Deck 23: Galaxies

Question 1

The Milky Way Galaxy:

A)contains almost all the mass in the universe. Much space but only a little mass lies outside it.
B)is the central mass in the universe with many smaller galaxies in orbit around it.
C)is one of about 300 known galaxies.
D)is one of billions of known galaxies.

Answer 1

D

Question 2

In size, the Milky Way Galaxy is:

A)one of the largest galaxies, with no other galaxy known to be much larger.
B)one of the smallest galaxies, with few others known to be much smaller.
C)a typical galaxy, with many others known to be larger and many known to be smaller.
D)virtually the entire universe, with very few objects known to be outside it.

Answer 2

C

Question 3

The great debate involving the nature of the nebulae took place in the year:

A)1794.
B)1885.
C)1920.
D)1954.

Answer 3

C

Question 4

It is the year 1920 and you are conducting a survey of the astronomy community on the question: "What is the nature of the spiral nebulae?" What response are you likely to receive?

A)The overwhelming opinion is that spiral nebulae are relatively small objects in the outer part of the Milky Way Galaxy.
B)The overwhelming opinion is that spiral nebulae are large, distant galaxies somewhat like the Milky Way.
C)There is a deep division of opinion between these two views of the nature of spiral nebulae.
D)Because spiral nebulae have just been discovered, no one has much of an opinion about them yet.

Question 5

The Whirlpool Galaxy (M51) (see Figure 23-1 of Universe, 11th ed.(in the text)) shows H II regions outlining the spiral arms. What causes their red color?

A)H II regions have the characteristic red H_α line excited by radiation from the large, hot, newly formed stars in the spiral arms.
B)These H II regions are dominated by red giants and supergiants.
C)The spiral arms are rotating rapidly away from us, and their radiation is Doppler shifted into the red.
D)Gas and dust in the plane of the galaxy cause interstellar reddening (extinction) as the light passes through the galaxy on its way toward us.

Question 6

The intrinsic brightness (represented by luminosity) of a Cepheid variable star compared to that of the Sun is:

A)several thousand times larger.
B)significantly less.
C)about 10 times larger.
D)about the same.

Question 7

How does the intrinsic brightness or luminosity of a Cepheid variable star compare to that of our Sun?

A)much less, about 1/10, because it is a variable star
B)larger, by 100
C)about the same
D)much larger, by 10⁴

Question 8

The Cepheid variables that Hubble observed in M31 had an apparent magnitude of about 18, and thus an apparent brightness relative to the Sun (b/b_Ÿ) of about 1.3 × 10^-18. What approximate periods would these Cepheids need in order to yield a distance to M31 of about 750 kpc?

A)less than 1 day
B)3 days
C)10 days
D)70 days

Question 9

A Cepheid variable is observed in a distant galaxy. Its period is 30 days, and its apparent magnitude of 19.8 corresponds to a brightness ratio of b/b_Ÿ = 2.35 x 10^-19. How far away is it?

A)1 kpc
B)180 kpc
C)1 Mpc
D)13.6 Mpc

Question 10

A Cepheid variable is observed in a galaxy 1 Mpc distant. Its apparent magnitude of 19.8 corresponds to a brightness ratio of b/b_Ÿ = 2.35 x 10^-19. What is its period?

A)10 days
B)20 days
C)30 days
D)45 days

Question 11

A Cepheid variable is observed in a galaxy 1 Mpc distant. It has a period of 30 days. What is its apparent magnitude?

A)12.8
B)15.9
C)19.8
D)21.7

Question 12

Over what distance does the Cepheid variable technique work? The faintest objects that can be photographed through the best telescopes have apparent magnitudes of about m = 30. Consider a bright Cepheid with an absolute magnitude of M = -2.4. At what distance could it just be seen?

A)30 pc
B)30 kpc
C)30 Mpc
D)30 Gpc

Question 13

Which of the following would you NOT be as likely to find in the central bulge of a spiral galaxy?

A)Population II stars
B)newly formed stars
C)red giants
D)a black hole

Question 14

What do we know about the direction in which spiral galaxies rotate?

A)We don't know anything; they rotate too slowly for us to have seen any motion in the time since galaxies were discovered.
B)They don't rotate; if they did, the spiral pattern would soon disappear. This is the winding dilemma.
C)The ends of the arms trail the rotation (point back).
D)The ends of the arms lead the rotation (point forward).

