Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Chapter 25, Problem 24E
The first clue that the Galaxy contains a lot of dark matter was the observation that the orbital velocities of stars did not decreases with increasing distance from the center of the Galaxy. Construct a rotation curve for the solar system by using the orbital velocities of the planets, which can be found in Appendix F. How does this curve differ from the rotation curve for the Galaxy? What does it tell you about where most of the mass in the solar system is concentrated?
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The figure below shows the spectra of two galaxies A and B.
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1. Which of these galaxies has ongoing star formation? How can you tell?2. One of these galaxies has Hubble type E3 while the other is SBb. Which is which? What does the 3 inE3 tell you about the galaxy? What does the SB in SBb tell you about the galaxy?3. What effects would dust have on the two spectra?4. Which galaxy would you expect to have more far-infrared emission? Expl
The Tully-Fischer method relies on being able to relate the mass of a galaxy to its rotation velocity.
Stars in the outer-most regions of the Milky Way galaxy, located at a distance of 50 kpc from the
galactic centre, are observed to orbit at a speed vrot
determine the mass in the Milky Way that lies interior to 50 kpc. Express your answer in units of
the Solar mass.
250 km s-1. Using Kepler's 3rd Law,
Observations indicate that each galaxy contains a supermassive black hole at its center. These black holes can be hundreds of
thousands to billions of times more massive than the Sun. Astronomers estimate the size of such black holes using
multiple methods.
One method, using the orbits of stars around the black hole, is an application of Kepler's third law. The mass of the black hole
can be found by using the given equation, where a is the semi-major axis in astronomical units, P is the period in years, and k is
a constant with a value of 1 Mo X year²/ AU³.
a³
M = k-
p²
What is the mass of a supermassive black hole if a star orbits it with a semimajor axis of 959 AU and a period of 13.3 years?
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Chapter 25 Solutions
Astronomy
Ch. 25 - Explain why we see the Milky Way as a faint band...Ch. 25 - Explain where in a spiral galaxy you would expect...Ch. 25 - Describe several characteristics that distinguish...Ch. 25 - Briefly describe the main parts of our Galaxy.Ch. 25 - Describe the evidence indicating that a black hole...Ch. 25 - Explain why the abundances of heavy elements in...Ch. 25 - What will be the long-term future of our Galaxy?Ch. 25 - Suppose the Milky Way was a band of light...Ch. 25 - Suppose somebody proposed that rather than...Ch. 25 - The globular clusters revolve around the Galaxy in...
Ch. 25 - Shapley used the positions of globular clusters to...Ch. 25 - Consider the following five kinds of objects: open...Ch. 25 - The dwarf galaxy in Sagittarius is the one closest...Ch. 25 - Suppose three stars lie in the disk of the Galaxy...Ch. 25 - Why does star formation occur primarily in the...Ch. 25 - Where in the Galaxy would you expect to find Type...Ch. 25 - Suppose that stars evolved without losing...Ch. 25 - Assume that the Sun orbits the center of the...Ch. 25 - The Sun orbits the center of the Galaxy in 225...Ch. 25 - Suppose the Sun orbited a little farther out, but...Ch. 25 - We have said that the Galaxy rotates...Ch. 25 - If our solar system is 4.6 billion years old, how...Ch. 25 - Suppose the average mass of a star in the Galaxy...Ch. 25 - The first clue that the Galaxy contains a lot of...Ch. 25 - The best evidence for a black hole at the center...Ch. 25 - The next step in deciding whether the object in...Ch. 25 - Suppose the Sagittarius dwarf galaxy merges...
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- Indicate whether the following statements are true or false. (Select T-True, F-False. If the first is T and the rest F, enter TFFFFF). A) If we find an O type star in our galaxy, it must be in the disk. B) The nearest large spiral Galaxy, similar in size to the Milky Way, is the Andromeda Galaxy (M31). It is located about 2 million light years from Earth. C) The disk of the Milky Way galaxy is about 100,000 light years in diameter. D) On very large scales, matter in the Universe is distributed in clumps and voids. E) Distances to most stars in the Milky Way are measured by parallax. F) RR Lyrae and Cepheid variable stars are used to measure the distance to nearby galaxies.arrow_forwardThe globular clusters revolve around the Galaxy in highly elliptical orbits. Where would you expect the clusters to spend most of their time? (Think of Kepler’s laws.) At any given time, would you expect most globular clusters to be moving at high or low speeds with respect to the center of the Galaxy? Why?arrow_forwardThe best parallaxes obtained with Hipparcos have an accuracy of 0.001 arcsec. If you want to measure the distance to a star with an accuracy of 10%, its parallax must be 10 times larger than the typical error. How far away can you obtain a distance that is accurate to 10% with Hipparcos data? The disk of our Galaxy is 100,000 light-years in diameter. What fraction of the diameter of the Galaxy’s disk is the distance for which we can measure accurate parallaxes?arrow_forward
