doubled. How does its final brightness compare with its initial brightness?

A) The lightbulb appears 1/16 as bright.
B) The lightbulb appears 4 times brighter.
C) The lightbulb appears 1/2 as bright.
D) The lightbulb appears 1/4 as bright.

Question 67

The faintest stars observable through the largest telescopes have apparent magnitudes of roughly m = 30. How many of these stars would it take to equal the brightness of Vega, which has m = 0?

A) 30
B) 30 * 2.512
C) 30^2.512
D) 2.512³⁰

Question 68

Star A has luminosity L_A = 100 L_Sun and it is 1000 pc away. Star B has the same luminosity as the Sun, L_Sun, and it is 100 pc away. What is true about the brightnesses of these two stars?

A) Star A is brighter than Star B.
B) Star B is brighter than Star A.
C) Star A and Star B have the same brightness.
D) It is not possible to answer the question without knowing L_Sun, the luminosity of the Sun.

Question 69

A star's absolute magnitude and its apparent magnitude have the same numerical value. How far is this star from Earth?

A) It is not possible for a star to have the same absolute and apparent magnitudes.
B) The star would have to be an infinite distance away.
C) 10 ly
D) 10 pc

Question 70

Sirius, visually the brightest star in Earth's night sky, has an apparent magnitude of about -1.5, while the Andromeda Galaxy has an apparent magnitude of about +3.5. What is the ratio of their brightnesses, as seen by Earthbound observers?

A) The Andromeda Galaxy is 100 times brighter than Sirius.
B) The Andromeda Galaxy is 2 times fainter than Sirius.
C) The Andromeda Galaxy is 5 times brighter than Sirius.
D) The Andromeda Galaxy is 100 times fainter than Sirius.

Question 71

How many second-magnitude stars would be needed in a close cluster to match the light intensity of a first-magnitude star?

A) about 2.5
B) 2
C) about 10
D) about 0.4, or 1/2.5

Question 72

Light leaving a point source spreads out so that the apparent brightness I of light per unit area varies with distance d according to which of these laws ( $\infty$ means "proportional to")?

A) I = constant
B) I $\infty$ 1/d²
C) I $\infty$ d²
D) I $\infty$ 1/d

Question 73

How many stars of sixth-magnitude would it take for a small cluster to appear as bright as a single first-magnitude star?

A) 10⁵
B) 5
C) 6
D) 100

Question 74

If a distant cluster were to be composed only of stars with apparent magnitude of +3, how many stars would there be in this cluster if its apparent magnitude matched that of a star with apparent magnitude of +1?

A) 2
B) 10², or 100
C) about 2.5
D) between 6 and 7

Question 75

A star has an absolute magnitude M = 1.69 and an apparent magnitude m = 1.04. How far away is this star?

A) 24.2 ly
B) 43.2 ly
C) 59.7 ly
D) 160.2 ly

Question 76

Luminosity is measured in

A) watts.
B) watts per second.
C) watts per square meter.
D) parsecs.

Question 77

How many fourth-magnitude stars would a star cluster need to have to appear as bright as a single second-magnitude star?

A) 2
B) 4
C) 2.512
D) 6.310

Question 78

The Sun's luminosity is 3.83 *10²⁶ watts. By the time this energy reaches Earth, it has spread out so that it provides only 1370 watts to each square meter. The orbit of Mars has a mean radius of 1.53 au. How many watts of the Sun's luminosity are provided to each square meter of the surface of Mars?

A) 34
B) 153
C) 585
D) 1578

Question 79

How many times brighter is a star with an apparent magnitude of +1.0 than a star with an apparent magnitude of +6.0?

A) 100 times brighter
B) 5 times brighter
C) The question is incorrectly worded; the magnitude +6 star will be 100 times brighter than the magnitude +1 star.
D) 2.512 times brighter

Question 80

What is the fundamental difference between absolute and apparent magnitude of a star?

A) The difference is +5 since absolute and apparent magnitude differ by this value by definition.
B) Apparent magnitude depends on the star's temperature, whereas absolute magnitude is independent of temperature.
C) Apparent magnitude depends on the size of the star, whereas absolute magnitude is independent of this parameter.
D) Absolute magnitude is an intrinsic property of the star, whereas apparent magnitude depends on its distance from Earth.