Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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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.
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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
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