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The Compensated Earth Moon Earth experiment is designed to demonstrate the benefit of adaptive optics in transmitting laser pulses to an array of retroreflectors on the surface of the moon, and measuring its return at a receiving station nearby the transmitter.
Adaptive optics techniques can be used to realize a robust low bit-error-rate link by mitigating the atmosphere-induced signal fades in optical communications links between ground-based transmitters and deep-space probes. Phase I of the Compensated Earth-Moon-Earth Retroreflector Laser Link (CEMERLL) experiment demonstrated the first propagation of an atmosphere-compensated laser beam to the lunar retroreflectors. A 1.06-micron Nd:YAG laser beam was propagated through the full aperture of the 1.5-m telescope at the Starfire Optical Range (SOR), Kirtland Air Force Base, New Mexico, to the Apollo 15 retroreflector array at Hadley Rille. Laser guide-star adaptive optics were used to compensate turbulence-induced aberrations across the transmitter's 1.5-m aperture. A 3.5-m telescope, also located at the SOR, was used as a receiver for detecting the return signals. JPL-supplied Chebyshev polynomials of the retroreflector locations were used to develop tracking algorithms for the telescopes. At times we observed in excess of 100 photons returned from a single pulse when the outgoing beam from the 1.5-m telescope was corrected by the adaptive optics system. No returns were detected when the outgoing beam was uncompensated. The experiment was conducted from March through September 1994, during the first or last quarter of the Moon.
Zond-6 circumlunar flight and controlled descent landing in U.S.S.R.
The requisite SNR for optical beacons or uplink command signals sent to deep space probes can be achieved by either developing high repetition rate high peak power lasers and associated high-damage-threshold optical components or by propagating near-diffraction-limited beams to the spacecraft.
Adaptive optics can mitigate the turbulence-induced wavefront distortions that limit the minimum practical beam divergence in a ground-to-space optical link, and enable high intensity laser beam propagation through the atmosphere. The CEMERLL experiment will use laser guide star adaptive optics to transmit a near-diffraction-limited laser beam from the Starfire Optical Range to the Apollo lunar retro-reflectors. The experiment will validate theoretical models that predict the effect of atmospheric turbulence on uncompensated and compensated laser beam propagation, and explore strategies to compensate for atmosphere-induced wavefront tilt not corrected for by laser guide star adaptive optics.
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).
Ephemerides of Earth-Moon barycenter, Venus, Mars, and Mercury considering Earth and Moon as separate bodies
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.
Earth-moon system formation theory, discussing condensation from terrestrial hot extended silicate atmosphere
Earth-moon test range for testing earth environmental characteristics in cislunar space, discussing administrative benefits
Optical location of moon in Earth-Moon system using artificial light reflector, on lunar surface
The Giant Impact Hypothesis was introduced in the mid-1970's after consideration of results from the Apollo Moon missions. This hypothesis best explains the similarity in elemental proportions in lunar and terrestrial rocks, the depletion of lunar volatiles, the lack of lunar iron. and the large angular momentum in the Earth-Moon system. Comparison between the radiometric ages of inclusions in the most primitive meteorites and those of inclusions in the oldest lunar rocks and the differentiation age of Earth suggests that the Earth-Moon system formed about 100 Myr after the oldest meteorites. In addition, the age of the famous Martian meteorite ALH84001 and an early solidification time estimated from the Martian crust, suggest that the inner Solar System was fairly clear of large bodies about 10 Myr after the oldest meteorites formed. Thus, the 'standard model' suggests that for a period of several tens of millions of years the terrestrial planet region had few. if any, lunar-sized bodies and there were five terrestrial planets, Mercury, Venus, the two progenitors of the Earth-Moon system, and Mars. To simulate the dynamics of the Solar System before the hypothesized Moon-forming impact, we are integrating the Solar System with the Earth-Moon system replaced by two bodies in heliocentric orbits between Venus and Mars. The total (orbital) angular momentum of the Earth-Moon progenitors is that of the present Earth-Moon system, and their total mass is that of the Earth-Moon system. We are looking at ranges in mass ratio and initial values for eccentricity, inclination. and semi-major axis. We are using the SYMBA integrator to integrate these systems until a collision occurs or a time of 200 Myr elapses. Results are presented in a companion paper.
