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NASA NTRS1978

Forced oscillations in quadratically damped systems

Bayliss (1975) has studied the question whether in the case of linear differential equations the relationship between the stability of the homogeneous equations and the existence of almost periodic solutions to the inhomogeneous equation is preserved by finite difference approximations. In the current investigation analogous properties are considered for the case in which the damping is quadratic rather than linear. The properties of the considered equation for arbitrary forcing terms are examined and the validity is proved of a theorem concerning the characteristics of the unique solution. By using the Lipschitz continuity of the mapping and the contracting mapping principle, almost periodic solutions can be found for perturbations of the considered equation. Attention is also given to the Lipschitz continuity of the solution operator and the results of numerical tests which have been conducted to test the discussed theory.

Bayliss, A.↗

NASA NTRS1989

Optimal feedback control infinite dimensional parabolic evolution systems: Approximation techniques

A general approximation framework is discussed for computation of optimal feedback controls in linear quadratic regular problems for nonautonomous parabolic distributed parameter systems. This is done in the context of a theoretical framework using general evolution systems in infinite dimensional Hilbert spaces. Conditions are discussed for preservation under approximation of stabilizability and detectability hypotheses on the infinite dimensional system. The special case of periodic systems is also treated.

Banks, H. T.↗

NASA NTRS1989

Optimal feedback control of infinite-dimensional parabolic evolution systems - Approximation techniques

Banks, H. T.↗

NASA NTRS1983

Structure and other properties of Jupiter's distant magnetotail

Analyses of data from Voyager 2 experiments provide evidence for, and characteristics of, a Jovian magnetotail extending at least to 9,000 Jovian radii from the planet. During approximately (25 day) periodic sightings of the tail, the magnetic field tended to point radially towards or away from Jupiter, indicating preservation to large distances of the bipolar, lobe like structure observed near the planet. This periodicity, along with various properties of the solar wind at this time, indicates that the tail is apparently influenced by recurrent solar wind features. Anomalous magnetic fields, not aligned with the nominal tail axis, also exist within the tail, especially in the low density, central (core) region, indicating some complexity of internal structure.

Lepping, R. P.↗

NASA NTRS1983

Structure and other properties of Jupiter's distant magnetotail

Lepping, R. P.↗

NASA NTRS1986

Trace elements in Antarctic meteorites: Weathering and genetic information

Antarctic meteorite discoveries have created great scientific interest due to the large number of specimens recovered (approximately 7000) and because included are representatives of hitherto rare or unknown types. Antarctic meteorites are abundant because they have fallen over long periods and were preserved, transported, and concentrated by the ice sheets. The weathering effects on the Antarctic meteorites are described. Weathering effects of trace element contents of H5 chondrites were studied in detail. The results are examined. The properties of Antarctic finds and non-Antarctic falls are discussed.

Lipschutz, M. E.↗

NASA NTRS2007

Iapetus' Geophysics: Rotation Rate, Shape, and Equatorial Ridge

Iapetus has preserved evidence that constrains the modeling of its geophysical history from the time of its accretion until now. The evidence is (a) its present 79.33-day rotation or spin rate, (b) its shape that corresponds to the equilibrium figure for a hydrostatic body rotating with a period of approximately 16 h, and (c) its high, equatorial ridge, which is unique in the Solar System. This paper reports the results of an investigation into the coupling between Iapetus' thermal and orbital evolution for a wide range of conditions including the spatial distributions with time of composition, porosity, short-lived radioactive isotopes (SLRI), and temperature. The thermal model uses conductive heat transfer with temperature-dependent conductivity. Only models with a thick lithosphere and an interior viscosity in the range of about the water ice melting point can explain the observed shape. Short-lived radioactive isotopes provide the heat needed to decrease porosity in Iapetus? early history. This increases thermal conductivity and allows the development of the strong lithosphere that is required to preserve the 16-h rotational shape and the high vertical relief of the topography. Long-lived radioactive isotopes and SLRI raise internal temperatures high enough that significant tidal dissipation can start, and despin Iapetus to synchronous rotation. This occurred several hundred million years after Iapetus formed. The models also constrain the time when Iapetus formed because the successful models are critically dependent upon having just the right amount of heat added by SLRI decay in this early period. The amount of heat available from short-lived radioactivity is not a free parameter but is fixed by the time when Iapetus accreted, by the canonical concentration of Al-26, and, to a lesser extent, by the concentration of Fe-60. The needed amount of heat is available only if Iapetus accreted between 2.5 and 5.0Myr after the formation of the calcium aluminum inclusions as found in meteorites. Models with these features allow us to explain Iapetus? present synchronous rotation, its fossil 16-h shape, and the context within which the equatorial ridge arose.

