Universal Variables
Universal Anomaly
Stumpff Functions
Reciprocal
of the semi-major axis
Universal Kepler’s Equation.
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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
...
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