Universal symbolic expression for radial distance of conic motion

IF 0.8 4区 物理与天体物理 Q4 ASTRONOMY & ASTROPHYSICS Serbian Astronomical Journal Pub Date : 2014-12-01 DOI:10.2298/SAJ1489087S
M. Sharaf, A. S. Saad, A. Alshaery
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引用次数: 1

Abstract

SUMMARY: 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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圆锥运动径向距离的通用符号表达式
摘要:本文建立了圆锥运动径向距离的递推幂级数形式的通用符号表达式。这种解析幂级数表示的重要性在于它在很多运算下是不变的,因为幂级数的加法、乘法、幂、积分、微分等运算的结果也是幂级数。这一事实为处理与径向距离有关的问题的分析和计算发展提供了极好的灵活性。对于计算的发展,开发了一个完整的递归算法的级数系数。给出了一种利用连分数理论求解级数演化的有效方法,并提出了两种保证时间间隔(t−t0)较大时收敛的方法。此外,该算法不需要求解抛物轨道和双曲轨道的开普勒方程及其变体。给出了该算法在三种不同偏心率轨道上的数值应用;结果表明,该方法对任何圆锥运动都是准确的。
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来源期刊
Serbian Astronomical Journal
Serbian Astronomical Journal ASTRONOMY & ASTROPHYSICS-
CiteScore
1.00
自引率
0.00%
发文量
6
审稿时长
12 weeks
期刊介绍: Serbian Astronomical Journal publishes original observations and researches in all branches of astronomy. The journal publishes: Invited Reviews - review article on some up-to-date topic in astronomy, astrophysics and related fields (written upon invitation only), Original Scientific Papers - article in which are presented previously unpublished author''s own scientific results, Preliminary Reports - original scientific paper, but shorter in length and of preliminary nature, Professional Papers - articles offering experience useful for the improvement of professional practice i.e. article describing methods and techniques, software, presenting observational data, etc. In some cases the journal may publish other contributions, such as In Memoriam notes, Obituaries, Book Reviews, as well as Editorials, Addenda, Errata, Corrigenda, Retraction notes, etc.
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