Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 31, Problem 40P
(a)
To determine
Prove that the velocity relative to the person together with the position vector of the galaxy cluster from the person satisfies Hubble’s law.
(b)
To determine
Prove that the position and velocity of cluster 2 relative to cluster 1 satisfy Hubble’s law.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Hubble's law can be stated in vector form as v = HR.
Outside the local group of galaxies, all objects are moving
away from us with velocities proportional to their positions
relative to us. In this form, it sounds as if our location in
the Universe is specially privileged. Prove that Hubble's
law is equally true for an observer elsewhere in the Uni-
verse. Proceed as follows. Assume we are at the origin of
coordinates, one galaxy cluster is at location R, and has
velocity v, = HR relative to us, and another galaxy cluster
has position vector R, and velocity v, = HR, Suppose the
speeds are nonrelativistic. Consider the frame of reference
of an observer in the first of these galaxy clusters. (a) Show
that our velocity relative to her, together with the position
vector of our galaxy cluster from hers, satisfies Hubble's
law. (b) Show that the position and velocity of cluster 2 rel-
ative to cluster 1 satisfy Hubble's law.
(a) Let L be the diameter of our galaxy.Suppose that a person in a spaceship of massm wants to travel across the galaxy at constantspeed, taking proper time τ. Find the kineticenergy of the spaceship. (b) Your friend is impa-tient, and wants to make the voyage in an hour.For L = 105 light years, estimate the energy inunits of megatons of TNT (1 megaton=4×109 J).
Consider the energy-momentum tensor
Tμv = (p+p) uu+P9μ
applied to the matter/energy distribution in the universe on large scales, and assume an equation
of state of the form p = wp, with w a constant. Determine the type of matter/energy dominating
the universe if the energy-momentum tensor is traceless, that is, T"μ = 0.
Chapter 31 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 31.2 - Given the identification of the particles in...Ch. 31.5 - Prob. 31.2QQCh. 31.5 - Prob. 31.3QQCh. 31.5 - Prob. 31.4QQCh. 31.9 - Prob. 31.5QQCh. 31 - Prob. 1OQCh. 31 - Prob. 2OQCh. 31 - Prob. 3OQCh. 31 - Prob. 4OQCh. 31 - Prob. 5OQ
Ch. 31 - Prob. 6OQCh. 31 - Prob. 7OQCh. 31 - Prob. 8OQCh. 31 - Prob. 1CQCh. 31 - Prob. 2CQCh. 31 - Prob. 3CQCh. 31 - Prob. 4CQCh. 31 - Prob. 5CQCh. 31 - Prob. 6CQCh. 31 - Prob. 7CQCh. 31 - Prob. 8CQCh. 31 - Prob. 9CQCh. 31 - Prob. 10CQCh. 31 - Prob. 11CQCh. 31 - Prob. 12CQCh. 31 - Prob. 13CQCh. 31 - Prob. 1PCh. 31 - Prob. 2PCh. 31 - Prob. 3PCh. 31 - Prob. 4PCh. 31 - Prob. 5PCh. 31 - Prob. 6PCh. 31 - Prob. 7PCh. 31 - Prob. 8PCh. 31 - Prob. 9PCh. 31 - Prob. 10PCh. 31 - Prob. 11PCh. 31 - Prob. 12PCh. 31 - Prob. 13PCh. 31 - Prob. 14PCh. 31 - Prob. 15PCh. 31 - Prob. 16PCh. 31 - Prob. 17PCh. 31 - Prob. 18PCh. 31 - Prob. 19PCh. 31 - Prob. 20PCh. 31 - Prob. 21PCh. 31 - Prob. 22PCh. 31 - Prob. 23PCh. 31 - Prob. 24PCh. 31 - Prob. 25PCh. 31 - Prob. 26PCh. 31 - Prob. 27PCh. 31 - Prob. 28PCh. 31 - Prob. 29PCh. 31 - Prob. 30PCh. 31 - Prob. 31PCh. 31 - Prob. 32PCh. 31 - Prob. 33PCh. 31 - Prob. 34PCh. 31 - Prob. 35PCh. 31 - Prob. 36PCh. 31 - Prob. 37PCh. 31 - Prob. 38PCh. 31 - Prob. 39PCh. 31 - Prob. 