Analytical Solution for Stellar Density in Globular Clusters

Sharaf, M. A.; Sendi, A M

doi:10.1007/s12036-011-9000-0

Cited by 2 publications

(2 citation statements)

References 7 publications

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“…A great effort has been devoted up to now, and is being devoted at present to develop symbolic computing algorithms for some problems of astrodynamics as well as astrophysics (e.g. Sharaf and Saad 1997, Sharaf et al 1998, Sharaf 2005, Sharaf 2008, Sharaf and Sendi 2011, Sharaf et al 2012, Sharaf and Saad 2013.…”

Section: Introductionmentioning

confidence: 99%

Universal symbolic expression for radial distance of conic motion

2014

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In the present paper, a universal symbolic expression for radial distance of conic motion in recursive power series form is developed. The importance of this analytical power series representation is that it is invariant under many operations because the result of addition, multiplication, exponentiation, integration, differentiation, etc. of a power series is also a power series. This is the fact that provides excellent flexibility in dealing with analytical, as well as computational developments of problems related to radial distance. For computational developments, a full recursive algorithm is developed for the series coefficients. An efficient method using the continued fraction theory is provided for series evolution, and two devices are proposed to secure the convergence when the time interval (t ? t0) is large. In addition, the algorithm does not need the solution of Kepler?s equation and its variants for parabolic and hyperbolic orbits. Numerical applications of the algorithm are given for three orbits of different eccentricities; the results showed that it is accurate for any conic motion.

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Section: Introductionmentioning

confidence: 99%

Universal symbolic expression for radial distance of conic motion

2014

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“…This involves inverting an Abel integral equation [3][4][5], a topic that has received attention in a wide range of fields, especially in recent years. Abel inversion techniques have been used in fields such as x-ray radiography [6][7][8], galactic astronomy [9,10], optical fiber evaluation (extensively so, see [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]), satellite photometry using radio occultation techniques [26][27][28][29][30][31][32][33], microscopy, plasma electron diagnostics [34][35][36][37], and seismology [38][39][40]. In particular, radio occultation experiments using radio links between the Earth spacecraft that pass behind planets as seen from Earth have provided valuable information about planetary atmospheres.…”

Section: Introductionmentioning

confidence: 99%

Zero-order bows in radially inhomogeneous spheres: direct and inverse problems

Adam¹

2011

Appl. Opt.

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Zero-order ray paths are examined in radially inhomogeneous spheres with differentiable refractive index profiles. It is demonstrated that zero-order and sometimes twin zero-order bows can exist when the gradient of refractive index is sufficiently negative. Abel inversion is used to "recover" the refractive index profiles; it is therefore possible in principle to specify the nature and type of bows and determine the refractive index profile that induces them. This may be of interest in the field of rainbow refractometry and optical fiber studies. This ray-theoretic analysis has direct similarities with the phenomenon of "orbiting" and other phenomena in scattering theory and also in seismological, surface gravity wave, and gravitational "lensing" studies. For completeness these topics are briefly discussed in the appendixes; they may also be of pedagogic interest.

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Analytical Solution for Stellar Density in Globular Clusters

Abstract: In this paper, four parameters analytical solution will be established for the stellar density function in globular clusters. The solution could be used for any arbitrary order of outward decrease of the cluster's density.

Cited by 2 publications

References 7 publications

Universal symbolic expression for radial distance of conic motion

Universal symbolic expression for radial distance of conic motion

Zero-order bows in radially inhomogeneous spheres: direct and inverse problems

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