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Recent developments in analytical celestial mechanics.
Periodic solutions for restricted three-body problem
Three-Dimensional Lunar Mission Studies
Some three-dimensional lunar trajectories have been calculated by integration of the equations of motion of the classical restricted three-body problem of celestial mechanics. The calculations have been used for analysis of several aspects of lunar flight including requirements for achieving lunar impact and for establishment of a close lunar satellite. The allowable errors in initial conditions for lunar missions are strongly dependent on the values of the initial injection velocity and the injection angle. There can be large differences in results obtained from two-dimensional analyses (in which the vehicle trajectory is assumed to remain always in the earth-moon plane) and those obtained from three-dimensional analyses. Some of the accuracy tolerances can be fairly well estimated by use of a two-body analysis which considers the inclination of the plane of the vehicle trajectory to the earth-moon plane. Satisfactory orbits for a relatively close lunar satellite can be obtained with accuracies in the initial conditions approximately equal to those required for lunar impact.
The binary collision in the n-body problem.
Binary collision in n-body problem of celestial mechanics using analytic differential equations
Geodesy and cartography
Geodesy and cartography provide the geometric framework on which most investigations of planets are ultimately based. Specifically, the products of these disciplines provide information on the following: (1) the dimensions of the planet, (2) a mathematical figure of reference for the planet, (3) the orientation of the body in the celestial coordinate system, (4) the rotational constants, (5) a defined system of coordinates, (6) the location of surface points in the defined coordinate system, (7) the gravity potential expressed in spherical harmonics, (8) topographic and thematic maps, and (9) surface albedo in various wavelengths. The relevance of geodesy and cartography to planetology is discussed, and the requirements of data acquisition and mission design are considered.
Space at JPL
Various aspects of space R&D at JPL are reviewed and illustrated with photographs. The career and achievements of interplanetary-spacecraft designer Ronald Draper (beginning with work on Mariner 2 in 1961) are described, with emphasis on the ongoing development of the Galileo Jupiter spacecraft and the proposed Comet Rendezvous Asteroid Flyby spacecraft; the technological challenges posed by the Magellan mission to Venus (scheduled launch in 1989) are examined; and the histories of three mathematical problems with space applications are briefly recalled: the study of conic sections (applicable to orbits and trajectories), the development of formal logic (applicable to expert systems and artificial intelligence), and the restricted three-body problem of celestial mechanics.
Celestial Navigation in Cislunar Space with autoNGC
Celestial navigation (CelNav) is a source of navigation observables where images of known solar system bodies are used to locate a spacecraft, beneficial within the solar system for both cislunar and deep space missions. CelNav provides a variety of design benefits to support and enable current and new autonomous space operations- using only a camera and a processor to produce in-situ measurements for navigation. This technology reduces subscription to ground-based tracking during all phases of a mission, freeing up resources for other operational needs. This also supports secure navigation since it eliminates the need for ground contact. CelNav enables missions where the light time delay between Earth and the spacecraft is too long (or the Earth to spacecraft line of sight is obscured) to support critical operations. It also enables smaller mission classes, where Deep Space Network (DSN)time is cost prohibitive, to reduce its cost by focusing primarily on data downlink. Finally, it enables the NASA Artemis program and other cislunar human space flight by providing redundant navigation to traditional radiometric tracking. In this presentation, we discuss the implementation of a CelNav app in autonomous Navigation, Guidance, and Control (autoNGC), a comprehensive flight software suite for onboard autonomy that is built on the core Flight System (cFS). The presentation also summarizes the results of flight software-in-the-loop (SIL) and processor-in-the-loop (PIL) demonstrations. Both are high-fidelity simulations with the use of a camera emulator hosted on a GPU server that simulates images that would be captured by the camera. The CelNav app leverages the use of cGIANT (cFS Goddard Image Analysis and Navigation Tool).Previously developed for the autoNGC software suite, cGIANT is an onboard autonomous image processing and optical navigation (OpNav) tool that performs limb-based OpNav and Terrain Relative Navigation. The added CelNav capability of cGIANT generates bearing measurements to multiple known celestial bodies (planets, moons, asteroids, comets, etc.) in monocular (2D) images. These observables are then fed to the Goddard Enhanced Onboard Navigation System (GEONS)navigation filter app, enabling us to navigate the spacecraft autonomously. In early 2025, the autoNGC CelNav capability is planned to be flight tested as part of the onboard autonomy experiment on the Cislunar Autonomous Positioning System Technology Operations and Navigation Experiment(CAPSTONE) spacecraft that is currently in a Lunar Near Rectilinear Halo Orbit(NRHO).