geophysics↗

NASA NTRSDate not supplied

The Effect of Temperature on the Preservation of Volatile-Rich Lunar Samples

Introduction. The Moon’s south pole is a high-priority target for human exploration and scientific study. This interest is, in part, due to the presence of Permanently Shadowed Regions (PSRs), which could contain high concentrations of unique volatiles at cryogenic temperatures [1]. Returned samples from PSRs may include a unique combination of rocks, regolith, and volatile species, providing unprecedented insights into the history of the Solar System and the potential for resource utilization on the Moon. However, because PSR samples are cryogenic up-on collection, lunar polar sample return will eventually require cold stowage for the journey from the Moon to Earth. Without cold stowage, PSR sample return will likely result in phase changes and chemical reactions within the volatile component of the sample, which would negatively impact the resulting scientific studies of those samples. This abstract summarizes the initial results from an ongoing characterization of analog PSR samples at a range of temperatures, with the goal of defining the temperatures needed for a flight cold stowage freezer. Background. Based on remote sensing observations of the Moon [2], south polar PSRs range in temperature from ~120K for small and/or shallow PSRs to ~20K at the most extreme locations in large, deep PSRs. A range of volatiles have been hypothesized to exist at the surface or subsurface of the lunar poles [3-5 and others]. This hypothesis was verified when the LCROSS mission impacted the <50-K PSR in the crater Cabeus, detecting a range of volatiles from water to low condensation temperature species such as H2S and methane [6]. Species such as H2S and ammonia (also detected by LCROSS) are also highly reactive, and increase the likelihood of chemical reactions at elevated (non-cryogenic) temperatures. At the Johnson Space Center’s Planetary Exploration and Astromaterials Research Laboratory (JSC-PEARL), we have developed a volatile-bearing lunar simulant that incorporates several of the species detected by LCROSS [Table 1] mixed cryogenically with the USGS Lunar Highlands Type (LHT) regolith simulant. The new volatile-regolith simulant will be used to assess the degree of sample alteration at room temperature, -20°C, -80°C, and -196°C (liquid nitro-gen), over a two-week period. Room temperature samples represent those likely to be returned during initial missions without cold stowage, -20°C provides an analog to Apollo cold curated samples, -80°C is the temperature of multiple flight payload freezers (e.g., MELFI), and -196°C is analogous to lunar PSRs. Two weeks is an approximation of the time between sample collection and Earth return for initial Artemis missions. Over this period of time, sample head-space gases will be analyzed using a Universal Gas Analyzer (UGA, a type of mass spectrometer) coupled with a Baratron pressure sensor. After testing, the regolith component of the simulant will be purged of volatiles and preserved for future electron beam and/or FTIR analysis. Experimental Procedure. Volatile-regolith simulants will be produced as an initial homogenous batch; this batch will then be distributed into aliquots (gas chromatography/GC vials or cryo vials), ensuring that each sample has the same starting composition and conditions [Fig. 1]. In addition to the “full” simulant shown in Table 1, less complex simulant compositions will be used as baseline and control samples [Table 2]. Aliquots will be produced in triplicate for each simulant composition, storage temperature, and date of sampling. Headspace gases in all Day 0 samples will be analyzed by the UGA immediately. Cold storage samples for future analytical days will be placed in freezers appropriate to their target temperatures (-20°C, -80°C, -196°C). For ambient-temperature samples, regolith and regolith-water samples will be stored in a fume hood, while the full simulant will be stored in a sealed Parr vessel for safety; no other simulants (RWCM/ RWCM+) will be stored at ambient temperature for this test. Samples will be analyzed by UGA in this manner on each Analysis Day outlined in Table 2. Analytical Data. The UGA measures the partial pressures in a single sample aliquot over a set mass range of 0-105 atomic mass units (AMU) [Figure 2]; this set range was selected to slightly exceed the mass of the highest-mass expected reaction product (H2SO4). The Baratron complements the UGA by measuring the total pressure in the headspace of a sample vial. Coupled together, the quantitative abundances of gases will be monitored throughout the test. UGA analyses of the triplicate samples for each storage temperature, day, and simulant composition will be averaged, and standard deviations for each will be calculated. The compositions of starting species (shown in Table 1) will be characterized as a function of time, and the presence of any new compounds (reaction products) will be monitored as well. Total pressures will be recorded for each sample analysis, and any samples that show signs of leakage (e.g., a significant reduction in pressure or simulant volatiles) will be discarded. Anticipated Results. Testing is planned to begin in January 2022. The resulting data will allow compositional and phase changes in the volatile component of the simulants to be determined. Both the reduction in initial compounds and the addition of reaction products are expected to be observed. In addition, the relative efficacy of the different temperatures at pre-serving the initial composition of the simulants will be quantified. Finally, the regolith component of each sample will be argon-purged and stored in a controlled environment for future laboratory analysis. Compositional and morphological changes in the regolith are expected for samples above 0°C. This test will be repeated three times over the course of 2022. Understanding the effect of temperature on both the volatile and regolith components of analog lunar materials will allow requirements for a cold stowage freezer to be developed. The implementation of cold stowage for lunar polar missions will maximize the preservation of returned samples, enabling ground-breaking lunar and Solar System volatiles science for decades to come.