40PCh. 31 - Prob. 41PCh. 31 - Prob. 42PCh. 31 - Prob. 43PCh. 31 - Prob. 44PCh. 31 - Prob. 45PCh. 31 - Prob. 46PCh. 31 - Prob. 47PCh. 31 - Prob. 48PCh. 31 - Prob. 49PCh. 31 - Prob. 50PCh. 31 - Prob. 51PCh. 31 - Prob. 52PCh. 31 - Prob. 53PCh. 31 - Prob. 54PCh. 31 - Prob. 55PCh. 31 - Prob. 56PCh. 31 - Prob. 57PCh. 31 - Prob. 58PCh. 31 - Prob. 59PCh. 31 - Prob. 60PCh. 31 - Prob. 61PCh. 31 - Prob. 62PCh. 31 - Prob. 63PCh. 31 - Prob. 64PCh. 31 - Prob. 65P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- Please help with this questionarrow_forwardConsider the energy-momentum tensorT_µν = (ρ + p) u_µ u_ν + p g_µνapplied to the matter/energy distribution in the universe on large scales, and assume an equation of state of the form p = wρ, with w a constant. Determine the type of matter/energy dominating the universe if the energy-momentum tensor is traceless, that is, T^µ_µ = 0.arrow_forwardAsap, Typed formatarrow_forward
- 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.arrow_forwardThe 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. _________ lyarrow_forwardEstimate the age of the universe (in Gyrs) at the time when radiation was emitted from an object with redshift z. For 1 < z < 3200, you can assume the Universe is matter dominated, in which case a ∝ t^2/3 and equation 5.102 should hold. Values: Assume H0 = 70 km/s/Mpc Ωm,0 = 0.3 z=3.6 Equation 5.102 is : a(t) = (3/2 (sqrtΩm,0 ) H0 t)^2/3arrow_forward
- 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.arrow_forwardConsider a cosmological spacetime in which the line element is given by ds? = a²(t)(-dt + dr² + dy² + dz²), where a(t) > 0 is the scale factor. Two light rays tangent to l = (1,1,0, 0) and l = (1,0, 1,0) are received at time t = u" = (a-'(to), 0, 0, 0). Compute the observed angle between the correspond- ing images. to by someone with 4-velocityarrow_forwardThe geometry of spacetime in the Universe on large scales is determined by the mean energy density of the matter in the Universe, ρ. The critical density of the Universe is denoted by ρ0 and can be used to define the parameter Ω0 = ρ/ρ0. Describe the geometry of space when: (i) Ω0 < 1; (ii) Ω0 = 1; (iii) Ω0 > 1. Explain how measurements of the angular sizes of the hot- and cold-spots in the CMB projected on the sky can inform us about the geometry of spacetime in our Universe. What do measurements of these angular sizes by the WMAP and PLANCK satellites tell us about the value of Ω0?arrow_forward
- every solution i keep recieveing is wrong. please help....arrow_forwardIn the red shift of radiation from a distant galaxy, a certain radiation, known to have a wavelength of 434 nm when observed in the laboratory, has a wavelength of 462 nm. (a)What is the radial speed of the galaxy relative to Earth? (b) Is the galaxy approaching or receding from Earth?arrow_forwardProblem 1: A pion 7 traveling at speed v decays into a muon u- and an antineutrino (T- → µ- + ūµ). To a good approximation, we can assume the antineutrino is massless. On the other hand, the pion and muon have masses m, and m,, respectively. If the antineutrino emerges at 90° to the original pion direction, show that the angle 0 at which the muon comes off is given by 1- m, /m² tan 0 23,2 where B = v/c and y = 1/V1 - 32.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning