Fundamentals of Physics, Volume 1, Chapter 1-20
10th Edition
ISBN: 9781118233764
Author: David Halliday
Publisher: WILEY
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Chapter 44, Problem 31P
To determine
To calculate:
the distance to a galaxy that has a certain shift in the sodium line.
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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.
40 Because the apparent recessional speeds of galaxies and
quasars at great distances are close to the speed of light, the rela-
tivistic Doppler shift formula (Eq. 37-31) must be used. The shift is
reported as fractional red shift z = AAg. (a) Show that, in terms of
z, the recessional speed parameter B = v/c is given by
z? + 2z
z? + 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 that
в-
Hubble's law is valid to these distances.
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
Chapter 44 Solutions
Fundamentals of Physics, Volume 1, Chapter 1-20
Ch. 44 - Prob. 1QCh. 44 - Prob. 2QCh. 44 - Prob. 3QCh. 44 - Prob. 4QCh. 44 - Prob. 5QCh. 44 - Prob. 6QCh. 44 - Prob. 7QCh. 44 - Prob. 8QCh. 44 - Prob. 9QCh. 44 - Prob. 10Q
Ch. 44 - Prob. 11QCh. 44 - Prob. 1PCh. 44 - Prob. 2PCh. 44 - Prob. 3PCh. 44 - Prob. 4PCh. 44 - Prob. 5PCh. 44 - a A stationary particle 1 decays into parties 2...Ch. 44 - Prob. 7PCh. 44 - GO A positive tau , rest energy = 1777 MeV is...Ch. 44 - Prob. 9PCh. 44 - Prob. 10PCh. 44 - Prob. 11PCh. 44 - Prob. 12PCh. 44 - Prob. 13PCh. 44 - Prob. 14PCh. 44 - Prob. 15PCh. 44 - Prob. 16PCh. 44 - Prob. 17PCh. 44 - Prob. 18PCh. 44 - Prob. 19PCh. 44 - Prob. 20PCh. 44 - Prob. 21PCh. 44 - Prob. 22PCh. 44 - Prob. 23PCh. 44 - Prob. 24PCh. 44 - Prob. 25PCh. 44 - Prob. 26PCh. 44 - Prob. 27PCh. 44 - Prob. 28PCh. 44 - Prob. 29PCh. 44 - Prob. 30PCh. 44 - Prob. 31PCh. 44 - Prob. 32PCh. 44 - Prob. 33PCh. 44 - Prob. 34PCh. 44 - Prob. 35PCh. 44 - What would the mass of the Sun have to be if Pluto...Ch. 44 - Prob. 37PCh. 44 - Use Wiens law see Problem 37 to answer the...Ch. 44 - Prob. 39PCh. 44 - Prob. 40PCh. 44 - Prob. 41PCh. 44 - Due to the presence everywhere of the cosmic...Ch. 44 - SSM Suppose that the radius of the Sun were...Ch. 44 - Prob. 44PCh. 44 - Prob. 45PCh. 44 - Prob. 46PCh. 44 - Prob. 47PCh. 44 - Prob. 48PCh. 44 - Prob. 49PCh. 44 - Prob. 50PCh. 44 - Prob. 51PCh. 44 - Prob. 52PCh. 44 - Prob. 53PCh. 44 - Prob. 54P
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- The rest-frame (natural) Wavelength of the H-a line of hydrogen is 656.3 nm. In the spectrum of light from a galaxy we observe, it is shifted to 763.8 nm. Calculate the reccession speed of the galaxy in m/s.arrow_forwardName: Hubble Distances Redshift z parameter The relativistic redshift is parametrized by z and given by Δ In terms of the scale factor, 2= X do - de de 1+z= ao a (2) Problem 01. Find the redshift z for a Hydrogen spectral line originally at 656 nm which has been observed at a wavelength of 1.64 μm. Astro 001 Fall 2022 Problem 02. How much smaller was the universe when this light was emitted? U₁ = DHO Using the redshift to measure the velocity, we find D~ (1) 0.1 Hubble's Law Hubble's Law states that the recession velocity of a redshifted galaxy is given by the product of the distance and the Hubble constant. (3) ZC Ho where c = 3 x 108 m/s and Ho = 2.3 x 10-18 s in standard units. The standard measurement of the Hubble constant is Ho = 71 (km/s)/Mpc. Problem 03. What is the distance in Mpc and ly to the galaxy measured in problem 01? 1 pc = 3.26 ly.arrow_forwardAssume that the radiation coming from Andromeda is all due to solar-like stars (MV, = 4.83). How many stars are there in the Andromeda galaxy according to this approximation?arrow_forward
- 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?arrow_forward*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.arrow_forwardNear 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?arrow_forward
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