UNDERSTANDING THE UNIVERSE(LL)-W/CODE
UNDERSTANDING THE UNIVERSE(LL)-W/CODE
3rd Edition
ISBN: 9780393869903
Author: PALEN
Publisher: NORTON
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Chapter 16, Problem 8QAP
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Does the universe have a center? Explain.
*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.
A star, which is 2.1 x 1020 m from the center of a galaxy, revolves around that center once every 2.8 x 108 years. Assuming each star in the galaxy has a mass equal to the Sun's mass of 2.0 x 1030 kg, the stars are distributed uniformly in a sphere about the galactic center, and the star of interest is at the edge of that sphere, estimate the number of stars in the galaxy.
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