Inverse Polynomial Based Explicit Guidance for Lunar Soft Landing During Powered Braking

In this paper an explicit guidance law for the powered descent phase of the soft lunar landing is presented. The descent trajectory, expressed in polynomial form is fixed based on the boundary conditions imposed by the precise soft landing mission. Adapting an inverse model based approach, the guidance command is computed from the known spacecraft trajectory. The guidance formulation ensures the vertical orientation of the spacecraft during touchdown. Also a closed form relation for the final flight time is proposed. The final time is expressed as a function of initial position and velocity of the spacecraft ( at the start of descent) and also depends on the desired landing site. To ensure the fuel minimum descent the proposed explicit method is extended to optimal guidance formulation. The effectiveness of the proposed guidance laws are demonstrated with simulation results.

Fuel-optimal G-MPSP Guidance for Powered Descent Phase of Soft Lunar Landing

A fuel optimal nonlinear sub-optimal guidance scheme is presented in this paper for soft landing of a lunar craft during the powered descent phase. The recently developed Generalized Model Predictive Static Programming (G-MPSP) is used to compute the required magnitude and angle of the thrust vector. Both terminal position and velocity vector are imposed as hard constraints, which ensures high position accuracy and facilitates initiation of vertical descent at the end of the powered descent phase. A key feature of the G-MPSP algorithm is that it converts the nonlinear dynamic programming problem into a low-dimensional static optimization problem (of the same dimension as the output vector). The control history update is done in closed form after computing a time-varying weighting matrix through a backward integration process. This feature makes the algorithm computationally efficient, which makes it suitable for on-board applications. The effectiveness of the proposed guidance algorithm is demonstrated through promising simulation results.

Optimal Guidance for Accurate Lunar Soft Landing with Minimum Fuel Consumption using Model Predictive Static Programming

In this paper the soft lunar landing with minimum fuel expenditure is formulated as a nonlinear optimal guidance problem. The realization of pinpoint soft landing with terminal velocity and position constraints is achieved using Model Predictive Static Programming (MPSP). The high accuracy of the terminal conditions is ensured as the formulation of the MPSP inherently poses final conditions as a set of hard constraints. The computational efficiency and fast convergence make the MPSP preferable for fixed final time onboard optimal guidance algorithm. It has also been observed that the minimum fuel requirement strongly depends on the choice of the final time (a critical point that is not given due importance in many literature). Hence, to optimally select the final time, a neural network is used to learn the mapping between various initial conditions in the domain of interest and the corresponding optimal flight time. To generate the training data set, the optimal final time is computed offline using a gradient based optimization technique. The effectiveness of the proposed method is demonstrated with rigorous simulation results.

Lunar and seasonal variations in the catches of Macrobrachium fisheries of the Cross River Estuary, SE Nigeria

Monthly catches of the Macrobrachium fisheries were recorded at a commercial shrimp landing site on the coasts of Calabar (Nigeria), from April 1997 to August 1998. Catches fluctuated over an annual cycle, with two peaks occurring from May-July and November-December. These peaks represented periods of major activities, reproduction, recruitment or migration. Also, mean catches decreased in the months of February and August, corresponding to the peak of dry season and the so-called 'August break', respectively. Catches from active gears (seine, push net) varied among the moon phases too, with a main peak during full moon, and the minimum catch was recorded during the first moon quarter. However, the catch from passive gear (trap) depicted an inverse relationship, showing a peak during the first moon quarter. Variation in catches at different months and moon phases were significant at P:0.05. Recognize these variations and trends would help in management decisions such as defining closed seasons without adversely affecting the economy of the fishers

The distribution and ages of regional lithologies in the lunar maria

A research program was designed (1) to map regional lithological units of the lunar surface based on measurements of spatial variations in spectral reflectance, and, (2) to establish the sequence of the formation of such lithological units from measurements of the accumulated affects of impacting bodies.

