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Lunar Flight Study Series: Volume 6. A Study of Geometrical and Terminal Characteristics of Earth-Moon Transits Embedded in the Earth-Moon Plane

This report represents the results of a study of coplanar earth-moon transits. The study was initiated to provide information concerning coplanar geometrical characteristics of earth-moon trnasits. The geometrical aspects of transit behavior are related to variations injection conditions. The model of the earth-moon system used in this investigation is the Jacobian model of the restricted three body problem. All transits considered in this study are restricted to the moon-earth plane (MEP).

TRAJECTORY MEASURING SYSTEM

Lunar Flight Study Series: Volume 7. Earth-Moon Transit Studies Based on Ephemeris Data and Using Best Available Computer Program: Principles for Reducing Earth-Moon Trajectory Analysis to Fundamentals - 2

This report presents an empirical investigation of earth-to-moon trajectories. The primary objective is to uncover relationships that result in the reduction of mission analysis or trajectory analysis problems to fundamentals. It is considered imperative that the results be accurate to the extent that any relationships that are uncovered are not brought about by simplifying or unrealistic assumptions. Consequently, the model used is as accurate as is presently available for use and the computations are performed under strict error controls. Procedures are reasonable from the engineering viewpoint. Some very helpful principles are uncovered. These may be briefly stated as follows: 1) Trajectories of constant flight time to the moon (in the 66 hour to 90 hour range), and arriving within a few minutes of the same time pass over a common point on the moon regardless of the arrival altitude and inclination, This common point of passage for such a family of trajectories is arbitrarily referred to as a VERTEX point; 2) These VERTEX points lie within a bounded region on the lunar surface as arrival time varies throughout the years, for a given flight time or flight time spread; 3) Increasing flight time results primarily in a longitude shift of the VERTEX point for a given arrival time; 4) Launch azimuth should be treated as a strong parameter regarding its influence on the vertex. Launch azimuth variations up to +/- 20 degrees about 90 degrees can shift the vertex as much as 3 degrees in latitude even when one is free to pick launch time, coast time, and S-IVB burn time appropriately with launch azimuth; and 5) The locus of periselenum, as arrival inclination takes on all possible values, is nearly circular about the vertex point for a given arrival altitude. A publication is now in preparation that applies these principles to much advantage in the solution of various trajectory analysis problems.

LUNAR FLIGHT

Lunar Flight Study Series: Volume 5. Trajectories in the Earth-Moon Space with Symmetrical Free Return Properties

An extensive investigation has been made of the characteristics of so-called "free return" trajectories. For the purposes of the study., these trajectories are defined as having certain symmetric properties which afford flight to the vicinity of the moon and return to earth without need for propulsion after the initial boost phase. The restricted three-body model for the earth-moon-probe system is used throughout. Two kinds of free return trajectories are shown to -exist and are studied. Of particular interest is the fact that for one kind of free return path, the largest inclination which can be achieved between the flight plane at periselenum and the plane of the moon's orbit about earth is about 10. 8 degrees while for the other kind of path the largest possible inclination is dependent on ·the radius at periselenum. In this case the inclination is limited to about 14 degrees or less for periselenum radius of 1938 km, but may be as great as 90 degrees with periselenum radius of 21150 km. Trajectories are also demonstrated which pass in front of the moon. These exhibit inclination behavior very much like that given by trajectories which go behind the moon. The injection velocity for these trajectories also changes only slightly from the circumlunar trajectories (less than 2 m/s for periselenum radius of 1938 km). However, the position of injection is changed considerably and the flight time may be increased by as much as five times that for circumlunar flight.

RETURN-TO-EARTH PHASE

Lunar Flight Study Series: Volume 8. Earth-Moon Transit Studies Based on Ephemeris Data and Using Best Available Computer Program. Part 3: Analysis of Some Lunar Landing Site Problems Utilizing Two Fundamental Principles

This report presents two fundamental properties of lunar trajectories and makes use of these properties to solve various lunar landing site problems. Not only are various problems treated and solved but the properties and methods are established for use in the solution of other problems. This report presents an analysis of lunar landing site problems utilizing the direct mission mode as well as the orbital mission mode. A particular landing site is then specified and different flight profiles are analyzed for getting an exploration vehicle to that landing site. Rendezvous compatible lunar orbits for various stay-times at the landing site are treated. Launch opportunities are discussed for establishing rendezvous compatible lunar orbits without powered plane changes. Then, the minimum required plane changes for rendezvous in the lunar orbit are discussed for launching from earth on any day. On days that afford rendezvous compatible opportunities, there are no powered plane change requirements in the operations from launch at AMR through the rendezvous in lunar orbit, after the stay at the lunar site.

Tucker, W. B.

Regenerative Environmental Control Systems for Manned-Lunar Spacecraft

The historic earth orbital flight of the Mercury space capsule on February 20, 1962 has illustrated that man has the capability of creating instrumentation and equipment which permit him to survive outside the protective earth atmosphere which, in time, has served both as a shield and a barrier. Because of this great achievement man need no longer restrict himself to earth-space but may direct his resources to expand his zone of operation to earth-moon space. However, in order to exploit this new frontier many problems must be solved which are not mere extensions or extrapolations of those already treated. The problem associated with providing man with an adequate environment for extended periods in the earth's atmosphere, earth-moon space and on the lunar surface is indeed extensive. Trapped radiation, solar flare activity, meteoroid bombardment, solar radiation and the hard vacuum of space are no longer merely phenomena. of scientific interest; they describe the operating environment of manned earth-lunar spacecraft. In order that man may effectively operate in the earth-moon space, myriads of systems and subsystems of varying types and functions must be devised and integrated into an efficient, reliable man-machine complex. This paper will consider only one small aspect of this problem--that is, the problem of providing man with an adequate gaseous and thermal environment in earth-lunar spacecraft. Control of atmospheric gases in manned sealed environments will be treated in Part I. Part II treats thermal regulation and atmosphere control requirements of mobile life support systems for lunar exploration.

Control

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.

Michael, William H., Jr.