Question 15

The Hubble classification for a spiral galaxy with a tiny central bulge and narrow, well-defined, loosely wound spiral arms is:

A)E0.
B)SBa.
C)Sa.
D)Sc.

Question 16

The Hubble classification for a galaxy having loosely wound spiral arms originating at the ends of a bar through the central bulge is:

A)Sb.
B)SBa.
C)S0.
D)SBc.

Question 17

Which of the following statements concerning spiral galaxies is TRUE and provides a possible reason for the differences between different classes of spiral galaxies Sa, Sb, and Sc?

A)The fraction of their total mass, which in the form of dust and gas is different; Sa has the lowest fraction whereas Sc has the highest.
B)The rate of star formation in their central bulges is different; the rate is highest for Sa type and lowest for Sc type.
C)The ratio of dust to gas in the interstellar medium is different in these types of galaxies; Sa has the most dust whereas Sc has the most gas.
D)The fraction of their total mass, which in the form of dust and gas is different; Sa has the highest fraction whereas Sc has the lowest.

Question 18

What assignment is given to a galaxy with a large nuclear bulge and tightly wound arms starting from a bar through the central part of the galaxy?

A)SBa
B)SBc
C)Sb
D)SBb

Question 19

Whether or not a galaxy has a bar is apparently determined by:

A)how fast it is rotating.
B)whether or not it has satellite galaxies with which it is interacting.
C)how much dark matter it has.
D)where it is in its evolutionary journey.

Question 20

How many barred spirals are there compared to ordinary spirals?

A)There are about one-half as many barred spirals as ordinary spirals.
B)There are about 6 times as many barred spirals as ordinary spirals.
C)There are about twice as many barred spirals as ordinary spirals.
D)There are about one-tenth as many barred spirals as ordinary spirals.

Question 21

What is the ratio of barred spirals to ordinary spirals in our universe?

A)1:100, very few spirals are barred.
B)10:1
C)2:1
D)1:2

Question 22

How does the number of barred spirals in the universe compare to the number of ordinary spirals?

A)Ordinary spirals outnumber barred spirals.
B)The question is meaningless; barred spirals are simply ordinary spirals seen edge on.
C)Barred spirals outnumber ordinary spirals.
D)There are about equal numbers of barred spirals and ordinary spirals.

Question 23

Do the shapes of elliptical galaxies really reflect their true shape?

A)No. The shapes of most of them have been severely distorted by gravitational lensing around the supermassive black hole at their centers.
B)No. They may all be the same shape but viewed either edge on, face on, or in between these two cases.
C)No, because we cannot see the outlying spherical shells of material detected by radio telescopes around elliptical galaxies.
D)Yes. The shapes we see have been shown to be their true three-dimensional shape.

Question 24

The Hubble classification for a galaxy with a circular outline and a smooth distribution of brightness is:

A)Sa.
B)Sc.
C)E7.
D)E0.

Question 25

According to the Hubble classification scheme, an E6 galaxy:

A)has a shorter central bar in its disk than an E2 galaxy.
B)has more tightly wound spiral arms than an E2 galaxy.
C)is flatter looking than an E2 galaxy.
D)is rounder looking than an E2 galaxy.

Question 26

The type or group of galaxies that contains both the largest and smallest galaxies in the universe is the:

A)ellipticals.
B)barred spirals.
C)Sc type galaxies.
D)irregulars.

Question 27

Which observation of elliptical galaxies provides a measure of the relative motions of stars and of the degree of randomness of their motions within these galaxies?

A)the redshift of spectral lines in their spectra
B)the broadening of spectral lines in their spectra
C)the relative brightnesses of central bulges and extended disks of these galaxies
D)the shapes of the galaxies

Question 28

The Hubble classification for a galaxy having a disk and central bulge, with a smooth light distribution but no spiral arms, is:

A)irregular.
B)S0.
C)SBa.
D)E0.

Question 29

Which of the following sequences shows the correct order of galaxy type in terms of the extent of rotational motion, from the least to the most rotation?