The giant impact hypothesis was introduced in the mid-1970s after consideration of results from the Apollo missions. This hypothesis best explains the similarity in elemental proportions in lunar and terrestrial rocks, the depletion of lunar volatiles, the lack of lunar Fe, and the large angular momentum in the Earth-Moon system. Comparison between the radiometric ages of inclusions in the most primitive meteorites and in the oldest lunar rocks and the differentiation age of Earth suggests that the Earth-Moon system formed about100 m.y. after the oldest meteorites. In addition, the age of the famous martian meteorite ALH 84001 and an early Martian solidification time obtained by Lee and Halliday suggest that the inner solar system was fairly clear of large bodies about 10 m.y. after the oldest meteorites formed. Thus, the "standard model" suggests that for several tens of millions of years, the terrestrial planet region had few, if any, lunar-sized bodies, and there were five terrestrial planets: Mercury, Venus, the two progenitors of the Earth-Moon system, and Mars. To simulate the dynamics of the solar system before the hypothesized Moon-forming impact, we are integrating the solar system with the Earth-Moon system replaced by two bodies in heliocentric orbits between Venus and Mars. The total (orbital) angular momentum of the Earth-Moon progenitors is that of the present Earth-Moon system, and their total mass is that of the Earth-Moon System. We are looking at ranges in mass ratio and initial values for eccentricity, inclination, and semimajor axis. We are using the SYMBA integrator to integrate these systems until a collision occurs or a time of 200 m.y. elapses. Results are presented in a companion abstract, (also presented at this meeting).
The dynamical evolution of the Earth-Moon system due to tidal friction is treated here. George H. Darwin used Laplace planes (also called proper planes) in his study of tidal evolution. The Laplace plane approach is adapted here to the formalisms of W.M. Kaula and P. Goldreich. Like Darwin, the approach assumes a three-body problem: Earth, Moon, and Sun, where the Moon and Sun are point-masses. The tidal potential is written in terms of the Laplace plane angles. The resulting secular equations of motion can be easily integrated numerically assuming the Moon is in a circular orbit about the Earth and the Earth is in a circular orbit about the Sun. For Earth-Moon distances greater than ∼10 Earth radii, the Earth's approximate tidal response can be characterized with a single parameter, which is a ratio: a Love number times the sine of a lag angle divided by another such product. For low parameter values it can be shown that Darwin's low-viscosity molten Earth, M. Ross's and G. Schubert's model of an Earth near melting, and Goldreich's equal tidal lag angles must all give similar histories. For higher parameter values, as perhaps has been the case at times with the ocean tides, the Earth's obliquity may have decreased slightly instead of increased once the Moon's orbit evolved further than 50 Earth radii from the Earth, with possible implications for climate. This is contrast to the other tidal friction models mentioned, which have the obliquity always increasing with time. As for the Moon, its orbit is presently tilted to its Laplace plane by 5.2deg. The equations do not allow the Moon to evolve out of its Laplace plane by tidal friction alone, so that if it was originally in its Laplace plane, the tilt arose with the addition of other mechanisms, such as resonance passages.
Within the context of manned spaceflight activities, Earth-Moon libration point orbits could support lunar surface operations and serve as staging areas for future missions to near-Earth asteroids and Mars. This investigation examines preliminary design considerations including Earth-Moon L1/L2 libration point orbit selection, transfers, and stationkeeping costs associated with maintaining a spacecraft in the vicinity of L1 or L2 for a specified duration. Existing tools in multi-body trajectory design, dynamical systems theory, and orbit maintenance are leveraged in this analysis to explore end-to-end concepts for manned missions to Earth-Moon libration points.
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.
This investigation is focused specifically on transfers from Earth-Moon L(sub 1)/L(sub 2) libration point orbits to Mars. Initially, the analysis is based in the circular restricted three-body problem to utilize the framework of the invariant manifolds. Various departure scenarios are compared, including arcs that leverage manifolds associated with the Sun-Earth L(sub 2) orbits as well as non-manifold trajectories. For the manifold options, ballistic transfers from Earth-Moon L(sub 2) libration point orbits to Sun-Earth L(sub 1)/L(sub 2) halo orbits are first computed. This autonomous procedure applies to both departure and arrival between the Earth-Moon and Sun-Earth systems. Departure times in the lunar cycle, amplitudes and types of libration point orbits, manifold selection, and the orientation/location of the surface of section all contribute to produce a variety of options. As the destination planet, the ephemeris position for Mars is employed throughout the analysis. The complete transfer is transitioned to the ephemeris model after the initial design phase. Results for multiple departure/arrival scenarios are compared.
Substantial evidence indicates that the Earth-Moon system formed about 100 m.y. after the oldest meteorites and that the inner solar system had five terrestrial planets for several tens of millions of years before the hypothesized Moon-forming impact. We present and discuss some results from a series of N-body integrations in which the mass ratio of the Earth-Moon progenitors is 8:1 or 1:1. We want to know if it is plausible to have the Earth-Moon progenitors collide between 8 m.y. and 200 m.y. after the other planets had formed and to have the resulting system look "similar" to the solar system. If a collision occurs, the integrations tell us which two bodies collide and the time of the collision. We also determine the angular momentum deficit (AMD) of the resulting terrestrial planets. Additionally, we calculate several parameters of the collision. We use the AMD of the terrestrial planets to compare the resulting system to our own. The AMD or a planet is the difference between its orbital angular momentum and its orbital angular momentum if it were in a circular orbit with zero inclination.