Spectral reflectance data were obtained by scanning luminance variations over the lunar surface at three wavelengths (0.4µ, 0.52µ, and 0.7µ). These luminance measurements were reduced to normalized spectral reflectance values relative to a standard area in More Serenitotis. The spectral type of each lunar area was identified from the shape of its reflectance spectrum. From these data lithological units or regions of constant color were identified. The maria fall into two major spectral classes: circular moria like More Serenitotis contain S-type or red material and thin, irregular, expansive maria like Mare Tranquillitatis contain T-type or blue material. Four distinct subtypes of S-type reflectances and two of T-type reflectances exist. As these six subtypes occur in a number of lunar regions, it is concluded that they represent specific types of material rather than some homologous set of a few end members.

The relative ages or sequence of formation of these more units were established from measurements of the accumulated impacts which have occurred since more formation. A model was developed which relates the integrated flux of particles which hove impacted a surface to the distribution of craters as functions of size and shape. Erosion of craters is caused chiefly by small bodies which produce negligible individual changes in crater shape. Hence the shape of a crater can be used to estimate the total number of small impacts that have occurred since the crater was formed. Relative ages of a surface can then be obtained from measurements of the slopes of the walls of the oldest craters formed on the surface. The results show that different maria and regions within them were emplaced at different times. An approximate absolute time scale was derived from Apollo 11 crystallization ages under an assumption of a constant rote of impacting for the last 4 x 10^9 yrs. Assuming, constant flux, the period of mare formation lasted from over 4 x 10^9 yrs to about 1.5 x 10^9 yrs ago.

A synthesis of the results of relative age measurements and of spectral reflectance mapping shows that (1) the formation of the lunar maria occurred in three stages; material of only one spectral type was deposited in each stage, (2) two distinct kinds of maria exist, each type distinguished by morphology, structure, gravity anomalies, time of formation, and spectral reflectance type, and (3) individual maria have complicated histories; they contain a variety of lithic units emplaced at different times.

Interpretation of lunar topography : impact cratering and surface roughness

This work seeks to understand past and present surface conditions on the Moon using two different but complementary approaches: topographic analysis using high-resolution elevation data from recent spacecraft missions and forward modeling of the dominant agent of lunar surface modification, impact cratering. The first investigation focuses on global surface roughness of the Moon, using a variety of statistical parameters to explore slopes at different scales and their relation to competing geological processes. We find that highlands topography behaves as a nearly self-similar fractal system on scales of order 100 meters, and there is a distinct change in this behavior above and below approximately 1 km. Chapter 2 focuses this analysis on two localized regions: the lunar south pole, including Shackleton crater, and the large mare-filled basins on the nearside of the Moon. In particular, we find that differential slope, a statistical measure of roughness related to the curvature of a topographic profile, is extremely useful in distinguishing between geologic units. Chapter 3 introduces a numerical model that simulates a cratered terrain by emplacing features of characteristic shape geometrically, allowing for tracking of both the topography and surviving rim fragments over time. The power spectral density of cratered terrains is estimated numerically from model results and benchmarked against a 1-dimensional analytic model. The power spectral slope is observed to vary predictably with the size-frequency distribution of craters, as well as the crater shape. The final chapter employs the rim-tracking feature of the cratered terrain model to analyze the evolving size-frequency distribution of craters under different criteria for identifying "visible" craters from surviving rim fragments. A geometric bias exists that systematically over counts large or small craters, depending on the rim fraction required to count a given feature as either visible or erased.

Depth-sensitive analysis of fluorine on lunar sample surfaces and in carbonaceous chondrites by a nuclear resonant reaction technique

The nuclear resonant reaction ¹⁹F(ρ,αγ)¹⁶O has been used to perform depth-sensitive analyses of fluorine in lunar samples and carbonaceous chondrites. The resonance at 0.83 MeV (center-of-mass) in this reaction is utilized to study fluorine surface films, with particular interest paid to the outer micron of Apollo 15 green glass, Apollo 17 orange glass, and lunar vesicular basalts. These results are distinguished from terrestrial contamination, and are discussed in terms of a volcanic origin for the samples of interest. Measurements of fluorine in carbonaceous chondrites are used to better define the solar system fluorine abundance. A technique for measurement of carbon on solid surfaces with applications to direct quantitative analysis of implanted solar wind carbon in lunar samples is described.

