UNIVERSE (LOOSELEAF):STARS+GALAXIES
6th Edition
ISBN: 9781319115043
Author: Freedman
Publisher: MAC HIGHER
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Chapter 22, Problem 29Q
To determine
To show:
That the form of the Kepler’s third law,
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You observe a star orbiting in the outer parts of a galaxy. The distance to this galaxy is known, and
you are able to take a spectra of this star and determine its velocity. The star is 19 kpc from the
galaxy center and moving in a circular orbit with speed 382 km/s. Compute the total mass of the
galaxy internal to the star's orbit. You will get a large number; express it in scientific notation and in
units of solar masses [e.g., 4.2e10].
[Hint: there is a Box in Chapter 22 of your textbook that will be of help. See also the course formula
sheet.]
(a) Estimate the height (z) above or below the Galactic plane for the globular cluster
M13 (1,b = 59°, 40.9°) and the Orion Nebula (1,b = 209°, -19.4°). M13 and the Orion
Nebula are 7 kpc and 450 pc away from Earth respectively.
(b) To which components of the Galaxy do these objects probably belong? Explain your
answers.
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…
Chapter 22 Solutions
UNIVERSE (LOOSELEAF):STARS+GALAXIES
Ch. 22 - Prob. 1QCh. 22 - Prob. 2QCh. 22 - Prob. 3QCh. 22 - Prob. 4QCh. 22 - Prob. 5QCh. 22 - Prob. 6QCh. 22 - Prob. 7QCh. 22 - Prob. 8QCh. 22 - Prob. 9QCh. 22 - Prob. 10Q
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- n(r) = 1ge where r represents the distance from the centre of the Galaxy, Ro is the distance of the Sun from the centre of the Galaxy, Ra is the typical size of disk and no is the stellar density of disk at the position of the Sun. All distances are expressed in kpc. An astronomer observes the center of the Galaxy within a small field of view. We take a particular type of Red giant stars as the standard candles for the observation with approximately constant absolute magnitude of M = -0.2, (a) A telescope has a limiting magnitude of m = 18. Calculate the maximum distance to which this telescope can detect these red giant stars. For simplicity we ignore the presence of interstellar medium so there is no extinction. (b) Assume an extinction of 0.7 mag/kpc for the interstellar medium. Repeat the calculation as done in the part 5a and obtain a rough number for the maximum distance these red giant stars can be observed. (c) Give an expression for the number of these red giant stars per mag-…arrow_forwardObservations 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? mass: Another method measures the speed of gas moving past the black hole. In the given equation, v is the velocity of the gas (in kilometers per second), r is the distance of the gas cloud from the black hole (in kilometers), and G is Newton's gravitational constant. In this equation, G = 1.33 ×…arrow_forwardIt can be shown that if an object orbiting a star of mass M in a circular orbit of radius R has speed v, then Rv? M Suppose a star orbits the center of the galaxy it is contained in with an orbit that is nearly circular with radius 18 R = 2.5 x 10 and velocity v = 230 km/s. Use the result above to estimate the mass of the portion of the galaxy inside the star's orbit (place all of this mass at the center of the orbit). Mass =arrow_forward
- The 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_forwardThe best evidence for a black hole at the center of the Galaxy also comes from the application of Kepler’s third law. Suppose a star at a distance of 20 light-hours from the center of the Galaxy has an orbital speed of 6200 km/s. How much mass must be located inside its orbit?arrow_forwardSuppose three stars lie in the disk of the Galaxy at distances of 20,000 light-years, 25,000 light-years, and 30,000 light-years from the galactic center, and suppose that right now all three are lined up in such a way that it is possible to draw a straight line through them and on to the center of the Galaxy. How will the relative positions of these three stars change with time? Assume that their orbits are all circular and lie in the plane of the disk.arrow_forward
- You observe the H-alpha line of Hydrogen in a distant galaxy to have a wavelength of 754.4 nm. What is the radial velocity of the galaxy? Hint: The rest wavelength of H-alpha is 656 nm.arrow_forwardA Cepheid variable in the Andromeda galaxy has a period of 22 days and a mean apparent magnitude of19.5.(a) Calculate the distance modulus of the Andromeda galaxy.(b) Given that the Andromeda galaxy is approaching the Milky Way with a velocity of 119 km/s, roughlyestimate how long before these two galaxies collide? Provide your answer in years.arrow_forwardSuppose there exists a hypothetical galaxy with mass MG around the center of which a solar system with mass Ms orbits with period T and radius r. Use the formula T = 2n(r³/GMG)¹/2 to calculate T if: MG = 1 x 1040 kg Ms = 2 x 1028 kg • R = 2.5 x 1020 m . .arrow_forward
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