A)Sb spiral, S0 lenticular, E7 elliptical, and E0 elliptical
B)S0 lenticular, E0 elliptical, E7 elliptical, and Sb spiral
C)E7 elliptical, E0 elliptical, S0 lenticular, and Sb spiral
D)E0 elliptical, E7 elliptical, S0 lenticular, and Sb spiral

Question 30

A standard candle is an object with a known luminosity, or, equivalently, a known absolute magnitude. To obtain the distance to the object one still has to use:

A)Kepler's third law.
B)the inverse-square law.
C)the distance modulus equation.
D)the Hubble law.

Question 31

Why are RR Lyrae variables NOT used to find distances to distant galaxies?

A)RR Lyrae variables are found in globular clusters. They are not found in other galaxies.
B)The periods of RR Lyrae variables are irregular and thus not reliable for distance measurements.
C)They are not bright enough to be seen at large distances.
D)By their nature, RR Lyrae variables are surrounded by clouds of gas and dust. The resulting extinction makes their luminosities difficult to determine.

Question 32

Scattering by interstellar dust can affect the results of some standard measuring techniques. Which one of the following is NOT affected by the presence of dust?

A)Cepheid variables
B)Type Ia supernovae
C)parallax
D)Tully-Fisher relation

Question 33

Which of the following properties would NOT be important for a type of astronomical object being considered for use as a "standard candle" for distance estimation?

A)It must be close enough for a parallax measurement.
B)It must be very bright.
C)It must be easily identifiable by some easily observed property.
D)It must have known and reproducible luminosity.

Question 34

Type Ia supernovae are frequently used as standard candles for the measurement of distances to galaxies, but they are not all equally luminous. What additional relationship between properties of supernovae is used to determine specific luminosities for individual supernovae?

A)the more blue the spectrum of the supernova, the more luminous the supernova
B)the faster the rise of light intensity during the explosion, the more luminous the supernova
C)the slower the decay of intensity after the explosion, the more luminous the supernova
D)the faster the decay of intensity after the explosion, the more luminous the supernova

Question 35

Type Ia supernovae are reliable distance indicators for distant galaxies. Which of the following is NOT a reason for this?

A)They occur in many galaxies.
B)They are giant stars and can be detected at large distances.
C)The intrinsic luminosity can be determined from the light curve.
D)Their identity as Type Ia supernovae can be determined from their light curves.

Question 36

Which spectral feature originating in a galaxy is used in the Tully-Fisher relation, by measuring its width, to determine the intrinsic luminosity of the galaxy?

A)the 2.3-mm microwave emission line from the molecule CO, which is closely associated with molecular hydrogen
B)the Lyman L $\alpha$ ultraviolet line from atomic hydrogen
C)the 21-cm radio emission line from atomic hydrogen gas
D)the Balmer H $\alpha$ red line from atomic hydrogen

Question 37

Why is the Tully-Fisher relation NOT used for elliptical galaxies?

A)Ellipticals do not emit 21-cm radiation.
B)The luminosity of an elliptical is not related to its mass.
C)The luminosity of an elliptical is not related to its age.
D)Ellipticals do not rotate.

Question 38

The fundamental plane technique for ellipticals can be used to determine galaxies at greater distances than the Tully-Fisher relation that is applied to spirals. Why?

A)The fundamental plane technique is not affected by interstellar reddening while the Tully-Fisher relation is.
B)Ellipticals rotate faster than spirals.
C)The brightest ellipticals are brighter than the brightest spirals.
D)Ellipticals exist in the farthest galaxy clusters. Spirals exist only in relatively nearby clusters.

Question 39

How does the maser technique work in providing a direct distance measurement to galaxies at intermediate distances (5-10 Mpc range)?

A)Velocity measurements of maser sources on either edge of the galaxy from Doppler shift of the very narrow maser spectral lines are combined with very precise angular motions of equivalent sources across the front of the galaxy, measured with radio interferometry, to calculate distances.
B)Velocity measurements of maser sources on either side of the galaxy from Doppler shift of the very narrow maser spectral lines are combined with observations of rates of intensity flickering of these small sources to calculate distances.
C)Velocity measurements of maser sources on either side of the galaxy from Doppler shift of the very narrow maser spectral lines are combined with very precise angular separation between the sources and the centers of the galaxies by radio interferometry to calculate distances.
D)Very precise angular motions of sources in front of the galaxy, measured with radio interferometry, are combined with observations of the rates of flickering of intensity of these small sources to calculate distances.

Question 40

Maser light in distant galaxies can be used to calculate the distance to the source. In what spectral range do we observe this light?