Applications of a nuclear technique for depth-sensitive hydrogen analysis : trapped H in lunar samples and the hydration of terrestrial obsidian

The resonant nuclear reaction ¹⁹F(p,αy)¹⁶O has been used to perform depth-sensitive analyses for both fluorine and hydrogen in solid samples. The resonance at 0.83 MeV (center-of-mass) in this reaction has been applied to the measurement of the distribution of trapped solar protons in lunar samples to depths of ~1/2µm. These results are interpreted in terms of a redistribution of the implanted H which has been influenced by heavy radiation damage in the surface region. Fluorine determinations have been performed in a 1-µm surface layer on lunar and meteoritic samples using the same ¹⁹F(p,αy)¹⁶O resonance. The measurement of H depth distributions has also been used to study the hydration of terrestrial obsidian, a phenomenon of considerable archaeological interest as a means of dating obsidian artifacts. Additional applications of this type of technique are also discussed.

Solubility and Diffusivity of Water in Lunar Basalt, and Chemical Zonation in Olivine-Hosted Melt Inclusions

I report the solubility and diffusivity of water in lunar basalt and an iron-free basaltic analogue at 1 atm and 1350 °C. Such parameters are critical for understanding the degassing histories of lunar pyroclastic glasses. Solubility experiments have been conducted over a range of fO₂ conditions from three log units below to five log units above the iron-wüstite buffer (IW) and over a range of pH₂/pH₂O from 0.03 to 24. Quenched experimental glasses were analyzed by Fourier transform infrared spectroscopy (FTIR) and secondary ionization mass spectrometry (SIMS) and were found to contain up to ~420 ppm water. Results demonstrate that, under the conditions of our experiments: (1) hydroxyl is the only H-bearing species detected by FTIR; (2) the solubility of water is proportional to the square root of pH₂O in the furnace atmosphere and is independent of fO₂ and pH₂/pH₂O; (3) the solubility of water is very similar in both melt compositions; (4) the concentration of H₂ in our iron-free experiments is <3 ppm, even at oxygen fugacities as low as IW-2.3 and pH₂/pH₂O as high as 24; and (5) SIMS analyses of water in iron-rich glasses equilibrated under variable fO₂ conditions can be strongly influenced by matrix effects, even when the concentrations of water in the glasses are low. Our results can be used to constrain the entrapment pressure of the lunar melt inclusions of Hauri et al. (2011).

Diffusion experiments were conducted over a range of fO₂ conditions from IW-2.2 to IW+6.7 and over a range of pH₂/pH₂O from nominally zero to ~10. The water concentrations measured in our quenched experimental glasses by SIMS and FTIR vary from a few ppm to ~430 ppm. Water concentration gradients are well described by models in which the diffusivity of water (D^*_water) is assumed to be constant. The relationship between D^*_water and water concentration is well described by a modified speciation model (Ni et al. 2012) in which both molecular water and hydroxyl are allowed to diffuse. The success of this modified speciation model for describing our results suggests that we have resolved the diffusivity of hydroxyl in basaltic melt for the first time. Best-fit values of D^*_water for our experiments on lunar basalt vary within a factor of ~2 over a range of pH₂/pH₂O from 0.007 to 9.7, a range of fO₂ from IW-2.2 to IW+4.9, and a water concentration range from ~80 ppm to ~280 ppm. The relative insensitivity of our best-fit values of D^*_water to variations in pH₂ suggests that H₂ diffusion was not significant during degassing of the lunar glasses of Saal et al. (2008). D^*_water during dehydration and hydration in H₂/CO₂ gas mixtures are approximately the same, which supports an equilibrium boundary condition for these experiments. However, dehydration experiments into CO₂ and CO/CO₂ gas mixtures leave some scope for the importance of kinetics during dehydration into H-free environments. The value of D^*_water chosen by Saal et al. (2008) for modeling the diffusive degassing of the lunar volcanic glasses is within a factor of three of our measured value in our lunar basaltic melt at 1350 °C.

