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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

When the beachhopper looks at the moon: The moon compass hypothesis

The function of moon position for shoreline orientation by talitrids is investigated. Three major results were found: (1) Observed cases of compensation for changes in the direction of the moon are based on physiological rhythm with a period of about 25 hours which can persist for at least several days under constant conditions. (2) The zeitgeber for physiological rhythm may be either moonlight or some other factor associated with the tides. (3) If talitrids are long removed from environmental entrainment, either artifically or naturally, the internal rhythm no longer exerts an appreciable influence on the angle of lunar orientation; in such cases the system deteriorates into constant angle orientation, with an angle which is determined by the beach orgin, but may be modified by lighting conditions.

Enright, J. T.

The intercrater plains of Mercury and the Moon: Their nature, origin and role in terrestrial planet evolution. Geologic mapping of Mercury and the Moon

The geologic framework of the intercrater plains on Mercury and the Moon as determined through geologic mapping is presented. The strategies used in such mapping are discussed first. Then, because the degree of crater degradation is applied to both mapping and crater statistics, the correlation of degradation classification of lunar and Mercurian craters is thoroughly addressed. Different imaging systems can potentially affect this classification, and are therefore also discussed. The techniques used in mapping Mercury are discussed in Section 2, followed by presentation of the Geologic Map of Mercury in Section 3. Material units, structures, and relevant albedo and color data are discussed therein. Preliminary conclusions regarding plains' origins are given there. The last section presents the mapping analyses of the lunar intercrater plains, including tentative conclusions of their origin.

Leake, M. A.

The intercrater plains of Mercury and the Moon: Their nature, origin and role in terrestrial planet evolution. Remote sensing and physical data and the Moon

Imagery data from Mariner 10 and Lunar Orbiter IV form the major base of observations analyzed. But a variety of other information aids in constraining the composition and structure of the Moon and Mercury, and in particular, provides input to the problem of the nature and origin of their intercrater plains. This information for Mercury is remotely sensed from Earth or from the Mariner 10 spacecraft. Lunar data includes, of course, ground truth information from the Apollo landing sites. Since neither intercrater region was sampled, lunar and Mercurian data are similar in type and limitations. Constraints on surface and interior composition and structure are reviewed.

Leake, M. A.

The intercrater plains of Mercury and the Moon: Their nature, origin and role in terrestrial planet evolution. Discussion of the nature, origin and role of the intercrater plains of Mercury and the Moon

The nature and origin of the intercrater plains of Mercury and the Moon as determined through geologic mapping, crater statistics, and remotely sensed data are summarized. Implications of these results regarding scarp formation, absolute ages, and terrestrial planet surfaces are included. The role of the intercrater plains is defined and future work which might lead to a better understanding of these units and terrestrial planet evolution is outlined.

Leake, M. A.

The intercrater plains of Mercury and the Moon: Their nature, origin and role in terrestrial planet evolution. Thermal histories of Mercury and the Moon

To determine a planet's thermal history, a wide range of data is necessary. These data include remote sensing results, photogeologic evidence, magnetic field and remanent magnetization data, composition and ages of samples, and physical parameters of the planet and its orbit. Few of these data form unambiguous constraints for thermal models of Mercury. Igneous Chronology as the time history of the differentiation and igneous activity, is defined. Igneous Chronology is used here in the sense of the apparent igneous or relative chronology of geologic events, such as plains formation (through whatever mechanism) relative to the crater production and tectonic history (lineament and scarp formation).

Leake, M. A.

The intercrater plains of Mercury and the Moon: Their nature, origin and role in terrestrial planet evolution. Chronology of surface history of the Moon

The sequence of events is described that occurred from the time that the ancient lunar crust solidified (about 4.4. billion years ago) and anorthositic high lands dominated the surface, until the global contraction (cooling) that began around 3.3 billion years ago when late stage basalts were emplaced at basin margins where fractures penetrated to subsurface tensional zones. The lunar intercrater plains may be linked with early KREEP volcanism, the LKFM basalt source region, and the first stages of mare volcanism. Ages of KREEP bracket the possible ages of the pre-Imbrian plains, and overlap the initial stages of mare basalt emplacement. Both plains are extruded under the same tensional tectonic regime.