A)ultraviolet
B)visible
C)infrared
D)microwave

Question 41

Parallax and masers are two techniques for measuring distances in astronomy. Although very different from each other, they share a characteristic that is different from the other main measuring techniques. This is that:

A)they can both be used to measure the same set of objects and can thus check each other.
B)the relative motion of the distant objects is not important, thus avoiding the complication of Earth's motion.
C)each is independent of the results of any other distance measuring technique.
D)only these two techniques are correct for relativistic as well as Newtonian situations.

Question 42

Scattering by interstellar dust can affect the results of some standard measuring techniques. Which one of the following is NOT affected by the presence of dust?

A)RR Lyrae stars
B)masers
C)spectroscopic parallax (use of H-R diagram)
D)fundamental plane

Question 43

The discovery of the expanding universe began in 1914 when V. M. Slipher realized that 11 of the 15 spiral "nebulae" he imaged showed redshifts. Why only 11?

A)His measuring instruments were not fine enough to show the redshifts in the others.
B)He included nearby open clusters in his sample.
C)By chance he included in his sample active galaxies with jets. The redshifts of the galaxies were masked by the blueshifts of the jets.
D)He was looking at nearby galaxies in the Local Group, and many of these have intrinsic velocities that are larger than their participation in the Hubble flow.

Question 44

Which of the following did Edwin Hubble NOT contribute to our understanding of galaxies and their behavior?

A)observations of Cepheid variable stars in spiral "nebulae" and their interpretation
B)a relationship between distance to galaxies and their apparent velocity of recession
C)determination of the ages of galaxies and the correct sequence of evolutionary progress of galaxies
D)a classification scheme for galaxy types

Question 45

The Hubble relationship shows a proportionality between the distance to a galaxy and the:

A)width of the 21-cm radio emission line from hydrogen.
B)parallax angle change of the galaxy as Earth moves through 1 year.
C)angular diameter of the galaxy as seen from Earth.
D)overall redshift of a galaxy's spectrum.

Question 46

The Hubble law describes how two properties of distant galaxies are related to each other. What are these two properties?

A)distance and velocity of recession
B)brightness and recession velocity
C)brightness and the width of the 21-cm radio emission line of hydrogen
D)distance and brightness

Question 47

The Hubble law, representing observations of distant galaxies in the universe, relates which two parameters?

A)mass of a distant galaxy and its luminosity
B)luminosity of a distant galaxy and the width of the 21-cm radio line of hydrogen
C)distance to a distant galaxy and its recession velocity
D)mass of a distant galaxy and its recession velocity

Question 48

What method is used to determine the distances of very remote galaxies?

A)use of their spectral redshifts and the Hubble law
B)measurement of the angular size of the galaxy and an assumption about the actual physical size of the galaxy
C)measurement of the apparent brightness and period of Cepheid variable stars within the galaxies
D)comparison of their apparent and absolute magnitudes

Question 49

Even though the Hubble law for galactic motions indicates that the spectra of all galaxies should show redshift as a consequence of the general expansion of the universe, the Andromeda Galaxy M31 appears to show a blueshift in its spectrum. Why is this?

A)M31 has an abnormally powerful black hole at its center that gravitationally blueshifts its entire spectrum.
B)The mutual attraction between M31 and the Milky Way Galaxy has overcome the general Hubble flow.
C)Young giant spiral galaxies such as M31 do not follow the normal Hubble flow because they have formed relatively recently.
D)One side of M31 is heavily obscured by dust and gas and the blueshift simply shows the Doppler shift of the other side of the galaxy, produced by galactic rotation.

Question 50

What does the Hubble law tell us, if H₀ is a constant?

A)H₀ × recessional speed = distance
B)recessional speed = H₀ = constant
C)distance × recessional speed = H₀
D)recessional speed = H₀ × distance

Question 51

What is the Hubble law, if V is recession velocity, d is the distance to a galaxy, and H₀ is a constant?

A)V = H₀ = constant
B)V = H₀ d
C)H₀ V = d
D)Vd = H₀

Question 52

Astronomers often speak of redshift z rather than distance d. If the speeds are a small fraction of the speed of light, the relationship between d and z is:

A)d = H₀ z.
B)d = H₀/(cz).
C)d = z/(H₀ c)
D)d = zc/H_0.

Question 53

Based on the most accurate measurements to date, what is believed to be the value of the Hubble constant?