In Chapter 4 of this thesis, I document significant zonation in major, minor, trace, and volatile elements in naturally glassy olivine-hosted melt inclusions from the Siqueiros Fracture Zone and the Galapagos Islands. Components with a higher concentration in the host olivine than in the melt (MgO, FeO, Cr₂O₃, and MnO) are depleted at the edges of the zoned melt inclusions relative to their centers, whereas except for CaO, H₂O, and F, components with a lower concentration in the host olivine than in the melt (Al₂O₃, SiO₂, Na₂O, K₂O, TiO₂, S, and Cl) are enriched near the melt inclusion edges. This zonation is due to formation of an olivine-depleted boundary layer in the adjacent melt in response to cooling and crystallization of olivine on the walls of the melt inclusions concurrent with diffusive propagation of the boundary layer toward the inclusion center.

Concentration profiles of some components in the melt inclusions exhibit multicomponent diffusion effects such as uphill diffusion (CaO, FeO) or slowing of the diffusion of typically rapidly diffusing components (Na₂O, K₂O) by coupling to slow diffusing components such as SiO₂ and Al₂O₃. Concentrations of H2O and F decrease towards the edges of some of the Siqueiros melt inclusions, suggesting either that these components have been lost from the inclusions into the host olivine late in their cooling histories and/or that these components are exhibiting multicomponent diffusion effects.

A model has been developed of the time-dependent evolution of MgO concentration profiles in melt inclusions due to simultaneous depletion of MgO at the inclusion walls due to olivine growth and diffusion of MgO in the melt inclusions in response to this depletion. Observed concentration profiles were fit to this model to constrain their thermal histories. Cooling rates determined by a single-stage linear cooling model are 150–13,000 °C hr^-1 from the liquidus down to ~1000 °C, consistent with previously determined cooling rates for basaltic glasses; compositional trends with melt inclusion size observed in the Siqueiros melt inclusions are described well by this simple single-stage linear cooling model. Despite the overall success of the modeling of MgO concentration profiles using a single-stage cooling history, MgO concentration profiles in some melt inclusions are better fit by a two-stage cooling history with a slower-cooling first stage followed by a faster-cooling second stage; the inferred total duration of cooling from the liquidus down to ~1000 °C is 40 s to just over one hour.

Based on our observations and models, compositions of zoned melt inclusions (even if measured at the centers of the inclusions) will typically have been diffusively fractionated relative to the initially trapped melt; for such inclusions, the initial composition cannot be simply reconstructed based on olivine-addition calculations, so caution should be exercised in application of such reconstructions to correct for post-entrapment crystallization of olivine on inclusion walls. Off-center analyses of a melt inclusion can also give results significantly fractionated relative to simple olivine crystallization.

All melt inclusions from the Siqueiros and Galapagos sample suites exhibit zoning profiles, and this feature may be nearly universal in glassy, olivine-hosted inclusions. If so, zoning profiles in melt inclusions could be widely useful to constrain late-stage syneruptive processes and as natural diffusion experiments.

Effects of lunar cycle and fishing operations on longline-caught pelagic fish: fishing performance, capture time, and survival of fish

Commercial longline fishing data were analyzed and experiments were conducted with gear equipped with hook timers and timedepth recorders in the Réunion Island fishery (21°5ʹS lat., 53°28ʹE long.) to elucidate direct and indirect effects of the lunar cycle and other operational factors that affect catch rates, catch composition, fish behavior, capture time, and fish survival. Logbook data from 1998 through 2000, comprising 2009 sets, indicated that swordfish (Xiphias gladius) catch-per unit of effort (CPUE) increased during the first and last quarter of the lunar phase, whereas albacore (Thunnus alalunga) CPUE was highest during the full moon. Swordfish were caught rapidly after the longline was set and, like bigeye tuna (Thunnus obesus), they were caught during days characterized by a weak lunar illumination—mainly during low tide. We found a significant but very low influence of chemical lightsticks on CPUE and catch composition. At the time the longline was retrieved, six of the 11 species in the study had >40% survival. Hook timers indicated that only 8.4% of the swordfish were alive after 8 hours of capture, and two shark species (blue shark [Prionace glauca] and oceanic whitetip shark [Carcharhinus longimanus]) showed a greater resilience to capture: 29.3% and 23.5% were alive after 8 hours, respectively. Our results have implications for current fishing practices and we comment on the possibilities of modifying fishing strategies in order to reduce operational costs, bycatch, loss of target fish at sea, and detrimental impacts on the environment.