- The dwarf galaxy in Sagittarius is the one closest to the Milky Way, yet it was discovered only in 1994. Can you think of a reason it was not discovered earlier? (Hint: Think about what else is in its constellation.)arrow_forwardA galaxy's rotation curve is a measure of the orbital speed of stars as a function of distance from the galaxy's centre. The fact that rotation curves are primarily flat at large galactocen- tric distances (vrot(r) ~ constant) is the most common example of why astronomer's believe dark matter exists. Let's work out why! Assuming that each star in a given galaxy has a circular orbit, we know that the accelera- tion due to gravity felt by each star is due to the mass enclosed within its orbital radius r and equal to v?/r. Here, ve is the circular orbit velocity of the star. (a) Show that the expected relationship between ve and r due to the stellar halo (p(r) xr-3.5) does not produce a flat rotation curve. (b) Show that a p(r) ∞ r¯² density profile successfully produces a flat ro- tation curve and must therefore be the general profile that dark matter follows in our galaxy.arrow_forwardFor each of the following parts, find the most possible type of object by considering the descriptions, and explain your answer. Each part is independent. The possible types are red giant, galaxy, planetary system, planet, dwarf planet, red dwarf, white dwarf, brown dwarf, satellite, asteroid, comet, protostar 2 star, star cluster, galaxy cluster, supercluster, emission nebula, reflection nebula, dark nebula (a) This object moves around the Sun. The nearest distance to the Sun is 0.5 AU, and the farthest distance from the Sun is 1000 AU. (b) This object is red in colour. The density is much lower than that of a star. (c) The mass of this object is the same as that of the Sun. It does not fuse hydrogen. (d) This object moves in a circular orbit about the Sun. Its orbit is between those of Mars and Jupiter. It is round in shape. (e) This object burns hydrogen in a region surrounding its helium core.arrow_forward
- H5. A star with mass 1.05 M has a luminosity of 4.49 × 1026 W and effective temperature of 5700 K. It dims to 4.42 × 1026 W every 1.39 Earth days due to a transiting exoplanet. The duration of the transit reveals that the exoplanet orbits at a distance of 0.0617 AU. Based on this information, calculate the radius of the planet (expressed in Jupiter radii) and the minimum inclination of its orbit to our line of sight. Follow up observations of the star in part reveal that a spectral feature with a rest wavelength of 656 nm is redshifted by 1.41×10−3 nm with the same period as the observed transit. Assuming a circular orbit what can be inferred about the planet’s mass (expressed in Jupiter masses)?arrow_forwardEstimating the mass of the Milky Way a) Assuming the Sun moves in a circular orbit of radius 8 kiloparsecs around the center of the Milky Way, and that its orbital speed is 220 km/s, calculate how many years it takes the Sun to complete one orbit of the Galaxy. Remember to convert kiloparsecs to kilometers. b) Using the modified form of Kepler's third law (introduced in Lecture 13, for measuring the combined masses of binary stars), R³ m+ M = estimate the mass of the Milky Way enclosed within 8 kpc (Sun's orbit radius). The mass of the Milky Way inside p² I the Sun's orbit can be represented as a single mass (M) located at its center, and the mass of the Sun (m) can be considered infinitesimally small compared to the Milky Way's (i.e., m < M). c) Is this estimate of the Milky Way's mass an upper or lower limit? Explain your reasoning.arrow_forwardA given star orbits the center of its galaxy at an average speed of v_star, at a distance of r_star from the center. The galaxy has 2 spiral arms, and the arms themselves orbit slower than the star -- at the same radius, they orbit at a speed of v_arm (in the same direction as the star). The galaxy's age is t_gal. In the history of this galaxy, how many times did this star cross through a spiral arm? Values: v_star = 200 km/s, r_star = 9 kpc, v_arms = 46 km/s, t_gal = 4 Gyrarrow_forward
- Figure 2 shows the "rotation curve" of NGC 2742. It plots the “radial velocity (V)" (how fast material is moving either toward or away from us) that is measured for objects at different distances (R = radius") from the center of the galaxy. The center of the galaxy is at 0 kpc (kiloparsecs) with a speed of 9 km/sec away from us. (These velocities have been corrected for the observed tilt of the galaxy and represent true orbital velocities of the stars and gas.) 200 100 U4779 -100 As you can see, one side of the galaxy is moving with a negative velocity (spinning toward us), while the other side has a positive velocity (spinning away from us). Using Newton's gravity equation, we will be able to determine the gravitational mass of the entire galaxy and how the mass varies versus distance from the galaxy's center. -200 -8 8 -4 Radius (kpc) Read the following text carefully and follow the instructions: Select five radii spaced evenly from 0-10 kpc across the galaxy. Your selections should…arrow_forwardLet’s say you’re looking for extrasolar planets. You observe a star that has a spectral shift in the line that is supposed to be at at 656.28011 nm – this star shows this line at 656.28005 nm. What is the radial velocity of star (in m/s) and in what direction in relation to you? a) 27.4 m/s, towards b) 27.4 km/s, away c) -27.4 m/s, toward d) -27.4 km/s, awayarrow_forwardThe Tully-Fischer method relies on being able to relate the mass of a galaxy to its rotation velocity. Stars in the outer-most regions of the Milky Way galaxy, located at a distance of 50 kpc from the galactic centre, are observed to orbit at a speed vrot = 250 km s−1. Using Kepler’s 3rd Law, determine the mass in the Milky Way that lies interior to 50 kpc. Express your answer in units of the Solar mass.arrow_forward
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