Stumpff functions are an infinite series that depends on the value of z. This value results from multiplying the reciprocal semi-major axis with a universal anomaly. The purpose from those functions is to calculate the variation of the universal parameter (variable) using Kepler's equation for different orbits. In this paper, each range for the reciprocal of the semi-major axis, universal anomaly, and z is calculated in order to study the behavior of Stumpff functions C(z) and S(z). The results showed that when z grew, Stumpff functions for hyperbola, parabola, and elliptical orbits were also growing. They intersected and had a tendency towards zero for both hyperbola and parabola orbits, but for elliptical orbits, Stumpff functions exhibited unstable behavior, with distinct, insignificant peaks disappearing as z increased. In comparison to other published studies in this section, the results showed good agreement.
Calculating the Variation of the Universal Parameter (Variable) Using
Kepler's Equation for Different Orbits
Universal Variables
Universal Anomaly
Stumpff Functions
Reciprocal
of the semi-major axis
Universal Kepler’s Equation.
Publication Date
Thu Aug 01 2019
Journal Name
Journal Of Economics And Administrative Sciences
مقارنة مقدرات بيز لدالة المعولية لتوزيع باريتو من النوع الاول باستعمال دوال معلوماتية مضاعفة مختلفة
Pareto type I distribution
reliability function
bayes method
double prior distributions (chi-gamma square distribution. gamma- erlang distribution
erlang exponential distribution
the squared error loss function.
توزيع باريتو من النوع الاول
دالة المعولية
طريقة بيز
الدوال المعلوماتية المضاعفة : توزيع مربع كاي- كاما
توزيع كاما - ارلنك
التوزيع ارلنك- الاسي
دالة الخسارة التربيعية.
The comparison of double informative priors which are assumed for the reliability function of Pareto type I distribution. To estimate the reliability function of Pareto type I distribution by using Bayes estimation, will be used two different kind of information in the Bayes estimation; two different priors have been selected for the parameter of Pareto type I distribution . Assuming distribution of three double prior’s chi- gamma squared distribution, gamma - erlang distribution, and erlang- exponential distribution as double priors. The results of the derivaties of these estimators under the squared error loss function with two different double priors. Using the simulation technique, to compare the performance for
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