[Previous] | [ 6] | [Next]

[6.14] On an Analytical Solution for the Minimum Distance between Two Confocal Elliptical Orbits Used as a Close Approach Filter

M. A. Murison (U.S. Naval Observatory), A. Munteanu (Benjamin Banneker Academic High School)

We present an analytical solution to the problem of the minimum distance between two elliptical orbits with common focus. By use of the eccentric anomaly as the independent variable, the algebraic complexity of the solution is reduced. An additional benefit is that one can immediately use the Kepler equation in combination with a very fast and simple integer search algorithm to quickly determine the times of close approach between objects. Thus, one use of the analytical solution is as a fast filter for selecting (for closer scrutiny later) asteroids that will suffer a close approach to a given planet or other asteroid within a specified time, without resorting to numerical integrations.

The author(s) of this abstract have provided an email address for comments about the abstract: murison@usno.navy.mil

[Previous] | [ 6] | [Next]

Bulletin of the American Astronomical Society, 35 #4
© 2003. The American Astronomical Soceity.