The motion of a satellite of the moon
Analytical solution for motion of lunar orbital satellite
LUNAR ORBITER↗
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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Analytical dynamics and optimum transfer
Weierstrass functions and Hamilton-Jacobi equation applied to trajectory optimization and optimum transfer orbits
Novoselov, V. S.↗
Radiation fields of energetic electrons in helical orbits within a magnetoactive plasma
Radiation fields produced by energetic electrons in helical orbit within magnetoactive plasma derived by solving Maxwell equations
Ogawa, T.↗
Use of Green's functions in the numerical solution of two-point boundary value problems Final report, 1 Apr. 1970 - 31 Mar. 1971
Green function in solving linear and nonlinear second order ordinary differential equations including examples in finding rendezvous and periodic orbits of restricted three body system
Gallaher, L. J.↗
On the determination of near body orbits using mass concentration models
Mathematical model for near-body orbit calculation using mass concentration, perturbation theory, nonlinear equations, geopotentials, and least squares method
Childs, B.↗
On the elliptic restricted three-body problem.
This article describes the most important features of the elliptic restricted three-body problem. The methods of numerical integration with recurrent power series are developed for both the equations of motion and the variational equations. The conditions for the existence of periodic orbits and families of periodic orbits are also outlined in detail, and finally illustrated with a family of symmetric periodic orbits.
Broucke, R.↗
The orbital mechanics of flight mechanics
A reference handbook on modern dynamic orbit theory is presented. Starting from the most basic inverse-square law, the law of gravity for a sphere is developed, and the motion of point masses under the influence of a sphere is considered. The reentry theory and the orbital theory are discussed along with the relative motion between two bodies in orbit about the same planet. Relative-motion equations, rectangular coordinates, and the mechanics of simple rigid bodies under the influence of a gravity gradient field are also discussed.
Dunning, R. S.↗
Advanced Earth Observation System Instrumentation Study (aeosis)
Various types of measurements were studied for estimating the orbit and/or attitude of an Earth Observation Satellite. An investigation was made into the use of known ground targets in the earth sensor imagery, in combination with onboard star sightings and/or range and range rate measurements by ground tracking stations or tracking satellites (TDRSS), to estimate satellite attitude, orbital ephemeris, and gyro bias drift. Generalized measurement equations were derived for star measurements with a particular type of star tracker, and for landmark measurements with a multispectral scanner being proposed for an advanced Earth Observation Satellite. The use of infra-red horizon measurements to estimate the attitude and gyro bias drift of a geosynchronous satellite was explored.
White, R.↗
A real-time digital computer program for the simulation of automatic spacecraft reentries
The automatic reentry flight dynamics simulator, a nonlinear, six-degree-of-freedom simulation, digital computer program, has been developed. The program includes a rotating, oblate earth model for accurate navigation calculations and contains adjustable gains on the aerodynamic stability and control parameters. This program uses a real-time simulation system and is designed to examine entries of vehicles which have constant mass properties whose attitudes are controlled by both aerodynamic surfaces and reaction control thrusters, and which have automatic guidance and control systems. The program has been used to study the space shuttle orbiter entry. This report includes descriptions of the equations of motion used, the control and guidance schemes that were implemented, the program flow and operation, and the hardware involved.
Kaylor, J. T.↗
Solar power satellite system definition study. Part 1 and part 2, volume 1: Executive summary
The Solar Power Satellite principle is illustrated and it shows that in a geostationary orbit 36,000 km above the earth's equator, each SPS is in sunlight 99% of the time and in continuous line of sight contact with its ground receiving station. Electrical power produced on the satellite by photovoltaic or heat engine conversion of sunlight is then converted to radio frequency energy at high efficiency, and formed into a focused beam precisely aimed at the SP ground stations. The ground station receiving antenna reconverts the energy into electricity for distribution.
Source record↗
Conical pitch angle distributions of very low-energy ion fluxes observed by ISEE 1
Observations are presented of conical distributions of low-energy ion fluxes from throughout the magnetosphere. The data were provided by the plasma composition experiment (PCE) on ISEE 1. ISEE 1 was launched in October 1977 into a highly elliptical orbit with a 30 deg inclination to the equator and 22.5 earth radii apogee. Particular attention is given to data taken when the instrument was in its thermal plasma mode, sampling ions in the energy per charge range 0-100 eV/e. Attention is given to examples of conical distributions in 0- to 100-eV/e ions, the occurrence of conical distributions of 0- to 100-eV ions in local time-geocentric distance and latitude-geocentric distance coordinates, the cone angles in 0- to 100-eV ion conics, Kp distributions of 0- to 100-eV ion conics, and some compositional aspects of 0- to 100-eV ion conics.
Horwitz, J. L.↗
Observations of E and F region Mg(+) from Spacelab 1
Images of airglow at 2800 A were taken on the Spacelab 1 Shuttle mission and have been interpreted to be solar resonant emission of magnesium ions. On two orbital passes, observations were made near the magnetic equator while observing in the 2800-A channel. The observations were made near the sunset terminator (approximately 1800 LT), in winter (1983, day 335). Three separate emission clouds were observed, all of which extended well into the F region. The location of the clouds in horizontal space is shown. The processed images have been pseudocolored to highlight the intensity distribution in the clouds. Observations included clouds with apparent magnetic-field aligned striations. Bright emissions were observed at the magnetic equator, at 12-deg north magnetic latitude, and at 12-deg south magnentic latitude. Cloud-center brightnesses varied between 680 rayleighs and 1700 rayleighs.
