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1. INTRODUCTION

Orbit9 is a software system designed to allow numerical experiments on orbits of solar system bodies, with different dynamical models. It was developed starting in 1989 (while I was at Cornell University). Orbit9 is a subsystem designed with user friendlyness as a design parameter, with the goal of becoming a public domain system.

The purpose of Orbit9 is to compute the orbits of real solar system small bodies, within a dynamical model as realistic as possible. The program handles a full gravitational N+M bodies problem, with the Sun and N-1 planets fully interacting between them, and M massless asteroids attracted by the N mases but not reacting on them. To compute the orbit of a known asteroid, initial conditions are taken from a catalogue (e.g. the Ephemerides of Minor Planets, or some other computer readable catalogue provided e.g. by the Minor Planets Center); in this case the only thing the user needs to specify to start the integration is the asteroid number. However, fictitious bodies can be handled, provided a suitable initial conditions file is provided; this input file can be written in a variety of coordinate systems, provided a header is supplied to explain what is meant. Unless otherwise requested by the user, all the input and output files contain a header with all the information needed to understand the content: e.g. which bodies' orbits are these, the initial epoch, the starting catalogue, the coordinate systems, etc.

The output is written in a standard format, but with choice of reference and coordinate systems. A separate program (Conv9) allows to convert the output into a variety of coordinate types, systems, references, and units, to be later analyzed either by means of GIFFv or by any program capable of reading a flat file. The output includes a sampled time series and a filtered one, with user-specified decimation. On request, the maximum Lyapounov exponent can be estimated -by solving a variational equation- for some of the asteroids. The angular variables always include counters for the number of revolutions, to allow for the determination of frequencies and/or for the monitoring of critical arguments. All these features, however, require some know-how to be used correctly; as an example, the choice of the sampling and decimation ratios is critical for the correct working of the output.

A safety dump feature allows almost always to restart an integration from where it was interrupted, regardless of whether this was due to a power failure or to a change of mind on the time span required. The computation of an estimate of the maximum Lyapounov exponent can also be continued in a consistent way. The accuracy of this continuation is very good, that is the jump -in both position and velocity- between the two orbits is at the rounding off level, if the right options are chosen. The output format is always compatible with the input format, but the special dump files have to be used to preserve full precision of the continuation.

This program is not meant to handle very unstable cases, which would require regularisation for close approaches; in practice, planet-crossing orbits are computed at the user's risk, with all the orbits integrated numerically with the same stepsize. The numerical methods include multistep and symplectic Runge-Kutta; the latter is generally used only as a starter (being very accurate but very inefficient). The program is not meant for dense output (that is, for a number of output times comparable to, or even larger than, the number of integration steps). Many features could be added, but this would betray the original purpose, which was (and is) the study of the dynamics of the asteroidal belt.

Together with Orbit9 the user can also obtain other programs meant to analyse the output, including the proper elements generation programs by myself and Z. Knezevic, the Graphic Interactive Fourier Filtering program (GIFF version v) to perform Fourier analysis and filtering, the Multiple Trigonometric Analysis Program (MTRAP) by M. Carpino, the TeXfor documentation system to print the listing with embedded TEXcomments and formulas, and so on. Everything is supplied in a self-service mode which allows at least the UNIX users to compile and run all the programs without any need to go into the details of the way they have been programmed; for other operating systems, although all the programs are machine-independent (apart from graphics), some work is needed to compile and install the software. Most modules are self explanatory, that is with embedded comments which should be enough; I cannot guarantee that everything is understandable and well documented.

The rest of this User Guide is organised as follows:




next up previous
Next: 2. INPUT AND TASK Up: ORBIT9 USER GUIDE Version Previous: ORBIT9 USER GUIDE Version
Andrea Milani
1999-10-31