5 research outputs found
Universal symbolic expression for radial distance of conic motion
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