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Two satellite concepts, Halo and Hummingbird, for a lunar libration point satellite to be used as a tracking and communications link with the far side of the moon were evaluated. Study areas included flight dynamics, communications, attitude control, propulsion, and system integration. Both concepts were proved feasible, but Halo was shown to be the better concept.
Analytical solutions for quasi-periodic orbits about the translunar libration point are obtained by using the method of Lindstedt-Poincare and computerized algebraic manipulations. The solutions include the effects of nonlinearities, lunar orbital eccentricity, and the sun's gravitational field. For a small-amplitude orbit, the orbital path as viewed from the earth traces out a Lissajous figure. This is due to a small difference in the fundamental frequencies of the in-plane and out-of-plane oscillations. However, when the amplitude of the in-plane oscillation is greater than 32,379 km, there is a corresponding value of the out-of-plane amplitude that will produce a path where the fundamental frequencies are equal. This synchronized trajectory describes a 'halo orbit' of the moon.
The equations of the physical libration of the moon are developed using a representation of the earth-moon orbit as a Kepler ellipse referred to the lunar equator and expanding the lunar potential in terms of these Kepler elements. The Improved Lunar Ephemeris is used to calculate solar perturbations, and a linear integration of all effects arising from lunar gravitational harmonics through the fourth degree is performed. Aside from unobservable constant offsets of the principal axes, the main effects of the higher harmonics on longitude are: 10-sec six-yearly (argument omega), 1.2-sec three-yearly, 0.5-sec annual, and 0.1-sec monthly; on pole direction they are on the order of 0.5-sec six-yearly and 1.0-sec monthly. The higher harmonics must hence be taken into account in analyzing ranging data of 10 cm accuracy.
Differential very-long-baseline interferometric observations of signals from Apollo Lunar Surface Experiment Package telemetry transmitters will yield the relative projected positions of the transmitters with uncertainty of only 1-3 m, set mainly by uncertainty of the lunar ephemeris. Noise and systematic instrumental errors which in the past affected similar observations have been reduced to the equivalent of a few centimeters on the lunar surface by the development of a new type of differential receiver. Continued observations should yield a determination of the motion of the moon about its center of mass with uncertainty less than 1 sec of selenocentric arc. Improvements (by other means) in our knowledge of the moon's orbital motion would allow a further order-of-magnitude refinement in the libration and relative position results obtainable by differential VLBI.
Data from 500 observation series, each one representing about five hours' continuous observation of a pair of ALSEPs by differential very long baseline interferometers (VLBI) have been compiled on magnetic tape. The theoretical models used to calculate the rotation of the earth, the orbit of the moon, the libration of the moon, and the basic VLBI observable were improved substantially. Analysis of data from long spans of VLBI observations was begun.
From a comparison of the 2:1 and 3:2 resonances (in the asteroidal belt) two possible explanations to the absence of 3:2 apocentric librators are suggested. The first one is that such 3:2 resonant motion is dynamically unstable. The second interpretation requires the absence of near-circular orbits originally at 4 AU. The latter view, if correct, is inconsistent with cosmogonic models which predict the original orbits of the asteroids to be nearly circular.
Values for the masses, radii, and certain mean orbital elements for most of the planets and many of the satellites of the solar system are presented. These values were used to produce computer-generated tables of libration point parameters.
Photometry of the lunar libration region L4 obtained in double umbra during the lunar orbital flight of Apollo 15 is reported. A four-minute photographic exposure of the region centered at celestial coordinates 23 h 14 m, -1.8 deg was made using a 35-mm camera at f/1.2 in the command module pilot's window. The film had been calibrated to the sun's surface brightness, and scene brightness information was converted to digital form, followed by high-speed digital processing with vignetting removal to obtain absolute photometric values. Results reveal an elliptical brightness region 16 x 12 deg in extent with an absolute brightness of 3.3 x 10 to the -14th sun surface brightness units. The mass of the scattering material responsible for the effect is estimated to be between 6 x 10 to the 18th and 2 x 10 to the 7th g.
The motion of a point particle in the neighborhood of a triangular libration point (L sub 4 or L sub 5) in the linearized, restricted problem of three bodies in the plane is described. The derivation of the equations of motion is standard. From these equations, three invariants of the motion are obtained; the Jacobi integral is expressed linearly in terms of two of these. The trajectories for varied initial conditions are drawn, and a complete geometric description of the particle motion is given in elementary terms. Each trajectory has an exterior boundary curve; its equation is found. An approximation to this boundary curve was known; the two curves are compared graphically. For certain initial conditions, there is an interior region from which the trajectory is excluded; the equation of the boundary of this region is given.
