PERIODIC LIBRATIONS ABOUT THE TRIANGULAR SOLUTIONS OF THE RESTRICTED EARTH-MOON PROBLEM AND THEIR ORBITAL STABILITIES
Determination of periodic orbits in lunar orbit plane about triangular points in earth-moon system
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Determination of periodic orbits in lunar orbit plane about triangular points in earth-moon system
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Restricted three-body problem for motion analysis of planetoid orbiting around triangular equilibrium point
Digital program containing Eulerian formalism for multiple interconnected rigid members applied to gravity gradient stabilized satellite with flexible booms
Solar system planetary mean motions calculation from characteristic equations roots at equilibrium points of restricted three body problem, using Taylor series solution
Developing general analytical methods for predicting planar and three dimensional attitude motion of gravity gradient spacecraft in elliptical orbit
Observations of signals from the ALSEP transmitters via differential very-long-baseline interferometry (VLBI) are being made to determine the relative selenocentric coordinates of the ALSEPs and the motion of the moon about its center of mass. By VLBI the relative positions of the ALSEPs can be determined with uncertainties less than 5 meters, and the orientation of the moon within 0.5 second of selenocentric arc.
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During the planning stage of the International Sun-Earth Explorer-3 (ISEE-3) mission, a recovery strategy was developed in case the Delta rocket underperformed during the launch phase. If a large underburn had occurred, the ISEE-3 spacecraft would have been allowed to complete one revolution of its highly elliptical earth orbit. The recovery plan called for a maneuver near perigee to increase the energy of the off-nominal orbit; a relatively small second maneuver would then insert the spacecraft into a new transfer trajectory toward the desired halo orbit target, and a third maneuver would place the spacecraft in the halo orbit. Results of the study showed that a large range of underburns could be corrected for a total nominal velocity deviation cost within the ISEE-3 fuel budget.
The flow in the projection of the phase space into the configuration space is presented in the neighborhood of a neutrally (or critically) stable equilibrium point in the restricted problem of three bodies. The projection is a line-element every point of which has zero initial velocity. After the elapse of various times the mapping (the rotations and elongations) of the line-element is described showing chaotic behavior.
By a three-dimensional Lagrangian formulation, an exact set of ten coupled nonlinear second-order differential equations has been derived for a system with an extensible tether connecting two end satellites of distributed mass. The effects of tether mass, small orbital eccentricity, central body oblateness, aerodynamic drag force, and solar radiation pressure are also included in the formulation. By linearizing the exact differential equations, the in-plane (orbital plane) differential equations are found to be decoupled from the out-of-plane ones. The characteristic equation of the in-plane differential equations is derived and some associated stability constraints are shown.
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It is shown that transfer trajectories to the halo orbit exist throughout the year, with a one week closure of the launch window each month because of unfavorable lunar perturbations that cannot be corrected in the case of transfer trajectory insertion errors. The launch window for transfers to large-amplitude Lissajous orbits is virtually the same as that for transfers to the baseline halo orbit. Details of these trajectories are described and questions about groundstation coverage are discussed.
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The Interplanetary Physics Laboratory, WIND, will be placed in a small-amplitude halo orbit in late 1995. A lunar swingby is used to achieve the halo orbit. Using the lunar swingby reduces the fuel required to achieve the desired orbit. The spacecraft's position and velocity with respect to the Moon near the time of swingby are shown to determine the characteristics of the halo orbit. The shape of the halo orbit, its x-, y-, and z-amplitudes, must be designed to meet mission constraints. A convenient set of parameters for displaying the dependence of the halo orbit's shape upon the lunar swingby is formulated. The use of the lunar swingby adds additional constraints to the trajectory in terms of attainable swingby parameters. Strategies for obtaining the desired swingby parameters in view of these mission constraints are discussed. The limits on attainable halo orbit shapes using the lunar swingby technique are discussed in terms of minimum and maximum x-, y-, and z-amplitudes. The relevance of previous work on this topic is discussed.
The development of the LEO (EOS) missions has led the way to new technologies and new science discoveries. However, LEO measurements alone cannot cost effectively produce high time resolution measurements needed to move the science to the next level. Both GEO and the Lagrange points, L1 and L2, provide vantage points that will allow higher time resolution measurements. GEO is currently being exploited by weather satellites, but the sensors currently operating at GEO do not provide the spatial or spectral resolution needed for atmospheric trace gas, ocean or land surface measurements. It is also may be possible to place active sensors in geostationary orbit. It seems clear, that the next era in earth observation and discovery will be opened by sensor systems operating beyond near earth orbit.
Cislunar space is a readily accessible region that may well develop into a prime staging area in the effort to colonize space near the Earth or to colonize the moon. While there have been statements made by various NASA programs regarding placement of resources in orbit about the Earth-Moon Lagrangian locations, there is no survey of the total cost associated with attaining and maintaining these unique orbits in an optimal fashion. Transfer trajectories between these orbits required for assembly, servicing, and positioning of these resources have not been extensively investigated. These orbits are dynamically similar to those used for the Sun-Earth missions, but differences in governing gravitational ratios and perturbation sources result in their having their own unique characteristics.