J L Mitchell↗

NASA NTRS2015

PAHs in the Ices of Saturn's Satellites: Connections to the Solar Nebula and the Interstellar Medium

Aliphatic hydrocarbons and PAHs have been observed in the interstellar medium (e.g., Allamandola et al. 1985, Pendleton et al. 1994, Pendleton & Allamandola 2002, Tielens 2013, Kwok 2008, Chiar & Pendleton 2008) The inventory of organic material in the ISM was likely incorporated into the molecular cloud in which the solar nebula condensed, contributing to the feedstock for the formation of the Sun, major planets, and the smaller icy bodies in the region outside Neptune's orbit (transneptunian objects, or TNOs). Additional organic synthesis occurred in the solar nebula (Ciesla & Sandford 2012). Saturn's satellites Phoebe, Iapetus, and Hyperion open a window to the composition of one class of TNO as revealed by the near-infrared mapping spectrometer (VIMS) on the Cassini spacecraft at Saturn. Phoebe (mean diameter 213 km) is a former TNO now orbiting Saturn (Johnson & Lunine 2005). VIMS spectral maps of Phoebe's surface reveal a complex organic spectral signature consisting of prominent aromatic (CH) and aliphatic hydrocarbon (=CH2, -CH3) absorption bands (3.2-3.6 micrometers). Phoebe is the source of a huge debris ring encircling Saturn, and from which particles ((is) approximately 5-20 micrometers size) spiral inward toward Saturn (Verbiscer et al. 2009). They encounter Iapetus and Hyperion where they mix with and blanket the native H2O ice of those two bodies. Quantitative analysis of the hydrocarbon bands on Iapetus demonstrates that aromatic CH is approximately 10 times as abundant as aliphatic CH2+CH3, significantly exceeding the strength of the aromatic signature in interplanetary dust particles, comet particles, and in carbonaceous meteorites (Cruikshank et al. 2014). A similar excess of aromatics over aliphatics is seen in the qualitative analysis of Hyperion and Phoebe itself (Dalle Ore et al. 2012). The Iapetus aliphatic hydrocarbons show CH2/CH3 (is) approximately 4, which is larger than the value found in the diffuse ISM ((is) approximately 2-2.5). Insofar as Phoebe is a primitive body that formed in the outer regions of the solar nebula and has preserved some of the original nebula inventory, it can be key in understanding the content and degree of processing of that nebular material. A dynamical subset of TNOs define the Kuiper Belt, from which the short-period comets originate. Particles collected from comet 81P/Wild contain PAHs with an interstellar signature of deuterium. By inference, the PAHs contained in Phoebe and now dusted on the surfaces of two other Saturn satellites share that interstellar origin. There are other Phoebe-like TNOs that are presently beyond our ability to study in the organic spectral region, but JWST will open that possibility for a number of objects.

