Pearson eText -- Physics for Scientists and Engineers with Modern Physics -- Instant Access (Pearson+)
Pearson eText -- Physics for Scientists and Engineers with Modern Physics -- Instant Access (Pearson+)
5th Edition
ISBN: 9780137488179
Author: Douglas Giancoli
Publisher: PEARSON+
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Chapter 44, Problem 19P
To determine

The proof that the Schwarzschild radius for a star with mass equal to that of earth is 8.9mm.

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*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.
(c) In the case of a binary-star system, with stars of mass my and m2 separated by a distance r, the period, T, of the system is given by T²= (d) D 472 Show from first principles that di, the orbital radius of the star of mass mi, is given by G (m₁+ m₂) +3 d₁=m₂ GT² 4π² (m₁ + m₂) ² ³
(Astronomy) PSR1913+16 Problem III. As the shape of the graph shown is not skewed, the orbit can be assumed circular. Also assume the system is viewed edge-on (that is, the orbital system is not inclined to the observer). Using these assumptions, the maximum radial velocities, and the orbital period T = 7.75 hours, find the orbital radii of the stars from the center of mass. (Hints: The figures below may be helpful. Use v = 2πr/P, where v is velocity, P is period, and r is radius. Note: redshifts have positive radial velocities values in the upper figure, whereas blueshifts have negative radial velocity values.)
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