By Thanu Padmanabhan
This distinctive e-book presents a transparent and lucid description of numerous facets of astrophysics and cosmology in a language comprehensible to a physicist or newbie in astrophysics. It offers the main themes in all branches of astrophysics and cosmology in an easy and concise language. The emphasis is on presently energetic study components and fascinating new frontiers instead of on extra pedantic issues. Many complex effects are brought with uncomplicated, novel derivations which boost the conceptual realizing of the topic. The ebook additionally includes over 100 routines in order 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 short take hold of of astrophysical innovations will locate this booklet important.
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A more interesting phenomenon is the forced precession of the axis of rotation of the Earth, which arises due to the torque exerted by Sun (and Moon; we will concentrate on the Sun) on Earth. This precession rate can be estimated fairly easily. Since the precession rate is small — something which we will verify at the end of the calculation — we can adopt a geocentric view and think of Sun as going around the Earth, once every year. For time scales much larger than a year, this is equivalent to the mass of the Sun, MQ, being distributed around earth along a circular ring of radius d Q (equal to the mean earth-sun distance) as far as computation of the torque causing the precession is concerned.
The former time scale occurs in different contexts; it is (i) the gravitational collapse time scale for matter with the density of earth as well as (ii) the orbital period of a satellite hovering just above earth. ) Of course, once the earth is taken to be non-spherical, the gravitational acceleration need to be worked out again in a self-consistent manner. This can be done and the e changes only by a factor (5/4). This flattening at the poles makes earth a solid body with two moments of inertia (about the principle axis) being nearly equal and the third one a little different from the other two: Ix = Iy ± Iz with SI/I = 6R/R = 1/300.
The gravitational force of Sun on Earth is, of course, significantly larger than that of Moon on Earth. But the tidal force due to Sun and the Moon has the ratio (M0/4) i™moon/'»mooiiJ (MQ/R3Q)(RQ/dQ)3 V-™ moon / - K m o o n i V-^moon/ " m o o n ) ^ ( ^ V ^ ^ O . 29) *J*<5 where 6 = (R/d) is the angle subtended by Sun or Moon at Earth and we have used the fact 9Q ~ 0mOon • So adding the effects of both sun and moon reduces the period to about 2 x 104 years which is close to what is observed. This means that the axis of rotation of earth will slowly precess and what we call the pole star, for example, will be different over few thousands of years!
An Invitation to Astrophysics by Thanu Padmanabhan