Mende, S. B.↗
Urey Prize Lecture - Chaotic dynamics in the solar system
Attention is given to solar system cases in which chaotic solutions of Newton's equations are important, as in chaotic rotation and orbital evolution. Hyperion is noted to be tumbling chaotically; chaotic orbital evolution is suggested to be of fundamental importance to an accounting for the Kirkwood gaps in asteroid distribution and for the phase space boundary of the chaotic zone at the 3/1 mean-motion commensurability with Jupiter. In addition, chaotic trajectories in the 2/1 chaotic zone reach very high eccentricities by a route that carries them to high inclinations temporarily.
Wisdom, Jack↗
The effects of general relativity on near-earth satellites
Whether one uses a solar system barycentric frame or a geocentric frame when including the general theory of relativity in orbit determination for near-earth satellites, the results should be equivalent to some limiting accuracy. The purpose of this paper is to clarify the effects of relativity in each frame and to demonstrate their equivalence through the analysis of three years of laser tracking data taken on the Lageos satellite. It is demonstrated that the simpler formulation in the geocentric frame is adequate for the purpose of near-earth satellite orbit determination. A correction to the conventional barycentric equations of motion is shown to be required.
Ries, J. C.↗
Finite grid radius and thickness effects on retarding potential analyzer measured suprathermal electron density and temperature
The effect of finite grid radius and thickness on the electron current measured by planar retarding potential analyzers (RPAs) is analyzed numerically. Depending on the plasma environment, the current is significantly reduced below that which is calculated using a theoretical equation derived for an idealized RPA having grids with infinite radius and vanishingly small thickness. A correction factor to the idealized theoretical equation is derived for the Pioneer Venus (PV) orbiter RPA (ORPA) for electron gasses consisting of one or more components obeying Maxwell statistics. The error in density and temperature of Maxwellian electron distributions previously derived from ORPA data using the theoretical expression for the idealized ORPA is evaluated by comparing the densities and temperatures derived from a sample of PV ORPA data using the theoretical expression with and without the correction factor.
Knudsen, William C.↗
Use of non-spherical gravity harmonics for relative motion GN/C (category 2)
Detailed analysis of the Automatic Rendezvous and Capture problem indicate a need for three different regions of mathematical description for the GN&C algorithms: (1) multi-vehicle orbital mechanics to the rendezvous interface point, i.e., within 100 nm; (2) relative motion solutions (such as Clohessy-Wiltshire type) from the far-field to the near-field interface, i.e., within 1 nm and; (3) close proximity motion - the near-field motion where the relative differences in the gravitational and orbit inertial accelerations can be neglected from the equations of motion. Limit boundaries to these regions can be precisely defined by further analysis and will be functions of the tracking measurement accuracies and the computer resources available for the solution of the algorithms. This paper analyzes the relative motion in Regions 2 and 3 above and present the derivation and discussion of the general case of non-spherical gravitational perturbed relative motion. Mathematical deviations from the numerically integrated spherical gravity case and solutions from the Clohessy-Wiltshire equations are presented in the analysis. Based upon this preliminary analysis, it is recommended that further efforts be used to assess the relative position and velocity differences in Region 2 due to non-spherical gravity harmonics and that viable GN&C algorithms be developed to include these gravity perturbations (especially the effects of the first gravity harmonic, J2).
Henderson, David M.↗
Nonlinear vortex trail dynamics. II - Analytic solutions
Spatially periodic large amplitude solutions of the von Karman model are obtained in the neighborhood of singularities. These singularities correspond to vortex clusters in the physical plane. The quasi-periodic and unbounded solutions found analytically confirm earlier numerical work and show qualitative agreement with experimental observations of large-scale phenomena of vortex trails. Separatrices or heteroclinic orbits were explicitly found for an integrable approximate equation, which indicate that the von Karman model itself supports chaotic solutions.
Lim, Chjan C.↗
A new approach to the linear theory of single-species tearing in two-dimensional quasi-neutral sheets
We have developed the linear theory of collisionless ion tearing in a two-dimensional magnetotail equilibrium for a single resonant species. We have solved the normal mode problem for tearing instability by an algorithm that employs particle-in-cell simulation to calculate the orbit integrals in the Maxwell-Vlasov eigenmode equation. The results of our single-species tearing analysis can be applied to ion tearing where electron effects are not included. We have calculated the tearing growth rate as a function of the magnetic field component B(sub n) normal to the current sheet for thick and thin current sheets, and we show that marginal stability occurs when the normal gyrofrequency Omega(sub n) is comparable to the Harris neutral sheet growth rate. A cross-tail B(sub y) component has little effect on the growth rate for B(sub y) approximately = B(sub n). Even in the limit B(sub y) much greater than B(sub n), the mode is strongly stabilized by B(sub n). We report than random pitch angle scattering can overcome the stabilizing effect of B(sub n) and drive the growth rate up toward the Harris neutral sheet (B(sub n) = 0) value when the pitch angle diffusion rate is comparable to Omega(sub n).
Brittnacher, M.↗