Solar nebula↗

NASA NTRS1988

Nitrogen geochemistry of a Cretaceous-Tertiary boundary site in New Zealand

Nitrogen in the basal layer of the K-T boundary clay at Woodside Creek, New Zealand, has an abundance of 1100 ppm, a 20-fold enrichment over Cretaceous and Tertiary values. The enrichment parallels that for Ir and elemental carbon (soot); all decrease over the next 6 mm of the boundary clay. The C/N ratio, assuming the nitrogen to be associated with organic rather than elemental carbon, is approximately 5 for the basal layer compared to 20 to 30 for the remainder of the boundary clay. The correlation between N and Ir abundances appears to persist above the boundary, implying that the N is intimately associated with the primary fallout and remained with it during the secondary redeposition processes that kept the Ir abundance relatively high into the lowermost Tertiary. Apparently the basal layer of the boundary clay represents the accumulation of a substantial quantity of N with an isotopic composition approximately 10 percent heavier than background delta value of N-15 values. If the boundary clay represents an altered impact glass from a meteorite impact than it probably denotes a time period of less than 1 year. Therefore, the changes in nitrogen geochemistry apparently occurred over a very short period of time. The high abundance of N and the correspondingly low C/N ratio may reflect enhanced preservation of organic material as a result of the rapid sweepout and burial of plankton by impact ejecta, with little or no bacterial degradation. It is conceivable that the shift in delta value of N-15 may represent an influx of nitrogen from a different source deposited contemporaneously with the impact ejecta. An interesting possibility is that it may be derived from nitrate, produced from the combustion of atmospheric nitrogen.

Gilmour, Iain↗

NASA NTRS1995

Global Stratigraphy of Venus: Analysis of a Random Sample of Thirty-Six Test Areas

The age relations between 36 impact craters with dark paraboloids and other geologic units and structures at these localities have been studied through photogeologic analysis of Magellan SAR images of the surface of Venus. Geologic settings in all 36 sites, about 1000 x 1000 km each, could be characterized using only 10 different terrain units and six types of structures. These units and structures form a major stratigraphic and geologic sequence (from oldest to youngest): (1) tessera terrain; (2) densely fractured terrains associated with coronae and in the form of remnants among plains; (3) fractured and ridged plains and ridge belts; (4) plains with wrinkle ridges; (5) ridges associated with coronae annulae and ridges of arachnoid annulae which are contemporary with wrinkle ridges of the ridged plains; (6) smooth and lobate plains; (7) fractures of coronae annulae, and fractures not related to coronae annulae, which disrupt ridged and smooth plains; (8) rift-associated fractures; and (9) craters with associated dark paraboloids, which represent the youngest 1O% of the Venus impact crater population (Campbell et al.), and are on top of all volcanic and tectonic units except the youngest episodes of rift-associated fracturing and volcanism; surficial streaks and patches are approximately contemporary with dark-paraboloid craters. Mapping of such units and structures in 36 randomly distributed large regions (each approximately 10(exp 6) sq km) shows evidence for a distinctive regional and global stratigraphic and geologic sequence. On the basis of this sequence we have developed a model that illustrates several major themes in the history of Venus. Most of the history of Venus (that of its first 80% or so) is not preserved in the surface geomorphological record. The major deformation associated with tessera formation in the period sometime between 0.5-1.0 b.y. ago (Ivanov and Basilevsky) is the earliest event detected. In the terminal stages of tessera fon-nation, extensive parallel linear graben swarms representing a change in the style of deformation from shortening to extension were formed on the tessera and on some volcanic plains that were emplaced just after, and perhaps also during the latter stages of the major compressional phase of tessera emplacement. Our stratigraphic analyses suggest that following tessera formation, extensive volcanic flooding resurfaced at least 85% of the planet in the form of the presently-ridged and fractured plains. Several lines of evidence favor a high flux in the post-tessera period but we have no independent evidence for the absolute duration of ridged plains emplacement. During this time, the net state of stress in the lithosphere apparently changed from extensional to compressional, first in the form of extensive ridge belt development, followed by the formation of extensive wrinkle ridges on the flow units. Subsequently, there occurred local emplacement of smooth and lobate plains units which are presently essentially undefortned. The major events in the latest 10% of the presently preserved history of Venus (less than 50 m.y. ago) are continued rifting and some associated volcanism, and the redistribution of eolian material largely derived from impact crater deposits.

