21st Century Astronomy
6th Edition
ISBN: 9780393428063
Author: Kay
Publisher: NORTON
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Chapter 23, Problem 22QP
To determine
The correct order of evolution of the stars and galaxies in the universe.
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A 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.
Suppose that stars were born at random times over the last 10e10 years. The rate ofstar formation is simply the number of stars divided by 10e10 years. The fraction ofstars with detected extrasolar planets is at least 9 %. The rate of star formation can bemultiplied by this fraction to find the rate planet formation. How often (in years) doesa planetary system form in our galaxy? Assume the Milky Way contains 7 × 10e11 stars.
I've done this problem 3 different times from scratch and looked at similar problems here. Each time my answer is 1.587 (1.59 rounded to 2 significant figures), but when I submit, it says the answer is wrong. What do you think?
Another explanation for the Universe is the Steady State Hypothesis. The Steady State Hypothesis says that the Universe has always existed and is infinite in extent. Which of the following supports the Big Bang Theory and which supports the Steady State Model.
(Select B-Big Bang Theory, S-Steady State Model, If the first is B and the rest S, enter BSSSSS).
A) An observation that some globular clusters show M-type stars that have evolved off the main sequence.
B) The measurement of redshifts that show galaxies appear to be moving away from each other and the Universe is expanding.
C) A measurement that shows the density of the Universe is close to the critical density.
D) The measurement of the microwave background radiation.
E) Observing that galaxies at very large distances look identical to those in the nearby universe.
Chapter 23 Solutions
21st Century Astronomy
Ch. 23.1 - Prob. 23.1CYUCh. 23.2 - Prob. 23.2CYUCh. 23.3 - Prob. 23.3CYUCh. 23.4 - Prob. 23.4CYUCh. 23 - Prob. 1QPCh. 23 - Prob. 2QPCh. 23 - Prob. 3QPCh. 23 - Prob. 4QPCh. 23 - Prob. 5QPCh. 23 - Prob. 6QP
Ch. 23 - Prob. 7QPCh. 23 - Prob. 8QPCh. 23 - Prob. 9QPCh. 23 - Prob. 10QPCh. 23 - Prob. 11QPCh. 23 - Prob. 12QPCh. 23 - Prob. 13QPCh. 23 - Prob. 14QPCh. 23 - Prob. 15QPCh. 23 - Prob. 16QPCh. 23 - Prob. 17QPCh. 23 - Prob. 18QPCh. 23 - Prob. 19QPCh. 23 - Prob. 20QPCh. 23 - Prob. 21QPCh. 23 - Prob. 22QPCh. 23 - Prob. 23QPCh. 23 - Prob. 24QPCh. 23 - Prob. 25QPCh. 23 - Prob. 26QPCh. 23 - Prob. 27QPCh. 23 - Prob. 28QPCh. 23 - Prob. 29QPCh. 23 - Prob. 30QPCh. 23 - Prob. 31QPCh. 23 - Prob. 32QPCh. 23 - Prob. 33QPCh. 23 - Prob. 36QPCh. 23 - Prob. 37QPCh. 23 - Prob. 38QPCh. 23 - Prob. 45QP
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- Suppose that stars were born at random times over the last 1010 years. The rate of star formation is simply the number of stars divided by 1010 years. The fraction of stars with detected extrasolar planets is at least 18%. The rate of star formation can be multiplied by this fraction to find the rate planet formation. How often (in years) does a planetary system form in our galaxy? Assume the Milky Way contains 8 × 1011 stars.arrow_forwardThe Milky Way grew through merging with many smaller galaxies. What are the observational signatures of this process? O The motion of old stars in the bulge and halo of our galaxy are randomly orientated, meaning they were formed from collisions of small, accreted, galaxies all on different paths. O The ordered motion of the bulge / halo stars means that they came from many objects. The random motions of stars in the disk means it was formed from collisions of small, accreted, galaxies. O The motion of young stars in the disk are all in the same direction, meaning they came in as seperate objects.arrow_forwardThe Sun is moving at 220 ??/? around the Galactic Center at a more-or-less constant distance of 8.5 ???. To appreciate how remarkable this is, consider the following questions: a) How massive would the Sun have to be for the Earth to have an orbital velocity of 220 km/s at 1 AU? b) How fast would the Earth move if it was in orbit around the Sun at a distance of 8.5 kpc? Of course, you may ignore the effects of all other stars in this calculation.arrow_forward
- 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 Milky Way galaxy has about 5 x 10⁹ solar masses of gas in total. If 13 solar masses of that gas is turned into stars each year, how many more years could the Milky Way keep up with such a star formation rate? years (Note for comparison that the age of the universe is about 13.5 billion years, which can be written 1.35e10 years. Also, the value given is in the ballpark of how much gas in the Milky Way is used to make new stars each year.)arrow_forwardIn the reading, you were told that there were roughly 10,000 galaxies in the image of the Hubble Ultra Deep Field alone. The image is roughly 10 square arcminutes and there are roughly 1.5*10^8 square arcminutes composing the entire sky. With that in mind and assuming that the Hubble Ultra Deep Field represents an average part of the sky, roughly how many galaxies may exist in the observable universe? (Please include commas for every factor of 1,000; for example 2,343,567,890)arrow_forward
- Among the globular clusters orbiting a distant galaxy, one is moving at 534 km/s and is located 14 kpc from the center of the galaxy. Assuming the globular cluster is located outside most of the mass of the galaxy, what is the mass of the galaxy? Convert your answer to solar masses. (Hint: Use the formula for circular velocity, Vc = GM r ; make sure you convert relevant quantities to units of meters, kilograms, and seconds. Note: 1 pc = 3.1 ✕ 1016 m.)arrow_forwardFigure 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_forwardIf astronomers were to find they have made a mistake and our solar system is actually 7.8 (rather than 8.2) kpc from the center of the galaxy, but the orbital velocity of the sun is still 240 km/s, what is the minimum mass of the galaxy? (Hint: Use Kepler's third law.)arrow_forward
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