Review of planetary and satellite theories

Planetary and satellite theories have been historically and are presently intimately related to the available computing capabilities, the accuracy of observational data, and the requirements of the astronomical community. Thus, the development of computers made it possible to replace planetary and lunar general theories with numerical integrations, or special perturbation methods. In turn, the availability of inexpensive small computers and high-speed computers with inexpensive memory stimulated the requirement to change from numerical integration back to general theories, or representative ephemerides, where the ephemerides could be calculated for a given date rather than using a table look-up process. In parallel with this progression, the observational accuracy has improved such that general theories cannot presently achieve the accuracy of the observations, and, in turn, it appears that in some cases the models and methods of numerical integration also need to be improved for the accuracies of the observations. Planetary and lunar theories were originally developed to be able to predict phenomena, and provide what are now considered low accuracy ephemerides of the bodies. This proceeded to the requirement for high accuracy ephemerides, and the progression of accuracy improvement has led to the discoveries of the variable rotation of the Earth, several planets, and a satellite. By means of mapping techniques, it is now possible to integrate a model of the motion of the entire solar system back for the history of the solar system. The challenges for the future are: Can general planetary and lunar theories with an acceptable number of terms achieve the accuracies of observations? How can numerical integrations more accurately represent the true motions of the solar system? Can regularly available observations be improved in accuracy? What are the meanings and interpretations of stability and chaos with respect to the motions of the bodies of our solar system? There has been a parallel progress and development of problems in dealing with the motions of artificial satellites. The large number of bodies of various sizes in the limited space around the Earth, subject to the additional forces of drag, radiation pressure, and Earth zonal and tesseral forces, require more accurate theories, improved observational accuracies, and improved prediction capabilities, so that potential collisions may be avoided. This must be accomplished by efficient use of computer capabilities.