Crash test for the Copenhagen problem

Abstract

The Copenhagen problem is a simple model in celestial mechanics. It serves to investigate the behavior of a small body under the gravitational influence of two equally heavy primary bodies. We present a partition of orbits into classes of various kinds of regular motion, chaotic motion, escape and crash. Collisions of the small body onto one of the primaries turn out to be unexpectedly frequent, and their probability displays a scale-free dependence on the size of the primaries. The analysis reveals a high degree of complexity so that long term prediction may become a formidable task. Moreover, we link the results to chaotic scattering theory and the theory of leaking Hamiltonian systems.

Poincaré recurrences and transient chaos in systems with leaks

“…Experimental and observational measurements often occur through holes or leaks that naturally exist or are deliberately introduced in an otherwise closed dynamical system [1,2,3,4,5,6,7,8,9,10]. The relevant observable quantity in such systems with leaks is the distribution of escape times from inside the system.…”

Dynamics of chaotic driving: Rotation in the restricted three-body problem

“…This driving originates from the planar, circular, restricted three-body problem that specifies the location ͓x͑t͒ , y͑t͔͒ of the center of mass of the small body according to the well-known equations [8][9][10][11] …”

“…As a particular example, we consider the planar circular three-body problem [8][9][10][11] with a small body of nonspherical shape that is able to rotate within the plane of the problem. The gravitational torque due to the two large bodies provides the driving for the small bodies' rotation dynamics.…”

On some new aspects of the photo-gravitational Copenhagen problem

“…Since then, a number of publications have been reported on this topic (Zagouras and Kalogeropoulou 1978;Michalodimitrakis 1979, etc.). Some of the most recent works are the ones by Nagler (2004Nagler ( , 2005 and Barrio T.J. Kalvouridis ( ) Faculty of Applied Sciences, Department of Mechanics, National Technical University of Athens, Athens, Greece e-mail: tkalvouridis@gmail.com et al (2006). On the other hand, the interstellar space is full of small corpuscles of various shapes, sizes, chemical composition and physicochemical properties.…”