Abstract
A root-finding method due to Laguerre (1834-1886) is applied to the solution of the Kepler problem. The speed of convergence of this method is compared with that of Newton's method and several higher-order Newton methods for the problem formulated in both conventional and universal variables and for both elliptic and hyperbolic orbits. In many thousands of trials the Laguerre method never failed to converge to the correct solution, even from exceptionally poor starting approximations. The non-local robustness and speed of convergence of the Laguerre method should make it the preferred method for the solution of Kepler's equation.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 199-211 |
| Number of pages | 13 |
| Journal | Celestial Mechanics |
| Volume | 39 |
| Issue number | 2 |
| DOIs | |
| State | Published - Jun 1986 |
ASJC Scopus subject areas
- Astronomy and Astrophysics
- Space and Planetary Science