By Thanu Padmanabhan

ISBN-10: 9812566384

ISBN-13: 9789812566386

ISBN-10: 9812566872

ISBN-13: 9789812566874

This special publication offers a transparent and lucid description of a number of features of astrophysics and cosmology in a language comprehensible to a physicist or newbie in astrophysics. It offers the main issues in all branches of astrophysics and cosmology in an easy and concise language. The emphasis is on presently energetic examine parts and fascinating new frontiers instead of on extra pedantic themes. Many complex effects are brought with easy, novel derivations which develop the conceptual knowing of the topic. The e-book additionally comprises over 100 workouts so as to support scholars of their self learn. Undergraduate and graduate scholars in physics and astrophysics in addition to all physicists who're drawn to acquiring a brief snatch of astrophysical suggestions will locate this booklet worthwhile.

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The metric for this case can be obtained in a heuristic manner, which we will now describe. Let us consider a point P a t a distance r from the origin where the gravitational potential is 4>N = —GM/r according to Newtonian theory. If we consider a small box around P which is freely falling towards the origin, then the metric in the coordinates used by a freely falling observer in the box will be just that of special relativity: ds2 = c2dt2n - dr? n . 76) This is because, in the freely falling frame, the observer is weight-less and Chapter 1: Gravitation 33 there is no effective gravity.

Consider a test body of mass Mt moving through a cluster of stars, say, where each "field" star has a mass m / . The energy exchanged between the test mass and the field stars is again governed by the same time scale as the one estimated above in Eq. 65), with Gm2 replaced by GMtrrif. If the field stars were moving with typical random velocities larger than that of the test mass, then the net effect of the stars on the test mass will be to exert a drag force on the mass. fri^ 2nG Mt(mfnf) 2 IQ^yr/ InN v VfA^VV (InTV) V l O k m s - V \MQ) Pf Y* Vl03MQpc-3; (166) V ; Note that the result only depends on the background mass density pf = 28 An Invitation to Astrophysics nrrif rather than on the mass TO/.

The potential due to the Moon is given by v 1/2 GM2 / I2 Z ~ l + ^-2-cos6N R \ R? 32) ^cos0+i(3cos20-l)-^ + 0 ( ^ where we have done a Taylor expansion in l/R. ) The term (l/R) cos 6 varies linearly along the z = I cos 0 direction from Mi to M2 so that its gradient gives a constant force. This is precisely canceled by a corresponding term in the centrifugal force; which is, of course, necessary for the centrifugal force to keep the bodies in circular orbits. 33) Using w2 = G{M\ + M2)/R? we see that the term linear in cos# indeed cancels.

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