Astrometry of Single-Chord Occultations: Application to the 1993 Triton Event
This paper outlines a method for reducing astrometric data to derive the closest approach time and distance to the center of an occultation shadow for a single observer. The method applies to CCD frames, strip scans or photographic plates and uses a set of field stars of unknown positions to define a common coordinate system for all frames. The motion of the occulting body is used to establish the transformation between this common coordinate system and the celestial coordinate system of the body's ephemeris. This method is demonstrated by application to the Tr6O occultation by Triton on 1993 July 10 UT. Over an interval of four nights that included the occultation time, 80 frames of Triton and Tr6O were taken near the meridian with the U.S. Naval Observatory (USNO) 61-inch astrometric reflector. Application of the method presented here to these data yields a closest approach distance of 359 +/- 133 km (corresponding to 0.017 +/- 0.006 arcsec) for the occultation chord obtained with the Kuiper Airborne Observatory (KAO). Comparison of the astrometric closest approach time with the KAO light-curve midtime shows a difference of 2.2 +/- 4.1 s. Relative photometry of Triton and Tr6O, needed for photometric calibration of the occultation light curve, is also presented.
Two-center problem orbits as intermediate orbits for the restricted three-body problem
Two-center problem orbit as intermediate orbit for restricted three-body problem
Outline of a theory of nonperiodic motions in the neighborhood of the long-period librations about the equilateral points of the restricted problem of three bodies
Nonperiodic motions near long-period librations about equilateral points of restricted three-body problem
Elements of a theory of librational motions in the elliptical restricted problem
Librational motion analysis for elliptical restricted three-body problem
Application of Krylov-Bogoliubov method to the solution of the stellar three body problem.
Higher order perturbations of elements in three- body problem determined using methods of Krylov- Bogoliubov and Poincare
Near-encounter geometry generation
Generation of near encounter spacecraft-target planet celestial geometry using two body trajectory computerized simulation
Hardware Demonstration and Improvements of the Stellar Positioning System
As the number of Lunar and Martian surface-exploration missions increases, precise surface navigation is becoming critical. Of most interest is navigation techniques that can generate an absolute state without reliance on Earth-based tracking. One such navigation technique is the Stellar Positioning System. Based on the practice of celestial navigation, this approach combines measurements of the body, star field orientation, and time, to calculate an absolute position on the surface of any planetary body with a known gravity field and known orientation in celestial space. A hardware prototype consisting of an inertial measurement unit, star tracker, and accurate time keeping was developed to demonstrate this concept. The stellar positioning system model was refined to fit this hardware, and was demonstrated by conducting live-sky tests in multiple locations around Marshall Space Flight Center in Huntsville, AL. This effort discusses the preliminary testing results, improvements of the stellar positioning system, feasibility for surface exploration missions, and planned further refinements that will improve the performance.
The dominant features of the long-period librations of the Trojan minor planets
Long-period librations of Trojan planetary orbits in rotating three-body coordinate system
Models of sporadic meteor body distributions
The distribution of orbital elements and flux density over the celestial sphere are the most common forms of representation of the meteor body distribution in the vicinity of the Earth's orbit. The determination of flux density distribution of sporadic meteor bodies was worked out. The method and its results are discussed.
Coordinate systems in lunar ranging
Three distinct coordinate systems are required in the interpretation of the lunar range observations: a celestial frame and two-body-fixed frames. However, there is no coordinate system that is uniquely, or even preferentially, related to the observations themselves. Effectively, one specifies the coordinate systems by the procedures used in data reduction and parameter improvement. Each of the three systems affects the others in some way, and internal inconsistencies are quite possible. The discussion examines some of the more important aspects of this problem.
Spaceflight mechanics 1992; Proceedings of the 2nd AAS/AIAA Meeting, Colorado Springs, CO, Feb. 24-26, 1992. Pts. 1 & 2
The present conference discusses topics in orbit determination, tethered satellite systems, celestial mechanics, guidance optimization, flexible body dynamics and control, attitude dynamics and control, Mars mission analyses, earth-orbiting mission analysis/debris, space probe mission analyses, and orbital computation numerical analyses. Attention is given to electrodynamic forces for control of tethered satellite systems, orbiting debris threats to asteroid flyby missions, launch velocity requirements for interceptors of short range ballistic missiles, transfers between libration-point orbits in the elliptic restricted problem, minimum fuel spacecraft reorientation, orbital guidance for hitting a fixed point at maximum speed, efficient computation of satellite visibility periods, orbit decay and reentry prediction for space debris, and the determination of satellite close approaches.