A digital Orrery

Chapter · January 1986with 8 Reads
DOI: 10.1007/BFb0116398
In book: Lecture Notes in Physics
Abstract
We have designed and built the Orrery, a special computer for high-speed high-precision orbital mechanics computations. On the problems the Orrery was designed to solve, it achieves approximately 10 Mflops in about 1 ft3 of space while consuming 150 W of power. The specialized parallel architecture of the Orrery, which is well matched to orbital mechanics problems, is the key to obtaining such high performance. In this paper we discuss the design, construction, and programming of the Orrery.

Do you want to read the rest of this chapter?

Request full-text
Request Full-text Paper PDF
This research hasn't been cited in any other publications.
  • Article
    The purpose of this review article is to demonstrate via a few simple models the mechanism for a very general, universal instability - the Arnold diffusion—which occurs in the oscillating systems having more than two degrees of freedom. A peculiar feature of this instability results in an irregular, or stochastic, motion of the system as if the latter were influenced by a random perturbation even though, in fact, the motion is governed by purely dynamical equations. The instability takes place generally for very special initial conditions (inside the so-called stochastic layers) which are, however, everywhere dense in the phase space of the systsm.The basic and simplest one of the models considered is that of a pendulum under an external periodic perturbation. This model represents the behavior of nonlinear oscillations near a resonance, including the phenomenon of the stochastic instability within the stochastic layer of resonance. All models are treated both analytically and numerically. Some general regulations concerning the stochastic instability are presented, including a general, semi-quantitative method-the overlap criterion—to estimate the conditions for this stochastic instability as well as its main characteristics.
  • Article
    The physical processes that occur in planetary rings are discussed. The theoretical arguments leading to the conclusion that Saturn's rings are solid particles in nonuniform rotation are summarized, and the optical depth, thickness, and particle size of the rings are discussed. The influence of nearby satellites on the rings is analyzed, and asymmetries in the rings are briefly discussed. What is known of the rings of Uranus and of Jupiter's ring is summarized. Some of the dynamical processes and influences that are expected to be incorporated in more advanced theories of planetary rings are reviewed in detail, including radiation drag, plasma drag, interparticle collisions and viscosity, resonances with external satellites, shepherd satellites and moonlets. Finally, the orbital evolution of the shepherd satellites caused by the rings is estimated.
  • Article
    The semianalytical approach to long-term solutions of resonant systems with three degrees of freedom, proposed by Giacaglia in 1965, is used to study the long-term motion of Pluto. The study takes into account the effects of Jupiter, Saturn and Uranus on the motion of Pluto. Modified periodic orbits of the third kind constitute the solutions; Pluto is found to librate about one of these periodic solutions. The long-term eccentricity, inclination, perihelion and librational amplitude of the planet are discussed.
  • Article
    The sudden eccentricity increases discovered by Wisdom (1982) are reproduced in numerical integrations of the planar ecliptic restricted three-body problem, verifying that this phenomenon is real. Mapping derivations are qualitatively reviewed and the maximum Liapunov characteristic exponent and its importance for determining the character of a trajectory are explained. The results of a number of calculations of this exponent using the differential equations for the unaveraged three-body problem are shown and compared to equivalent calculations using a mapping. In all cases the two approaches agree whether the orbits are chaotic or quasiperiodic. The mappings are used to trace out the chaotic zone near the 3/1 commensurability, both in the planar-ecliptic problem and in the three-dimensional elliptic problem. The outer boundary of the chaotic zone coincides with the boundary of the 3/1 Kirkwood gap in the actual distribution of asteroids within the errors of the asteroid orbital elements.
  • Article
    A mapping of the phase space onto itself with the same low-order resonance structure as the 3/1 commensurability in the planar-elliptic restricted three-body problem is obtained. This mapping is about 1,000 times faster than the usual method of numerically integrating the averaged equations of motion. It exhibits some surprising behavior that might provide a key to the origin of the Kirkwood gaps. It is noted that a test asteroid placed in the gap may evolve for a million years with low eccentricity (less than 0.05) and then suddenly jump to large eccentricity (greater than 0.3), becoming a Mars crosser. The removal of the asteroid by a close encounter with Mars would then be possible. As a first test of this hypothesis, a distribution of 300 test asteroids in the area of the 3/1 commensurability was evolved for two million years. When the Mars crossers are removed, the distribution of initial conditions reveals a gap at the location of the 3/1 Kirkwood gap.
  • Article
    Full-text available
    Pluto orbit integration over 4.5 million years by variation of parameters technique and confirming Neptune-Pluto orbital resonances
  • Article
    Full-text available
    The reasons for the creation of Illiac IV are described and the history of the Illiac IV project is recounted. The architecture or hard-ware structure of the Illiac IV is discussed--the Illiac IV array is an array processor with a specialized control unit (CU) that can be viewed as a small stand-alone computer. The Illiac IV software strategy is described in terms of current user habits and needs. Brief descriptions are given of the systems software itself, its history, and the major lessons learned during its development. Some ideas for future development are suggested. Applications of Illiac IV are discussed in terms of evaluating the function f(x) simultaneously on up to 64 distinct argument sets x i . Many of the time-consuming problems in scientific computation involve repeated evaluation of the same function on different argument sots. The argument sets which compose the problem data base must be structured in such a fashion that they can be distributed among 64 separate memories. Two matrix applications: Jacobi's algorithm for finding the eigenvalues and eigenvectors of real symmetric matrices, and reducing a real nonsymmetric matrix to the upper-Hessenberg form using Householder's transformations are discussed in detail. The ARPA network, a highly sophisticated and wide ranging experiment in the remote access and sharing of computer resources, is briefly described and its current status discussed. Many researchers located about the country who will use Illiac IV in solving problems will do so via the network. The various systems, hardware, and procedures they will use is discussed.