By Kenneth R. Lang

ISBN-10: 3540090649

ISBN-13: 9783540090649

ISBN-10: 3662111888

ISBN-13: 9783662111888

This booklet is intended to be a reference resource for the basic formulae of astrophysics. at any place attainable, the unique resource of the fabric being provided is referenced including references to more moderen alterations and functions.

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1-8) the resulting dipole field at the surface of a spherical molecule will be Es d exE' a a (1-26) = ---:3 = - 3 ' where a is the molecular radius. Thus the observed field, E, from an isotropic medium with a number density of N molecules will be , [43" E= E - N n a3 Es ] = [ J' 1 - 4n 3 N ex E . (1-27) The total electric polarization of the medium, P, is given by P=NexE , =Xe E = [Nex -1- 4 - -] E, -3 nNex (1-28) where P is the volume density of the electric dipole moment, and the constant Xe is called the electric susceptibility.

1' perpendicular to the magnetic field. , due to gyroradiation is given by (SITENKO and STEPANOV, 1957; WILD, SMERD, and WEISS, 1963) 4n 3 / 2 v2 (n/2)2n (sine)2n-2(1 +cos 20) _ [(1-nv H/V)2] oc = - - --"- - ß2n 3 exp , • e v n! cosO 0 ß~COS20 (1-171) where the plasma frequency vp=[e 2N e/(nm)]1/2, the frequency ofthe radiation is v, the ß~=2kT/(me2), and the gyrofrequency vH=eH/(2nme). For optical depth calculations, the effective thickness, L, of a layer of thermal electrons is given by L=2LHßOcosO where the sc ale of the magnetic field LH=H/V H, is the characteristic distance over which a change in VH is significant.

Consider a spherical shell of thickness dr at the distance R from the origin of the coordinate system used in the integration. During the time dt=dr/c, the amount of charge flowing through the inner surface of the shell is n 'V pn;vdt=p_r-dr, (1-105) c where nr is a unit vector in the radial direction and v is the velocity vector. vJ n dq=p [ 1-~ dv. (1-106) For a point charge, q, moving at the velocity, v, Eqs. (1-104) and (1-106) give the Lienard-Wiechert potentials (LIENARD, 1898; WIECHERT, 1901) q

### Astrophysical Formulae: A Compendium for the Physicist and Astrophysicist by Kenneth R. Lang

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