Leake, M. A.

Accretion process of the moon

Recent geochemical and geophysical data suggest that the initial temperature of the moon was strongly peaked toward the lunar surface. To explain such an initial temperature distribution, a simple model of accretion process of the moon is presented. The model assumes that the moon was formed from the accumulation of the solid particles or gases in the isolated, closed cloud. Two equations are derived to calculate the accretion rate and surface temperature of the accreting moon. Numerical calculations are made for a wide range of the parameters particle concentration and particle velocity in the cloud. A limited set of the parameters gives the initial temperature profiles as required by geochemical and geophysical data. These models of the proto-moon cloud indicate that the lunar outermost shell, about 400 km thick, was partially or completely molten just after the accretion of the moon and that the moon should have been formed in a period shorter than 1000 years. If the moon formed at a position nearer to the earth than its present one, the moon might have been formed in a period of less than one year.

Mizutani, H.

Properties of the solar nebula and the origin of the moon.

The basic geochemical model of the structure of the moon proposed by Anderson, in which the moon is formed by differentiation of the calcium, aluminium, and titanium-rich inclusions in the Allende meteorite, is accepted, and the conditions for formation of this moon within the solar nebula models of Cameron and Pine are discussed. The basic material condenses while iron remains in the gaseous phase, which places the formation of the moon slightly inside the orbit of Mercury. Some condensed metallic iron is likely to enter the moon in this position, and since the moon is assembled at a very high temperature, it is likely to have been fully molten, so that the iron can remove the iridium from the silicate material and carry it down to form a small core. Interactions between the moon and Mercury lead to the present rather eccentric Mercury orbit and to a much more eccentric orbit for the moon, reaching past the orbit of the earth, establishing conditions which are necessary for capture of the moon by the earth.

Cameron, A. G. W.

The moons of Saturn

Knowledge gained of the 17 Saturn moons with observations by the Voyager spacecraft are reviewed. Titan was found to have the only atmosphere, which is opaque and precludes geologic inferences. Synchronous rotation is experienced by the 14 inner moons, with a constant inner face turned toward the planet. Phoebe is too far away from the planet to lose its spin to planetary tidal forces, and has an orbit inclined 150 deg from the equatorial plane, while Iapetus is inclined 14.7 deg in its orbit. The abundance of ice on the moons is accepted as evidence of condensation formation of the moons at very low temperatures. Newly discovered moons of Saturn, including both the shepherd moons, which are suspected to maintain the rings in place, and the moons discovered by earth-based astronomy, are discussed. Finally, photographs of all the moons are examined for definitive details.

Soderblom, L. A.

Accretion process of the moon.

Development of a simple model of the accretion process of the moon to explain its initial temperature distribution. The model assumes that the moon was formed from the accumulation of the solid particles or gases in the isolated, closed cloud. Two equations are derived to calculate the accretion rate and surface temperature of the accreting moon. Numerical calculations are made for a wide range of the particle concentrations and particle velocities in the cloud. A limited set of parameters gives the initial temperature profiles as required by geochemical and geophysical data. These models of the protomoon cloud indicate that the lunar outershell, about 400 km thick, was partially or completely molten just after the accretion of the moon and that the moon should have been formed in a period shorter than 1000 yr. If the moon formed at a position nearer to the earth than its present one, the moon might have been formed in a period of less than one year.

Mizutani, H.

The Motion of a Satellite of the Moon

The motion of a satellite of the Moon depends on the potential field due to the Moon as well as the gravitational effects of the Earth and Sun. If one chooses a frame of reference attached to the Moon, it can be shown that the force field resulting from the Sun can be neglected when compared with the perturbing field of the Moon resulting from its oblateness. The effect of the Earth's field on the satellite is of the some order of magnitude as the Moon's perturbing field and must be included in an analysis of the motion of a satellite of the Moon. We will assume that the distance between Earth and Moon remains constant, and we will consider satellite orbits of small eccentricity. It will be shown that a nearly circular polar orbit will digress less than 1 deg from a polar orbit and that the change in eccentricity is less than a factor of e in one year.

Lass, Harry