Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 21, Problem 29Q
To determine
The speed of a meter stick.
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Students have asked these similar questions
A galaxy is observed to recede from Earth with an approximate speed of 0.81c.
Approximately how far d from Earth is this galaxy? Give an answer in units of megaparsecs (Mpc).
d = ? Mpc
How long ago t was the light that we see emitted by the galaxy? Give an answer in units of years.
t = ? years
*39 Will the universe continue to expand forever? To attack this
question, assume that the theory of dark energy is in error and that
the recessional speed v of a galaxy a distance r from us is determined
only by the gravitational interaction of the matter that lies inside
a sphere of radius r centered on us. If the total mass inside this
sphere is M, the escape speed v, from the sphere is v. = V2GMIT
(Eq. 13-28). (a) Show that to prevent unlimited expansion, the aver-
age density p inside the sphere must be at least equal to
ЗН
87G
(b) Evaluate this "critical density" numerically; express your an-
swer in terms of hydrogen atoms per cubic meter. Measurements
of the actual density are difficult and are complicated by the pres-
ence of dark matter.
If p = 2.7 x 10-27 kgm-3, what is the radius of curvature R, of Einstein's static universe? How
long would it take a photon to circumnavigate such a universe?
Chapter 21 Solutions
Universe: Stars And Galaxies
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- E2arrow_forwardFigure P9.21 shows a jet of material (at the upper right) being ejected by galaxy M87 (at the lower left). Such jets are believed to be evidence of supermassive black holes at the center of a galaxy. Suppose two jets of material from the center of a galaxy are ejected in opposite directions. Both jets move at 0.750c relative to the galaxy center. Determine the speed of one jet relative to the other. Figure P9.21arrow_forwardA stellar black hole may form when a massive star dies. The mass of the star collapses down to a single point. Imagine an astronaut orbiting a black hole having eight times the mass of the Sun. Assume the orbit is circular. a. Find the speed of the astronaut if his orbital radius is r = 1 AU. b. Find his speed if his orbital radius is r = 11.8 km. c. CHECK and THINK: Compare your answers to the speed of light in a vacuum. What would the astronauts orbital speed be if his orbital radius were smaller than 11.8 km?arrow_forward
- (a) What Hubble constant corresponds to an approximate age of the universe of 1010 y? To get an approximate value, assume the expansion rate is constant and calculate the speed at which two galaxies must move apart to be separated by 1 Mly (present average galactic separation) in a time of 1010 y. (b) Similarly, what Hubble constant corresponds to a universe approximately 21010years old?arrow_forwardThe nearest neutron star (a collated star made primarily of neutrons) is about 3.00 1018 m away from Earth. Given that the Milky Way galaxy (Fig. P1.81) is roughly a disk of diameter 1021 m and thickness 1019 m, estimate the number of neutron stars in the Milky Way to the nearest order of magnitude. Figure P1.81arrow_forwardThe distance of a galaxy from our solar system is 10 Mpc. (a) What is the recessional velocity of the galaxy? (b) By what fraction is the starlight from this galaxy red shifted (that is, what is its z value)?arrow_forward
- The classical Doppler shift for light. A light source recedes from an observer with a speed v that is small compared with c. (a) Show that in this case, Equation 1.15 reduces to ffvc (b) Also show that in this case vc (Hint: Differentiate f = c to show that / = f/f) (c) Spectroscopic measurements of an absorption line normally found at = 397 nm reveal a redshift of 20 nm for light coming from a galaxy in Ursa Major. What is the recessional speed of this galaxy?arrow_forward. A compact neutron star has a mass of kg (about 1.4 times the mass of the Sun) but a radius of only m (approximately 6.2 mi!). If a clock on the surface of this exotic star marks the passage of 1 h of time, how much time is observed to pass on an identical clock located a very large distance from the neutron star?arrow_forwardThe spectral lines of various elements are detected in light from a galaxy in the constellation Ursa Major. An ultraviolet line from singly ionized calcium (lS = 393 nm) is observed at wavelength l0 = 414 nm, redshifted into the visible portion of the spectrum. At what speed is this galaxy receding from us?arrow_forward
- If we knew that a distant galaxy were 8.56 x 1021 meters away from earth, what velocity could we expect to measure for the galaxy in km/s?arrow_forwardB4arrow_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
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