40 Because the apparent recessional speeds of galaxies andquasars at great distances are close to the speed of light, the rela-tivistic Doppler shift formula (Eq. 37-31) must be used. The shift isreported as fractional red shift z = AAg. (a) Show that, in terms ofz, the recessional speed parameter B = v/c is given byz? + 2zz? + 2z + 2(b) A quasar detected in 1987 has z = 4.43. Calculate its speed pa-rameter. (c) Find the distance to the quasar, assuming thatв-Hubble's law is valid to these distances.

Answered: Image /qna-images/answer/34c5966c-4f0b-4c4a-a1fc-e96edc557709.jpg

Answered: 40 Because the apparent recessional…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 81AP: The nearest neutron star (a collated star made primarily of neutrons) is about 3.00 1018 m away...

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(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?
The 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 P1.81
In vacuum, the H-alpha line has a rest-frame wavelength of 656.461 nm. You took a spectrum of the center of a galaxy at an observatory on the ground and measured a wavelength of 656.65 nm for the H-alpha line. What is the radial velocity of the galaxy relative to the observer [km/s]? Note that the index of refraction of air is 1.0003 at that wavelength. As a result, the rest-frame wavelength of the H-alpha line in air differs from the rest-frame wavelength in vacuum.
*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.
The bright radio galaxy, 3c84, is observed to be moving away from the Earth at such high speed that the emitted blue 434-nm Hγ line of hydrogen is Doppler-shifted to 442 nm. Edwin Hubble discovered that all objects outside the local group of galaxies are moving away from us, with speeds v proportional to their distances R. Hubble's law is expressed as v = HR, where the Hubble constant has the approximate value H ≈ 22 ✕ 10−3 m/(s · ly). Determine the distance from the Earth to this galaxy. _________ ly
In the laboratory, one of the lines of sodium is emitted at a wavelength of 590.0 nm. In the light from a particular galaxy, however, this line is seen at a wavelength of 602.0 nm. Calculate the distance to the galaxy, assuming that Hubble’s law holds and that the Doppler shift of Eq. 37-36 applies.
If a galaxy moving away from the Earth has a speed of 1000 km/s and emits 656 nm light characteristic of hydrogen (the most common element in the universe). Why is the speed of the Earth in its orbit negligible here?
Near the center of our galaxy, hydrogen gas is moving directly away from us in its orbit about a black hole. We receive electromagnetic radiation of wavelength 1908 nm and know that it was 1875 nm when emitted by the hydrogen gas.Randomized Variablesλ = 1908 nm What is the ratio of the speed of the gas to the speed of light?
3) (a) How fast and in what direction must galaxy A be moving if an absorp- tion line found at wavelength 550nm (green) for a stationary galaxy is shifted to 450 nm (blue) (a "blue-shift") for galaxy A? (b) How fast and in what direction is galaxy B moving if it shows the same line shifted to 700 nm (red) (a "red shift")?
The expanding universe is carrying distant objects away from each other at a rate proportional to their separations. We use the Doppler effect observed in spectra of distant galaxies and quasars to calculate recession speeds. For the most distant objects recession speeds approach c, and therefore, the relativistic Doppler shift expression must be used. We define the redshift, z, as the fractional change in wavelength. a) The most distant quasar currently known is ULAS J1120+0641, discovered with the UK Infrared Telescope on Mauna Kea. It has a redshift of 7.1. Calculate its radial velocity in terms of v/c. b) Determine the distance to this quasar. c) At what wavelength would the Ha line (656.28 nm) be observed for this quasar?
A galaxy is oberverd to have emission lines of blue hydrogen lines of 434 nm. What will be the observed wavelength if the galaxy is moving away at a velocity of 0.56c.
A space based observatory collects light emitted by a given galaxy. The light was initially emitted with a frequency of 600*10^12Hz but the detected signal is red shifted by 40*10^12Hz How fast is the galaxy moving and in what direction? Show the algebraic form of any equation(s) that you apply and report your calculation in the correct units and with the correct number of significant figures.

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