A)between 50 and 60 (km/s)/Mpc
B)between 100 and 120 (km/s)/Mpc
C)between 70 and 75 (km/s)/Mpc
D)between 80 and 90 (km/s)/Mpc

Question 54

On the basis of the distance to the Coma Cluster of galaxies (90 Mpc) and the Hubble relation, using for the Hubble constant H₀ the value 73 km/sec per million pc, what would be the approximate wavelength shift of the Balmer H $\alpha$ spectral line at 656.3 nm emitted by a galaxy in the cluster because of the general expansion of the universe? (See Box 23-2, Universe, 11th ed.)

A)1.44 × 10^-2 nm
B)2.87 × 10^-3 nm
C)143.7 nm
D)14.4 nm

Question 55

One astronomer (astronomer A) claims that the Hubble constant is 84 km/s/Mpc, while another (astronomer B) claims that it is 63 km/s/Mpc. If, based on the Hubble constant, astronomer A claims that a particular galaxy is 3.00 billion ly away, then astronomer B would claim that it is:

A)4.00 billion ly away.
B)2.25 billion ly away.
C)3.75 billion ly away.
D)2.00 billion ly away.

Question 56

The Hercules Cluster of galaxies shown in Figure 23-18 (Universe, 11th ed.) is at a distance of 650 million ly from our galaxy. Using a Hubble constant of 23 (km/s)/Mly, at what wavelength will the Balmer H $\alpha$ spectral line, with rest wavelength = 656.3 nm, be seen in the spectrum of a galaxy in this cluster?

A)623.6 nm
B)689.0 nm
C)656.7 nm
D)32.7 nm

Question 57

If the elliptical galaxy in Hydra, whose image and spectrum are shown at the bottom of Figure 23-16 (Universe, 11th ed.), were to be at a distance of 3 billion ly, what would be the value of the Hubble constant H₀? (Be careful with units.)

A)about 215 km/s/Mly
B)about 20 km/s/Mly
C)about 20,000 km/s/Mly
D)about 66 km/s/Mly

Question 58

Suppose that a particular galaxy is 400 million pc from Earth. What is the recessional velocity of this galaxy? Take the Hubble constant to be 73 km/s/Mpc.

A)5.8 km/s
B)175,000 km/s
C)5.8 million km/s
D)29,200 km/s

Question 59

An astronomer studying the spectrum of a distant galaxy finds that its recessional velocity is 14,000 km/s. What is the distance to the galaxy? Take the Hubble constant to be 73 km/s/Mpc.

A)96 Mpc
B)959,000 Mpc
C)1918 Mpc
D)192 Mpc

Question 60

Suppose an astronomer discovers a distant quasar whose recessional velocity is 1/3 the speed of light. If the Hubble constant is 73 km/s/Mpc, how far away is the quasar?

A)6,850,000 Mpc
B)1370 Mpc
C)137 Mpc
D)68 Mpc

Question 61

Which one of the following formulas is not valid when the speed of the object under consideration becomes large-say, 10% of the speed of light?

A)v = H₀ d
B)z = v/c
C)z = Δλ / λ₀
D)All the equations above are generally valid at all speeds.

Question 62

If the recessional speed of a galaxy is a significant fraction of the speed of light, each of the following expressions will be valid EXCEPT ONE. Which one is ONLY valid when the velocity is much less than the speed of light?

A)z = Δλ / λ₀
B)v = H₀ d
C)H₀ = 73 (km/sec)/Mpc
D)z = v/c

Question 63

For galaxies in the Hydra cluster, the recessional velocity is 61,000 km/sec. Assuming the nonrelativistic solution, what is the shift in frequency for the Balmer H $\alpha$ line, the rest wavelength of which is 656.3 nm?

A)92 nm
B)133 nm
C)151 nm
D)584 nm

Question 64

Approximately how many galaxies are included in the collection known as the Local Group of galaxies?

A)5
B)11
C)15
D)40

Question 65

How many large spiral galaxies are there in the Local Group of galaxies?

A)The Milky Way Galaxy is the only one.
B)There are only two, Andromeda and the Milky Way.
C)There are three.
D)We really don't know how many because some could be hidden unseen on the other side of our galaxy, cut off from our view by clouds of gas and dust.

Question 66

What is the galaxy content of a rich, irregular cluster of galaxies, like the Hercules Cluster?