Previously published positions of Dione B are combined with new observations reported in this paper to determine its motion. The data are fit to the analytic solution of Erdi (1978) to derive the parameters of the libratory motion. The satellite oscillates about the leading equilateral libration point (L4) of Dione with a period of 785.0 + or - 0.5 days. The maximum separation in orbital longitude from Dione of 76.7 deg was reached on UT 1980 April 20.3 + or - 1 day; the minimum separation is 46.7 deg.
The global effects on non-linear stability are investigated at and around the triangular libration points. The model of the circular restricted problem of three bodies is used, considering the earth and the moon as the primaries. Areas of the initial conditions in the configuration space leading to stability with zero initial velocity around the equilibrium points are compared to stable areas in the phase space with variable initial velocity and zero initial deviations at the equilibrium points. The behavior of the system concerning errors due to initial conditions in the configuration space is studied for 6 years and the effects of initial velocity errors are considered for 7.73 years.
Because the halo-orbit about the sun-earth L(1) libration point in which the satellite ISEE-3 was maintained for nearly four years is unstable, a loose control scheme about a precomputed nominal path was implemented which required orbit maneuvers approximately every three months. Execution errors were minimized by processing on-board accelerometer telemetry data in real time, and adjusting the maneuvers. Because spacecraft vibrations caused oscillations in the accelerometer data, smoothing techniques were applied to provide accurate estimates of the performance of pulse mode thrusters employed in the spin stabilization of the spacecraft. It has been found that the processed accelerometer data has an average error of only + or - 1.3 per cent.
Second generation stations or Manned Space Habitats (MSHs) are discussed for an Earth-Moon libration point and in lunar orbit. The conceptual design of such a station is outlined. Systems and subsystems described reflect anticipation of moderate technology growth. The evolution of the L1 environments is discussed, several selected subsystems are outlined, and how the L1 MSH will complete some of its activities is described.
Spacecraft in orbit near libration point L1 in the Sun-Earth system are excellent platforms for research concerning solar effects on the terrestrial environment. One spacecraft mission launched in 1978 used an L1 orbit for nearly 4 years, and future L1 orbital missions are also being planned. Orbit determination and station-keeping are, however, required for these orbits. In particular, orbit determination error analysis may be used to compute the state uncertainty after a predetermined tracking period; the predicted state uncertainty levels then will impact the control costs computed in station-keeping simulations. Error sources, such as solar radiation pressure and planetary mass uncertainties, are also incorporated. For future missions, there may be some flexibility in the type and size of the spacecraft's nominal trajectory, but different orbits may produce varying error analysis and station-keeping results. The nominal path, for instance, can be (nearly) periodic or distinctly quasi-periodic. A periodic 'halo' orbit may be constructed to be significantly larger than a quasi-periodic 'Lissajous' path; both may meet mission requirements, but perhaps the required control costs for these orbits are probably different. Also for this spacecraft tracking and control simulation problem, experimental design methods can be used to determine the most significant uncertainties. That is, these methods can determine the error sources in the tracking and control problem that most impact the control cost (output); it also produces an equation that gives the approximate functional relationship between the error inputs and the output.
The sun-earth libration points, L1 and L2, are located 1.5 million kilometers from the earth toward and away from the sun. Halo orbits about these points have significant advantages for space observatories in terms of viewing geometry, thermal and radiation environment, and delta-V expediture.
The 'Swingby' interactive tool for design, analysis, and support of maneuver planning for missions that involve transfers to the moon, the lunar orbits, multiple-gravity assists, and the libration-point orbits, runs on a PC and uses pull-down and pop-up menus to allow users to change physical constants and select perturbations for inclusion. Swingby can also target by ascertain parameters, or allow the computer to generate goals on the basis of mission requirements. Rapid mission analyses, operational maneuvers, and contingency plans are thereby obtainable.
The energetics of Europa are usually considered only in the context of eccentricity driven tides. We note that the existence of differential librations, and of a finite obliquity, both contribute significantly to the energy budget. Additional information is contained in the original extended abstract.
A growing interest in formation flying satellites demands development and analysis of control and estimation algorithms for station-keeping and formation maneuvering. This paper discusses the development of a discrete linear-quadratic-regulator control algorithm for formations in the vicinity of the L2 sun-earth libration point. The development of an appropriate Kalman filter is included as well. Simulations are created for the analysis of the station-keeping and various formation maneuvers of the Stellar Imager mission. The simulations provide tracking error, estimation error, and control effort results. From the control effort, useful design parameters such as delta V and propellant mass are determined. For formation maneuvering, the formation spacecraft track to within 4 meters of their desired position and within 1.5 millimeters per second of their desired zero velocity. The filter, with few exceptions, keeps the estimation errors within their three-sigma values. Without noise, the controller performs extremely well, with the formation spacecraft tracking to within several micrometers. Each spacecraft uses around 1 to 2 grams of propellant per maneuver, depending on the circumstances.