Seasonal, diel, and lunar spawning periodicities and associated sound production of white seabass (Atractoscion nobilis)

Spawning periodicities of white seabass (Atractoscion nobilis) were evaluated by observing spawning behavior, by collecting eggs, and monitoring recognizable sounds produced during the release of gametes. A total of 297 spawning events were documented from 15 male and 47 female white seabass contained within the seminatural confines of a 526-m3 net pen located in Catalina Harbor, Santa Catalina Island, California. Consistent spawning occurred from March through July 2001−03, and peaked in May at a photoperiod of 14 hours. Most spawning occurred within the 2-hour period following sunset or from 19:00−20:00 hours Pacific Standard Time. White seabass spawned at every phase of the lunar cycle; but an increase in successive spawning events followed the new moon. Most spawning occurred in water temperatures from 15 to 18°C, and there was no apparent correlation with tidal cycles. Seasonal and diel spawning periods were directly correlated with increases in the rate, intensity, and variety of white seabass sounds; this correlation may indicate that sounds function to enhance reproductive success. These findings can be extended to further develop seasonal fishery regulations and to better comprehend the role of sound in the reproduction of sound-producing fishes.

Lunar, diurnal and tidal periodicity in relation to the prawn abundance and migration in the Godavari estuarine systems

Preliminary investigations to study the lunar, diurnal and tidal periodicity in abundance and migrations of prawns were made in the Bairavapalam distributary of the Goutami branch of the Godavari estuary during the period of November 1961 to July 1962. The study was based on observation of the catches of a stake net (bag net) operated near the mouth of the estuary. Records of the catches were maintained tidewise daily. Comparative estimates of abundance were made on the basis of catch per hour's operation. It was generally observed that the catches were higher during the darker half of the month than in the brighter fortnight. The landings during low tides were generally higher than those during high tides and usually heavier catches were made during nocturnal low tides than during the day low tides. A continuous inward and outward (immigration and emigration) movement of prawns of all size groups was observed in the estuary from November to July. In general, more penaeid prawns were found to be immigrating at dawn than at dusk. Similarly, the number of emigrants was also found to be generally higher during the new moon period than during the full moon. Metapenaeus monoceros showed an almost distinct nocturnal periodicity in migration, while no such periodicity was observed, distinctly, in other species. In the case of Penaeus indicus the movement of migrants was prolonged. In M. brevicornis the migrants were scarce till March and thereafter increased numerically. The migrant forms of Metapenaeus dobsoni continued to be abundant till May with peak periods in January and February. The migratory pattern of Metapenaeus affinis was similar to that of Metapenaeus brevicornis, though the migrants of the former species appeared a month earlier than the latter. Intensive studies over extended areas for longer periods are required to understand clearly the migratory pattern of the various species. The phenomenon of immigration of prawns can be clearly understood only by vital staining or tagging studies. Perhaps the emigrants might be returning with the succeeding changing life. To verify this, laboratory experiments, by vital stains, were conducted. The marked specimens, if released during the low tides on a large scale, may be recaptured during the subsequent high tides and the duration also may be calculated. At least some percentage of the emigrants remains in the sea for maturity and breeding.

Observation on the lunar and tidal influence on gill netting in the Bay of Bengal

The effect of lunar and tidal influence on the landing of pelagic fish with drift gill nets has been studied for the first time from Bay of Bengal along the Orissa coast. The catchability of the gear was highest during the first quarter and lowest in the fourth quarter of the moon. The variation in catch rates during the four different quarters was not statistically significant. Contrary to the earlier belief, landing with gill net was not poor during the moonlit nights. The extensive use of bluish grey nylon twine matching with seawater in place of indigenous hemp or cotton twine, has largely eliminated the visibility of gear during the brighter phase of the moon. The rate of exploitation was found to be significantly higher during the nights of neap tide, compared to those of spring tide. A plausible explanation for this phenomenon has been offered.