A)entirely elliptical galaxies
B)more or less equal numbers of spirals and ellipticals
C)many more ellipticals than spirals
D)many more spirals than ellipticals

Question 67

What is distinctive about the Coma Cluster of galaxies?

A)It is the cluster in which our Milky Way Galaxy is located.
B)It contains many quasars.
C)It is the nearest rich, regular cluster.
D)It is moving rapidly toward the Local Group of galaxies, which contains the Milky Way Galaxy.

Question 68

What is the Great Attractor?

A)an empty point at the center of one of the largest voids, now believed to be the center of the universe
B)the largest known black hole, believed to be the site of the original Big Bang
C)a particularly massive cluster of galaxies
D)the name given to the combined gravitational effects of the nearest several dozen clusters of galaxies

Question 69

If the estimated distance from Earth to the Coma Cluster of galaxies is about 300 million ly (see Figure 23-21 of Universe, 11th ed.(in the text)), what is its velocity of recession?

A)14 km/s
B)6600 km/s
C)0.072 km/s
D)21,000 km/s

Question 70

The overall distribution of galaxies through space is now found to be galaxies:

A)clustered together in several high-density centers, with very little matter between them.
B)concentrated on the surfaces of huge open spaces or voids, like soap bubbles.
C)concentrated around one position in space, presumably the original site of the Big Bang.
D)distributed uniformly throughout space, out to the furthest distances.

Question 71

Which common household phenomenon represents a close analogy to the distribution of galaxies in our universe?

A)a bowl of sugar crystals, uniformly distributed, close-packed, and evenly spaced apart
B)lemonade in a glass, surrounding small moving gas bubbles, the bubble's motion being similar to the Hubble flow
C)ice crystals forming on a cold, flat window in regular patterns
D)soap films surrounding air bubbles in soap suds

Question 72

Voids are believed to contain:

A)nothing.
B)gas and faint galaxies.
C)supergiant elliptical galaxies in the center.
D)gravitational lenses.

Question 73

Gravity is a long-range force, and its effect can be seen in each of the following cases EXCEPT ONE. Which is the EXCEPTION?

A)Globular clusters move in orbits about the center of the Milky Way.
B)A recently discovered member of the Local Group, Canis Major Dwarf, a close companion of the Milky Way Galaxy, is being disrupted by tidal forces from the Milky Way.
C)Clusters of galaxies are bound systems.
D)Superclusters of galaxy clusters are bound systems.

Question 74

Large clouds of very hot gas that emit vast quantities of x rays are detected between the galaxies in rich clusters of galaxies. How has this gas been heated?

A)by the intense radiation from nearby galaxies
B)by the compression of gas as it falls into an unseen supermassive black hole between the galaxies
C)by the annihilation of antimatter in this region of space by matter ejected by nearby galaxies
D)by the collision of two galaxies

Question 75

A starburst galaxy is characterized by a particularly large number of:

A)Population I stars.
B)Population II stars.
C)red giants.
D)white dwarfs.

Question 76

One unusual result of galaxy interactions is:

A)large numbers of gamma-ray bursters.
B)at least a dozen spiral arms.
C)radio wavelength emissions from cold gas.
D)globular clusters dominated by blue supergiants.

Question 77

Our theories for the origin of spiral arms include each of the following EXCEPT ONE. Which is the EXCEPTION?

A)density waves
B)self-propagating star formation
C)the natural, gradual evolution from ellipticals into spirals
D)interactions between galaxies

Question 78

How much of the mass of a galaxy plays a role in emitting radiation into space?

A)10%
B)50%
C)only about 1%
D)almost 100%

Question 79

In the galaxy cluster 1E0657-56, the dark matter seems to have been displaced from the luminous matter during a collision with another cluster. Our understanding of how this might have occurred depends on the premise that:

A)the second cluster contains no dark matter.
B)the second cluster contains only dark matter.
C)dark matter is influenced only by gravitational force.
D)dark matter consists mostly of dim red and brown dwarfs.

Question 80

It is proposed that the ordinary matter and the dark matter in the galaxy cluster 1E0657-56 have become separated. This is based on the assumption that:

A)the amounts of ordinary and dark matter are equal.
B)dark matter responds only to gravitational forces.
C)the gravitational force for dark matter decreases with distance like 1/r.
D)dark matter is repelled from ordinary matter.