Astronomy and Astrophysics – Astronomy
Scientific paper
Nov 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999cemda..75..201f&link_type=abstract
Celestial Mechanics and Dynamical Astronomy, v. 75, Issue 3, p. 201-226 (1999).
Astronomy and Astrophysics
Astronomy
3
Universal Kepler&Rsquo, S Equation, Orbital Motion
Scientific paper
We developed a procedure to solve a modification of the standard form of the universal Kepler’s equation, which is expressed as a nondimensional equation with respect to a nondimensional variable. After reducing the domain of the variable and the argument by using the symmetry and the periodicity of the equation, the method first separates the case where the solution is so small that it is given an inverted series. Second, it separates the cases where the elliptic, parabolic, or hyperbolic standard forms of Kepler’s equation are suitable. Here the separation is done by judging whether detouring these nonuniversal equations will cause a 1-bit loss of information to their nonuniversal solutions or not. Then the nonuniversal equations are solved by the author’s procedures to solve the elliptic Kepler’s equation (Fukushima, 1997a), Barker’s equation (Fukushima, 1998), and the hyperbolic Kepler’s equation (Fukushima, 1997b), respectively. And their nonuniversal solutions are transformed back to the solution of the universal equation. For the rest of the case, we obtain an approximate solution by solving roughly the approximated cubic equation as we did in solving Barker’s equation. Then the correction to the approximate solution is obtained by Halley’s method precisely. There the special function appeared in the universal equation is rewritten into a combination of similar special functions of small arguments, so that they are efficiently evaluated by their Taylor series. Numerical measurements showed that, in the case of Intel Pentium II processor, the new method is 10 25 times as fast as Shepperd’s method (Shepperd, 1985) and 7 13 times as fast as the standard Newton method.
No associations
LandOfFree
Fast Procedure Solving Universal Kepler's Equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Fast Procedure Solving Universal Kepler's Equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fast Procedure Solving Universal Kepler's Equation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1285510