Basilevsky, Alexander T.↗

NASA NTRS2005

The Effect of Impacts on the Martian Climate

Evidence for the presence of liquid water early in Mars history continues to accumulate. The most recent evidence for liquid water being pervasive early in Mars history is the discoveries of sulfate and gypsum layers by the Mars Exploration Rovers and Mars Express. However, the presence of liquid water at the surface very early in Mars history presents a conundrum. The early sun was most likely approximately 75% fainter than it is today. About 65-70 degrees of greenhouse warming is needed to bring surface temperatures to the melting point of water. To date climate models have not been able to produce a continuously warm and wet early Mars. This may be a good thing as there is morphological and mineralogical evidence that the warm and wet period had to be relatively short and episodic. The rates of erosion appear to correlate with the rate at which Mars was impacted thus an alternate possibility is transient warm and wet conditions initiated by large impacts. It is widely accepted that even relatively small impacts (approximately 10 km) have altered the past climate of Earth to such an extent as to cause mass extinctions. Mars has been impacted with a similar distribution of objects. The impact record at Mars is preserved in the abundance of observable craters on it surface. Impact induced climate change must have occurred on Mars.

Colaprete, A.↗

NASA NTRS2007

Alaska: Glaciers of Kenai Fjords National Park and Katmai National Park and Preserve (Chapter 12)

Much recent research points to the shrinkage of the Earth's small glaciers, however, few studies have been performed to quantify the amount of change over time. We measured glacier-extent changes in two national parks in southeastern Alaska. There are hundreds of glaciers in Kenai Fjords National Park (KEFJ) and Katmai National Park and Preserve (KATM) covering over 2373 sq km of parkland. There are two primary areas of glaciation in KEFJ - the Harding Icefield and the Grewingk-Yalik Glacier Complex, and three primary areas of glaciation in KATM - the Mt. Douglas area, the Kukak Volcano to Mt. Katmai area and the Mt. Martin area. We performed glacier mapping using satellite imagery, from the 1970s, 1980s, and from 2000. Results of the analysis show that there has been a reduction in the amount of glacier ice cover in the two parks over the study period, of approximately 22 sq km of ice, approximately - 1.6% from 1986 to 2000 (for KEFJ), and of approximately 76 sq km of glacier ice, or about -7.7% from 1986187 to 2000 (for KATM). In the future, measurements of surface elevation changes of these ice masses should be acquired; together with our extent-change measurements, the volume change of the ice masses can then be determined to estimate their contribution to sea-level rise. The work is a continuation of work done in KEFJ, but in KATM, our measurements represent the first comprehensive study of the glaciers in this remote, little-studied area.

Giffen, Bruce A.↗

NASA NTRS2012

Variability of Black Carbon Deposition to the East Antarctic Plateau, 1800-2000 AD

Refractory black carbon aerosols (rBC) from biomass burning and fossil fuel combustion are deposited to the Antarctic ice sheet and preserve a history of emissions and long-range transport from low- and mid-latitudes. Antarctic ice core rBC records may thus provide information with respect to past combustion aerosol emissions and atmospheric circulation. Here, we present six East Antarctic ice core records of rBC concentrations and fluxes covering the last two centuries with approximately annual resolution (cal. yr. 1800 to 2000). The ice cores were drilled in disparate regions of the high East Antarctic ice sheet, at different elevations and net snow accumulation rates. Annual rBC concentrations were log-normally distributed and geometric means of annual concentrations ranged from 0.10 to 0.18 m cro-g/kg. Average rBC fluxes were determined over the time periods 1800 to 2000 and 1963 to 2000 and ranged from 3.4 to 15.5 m /a and 3.6 to 21.8 micro-g/sq m/a, respectively. Geometric mean concentrations spanning 1800 to 2000 increased linearly with elevation at a rate of 0.025 micro-g/kg/500 m. Spectral analysis of the records revealed significant decadal-scale variability, which at several sites was comparable to decadal ENSO variability.

Bisiaux, M. M.↗

NASA NTRS1994

Distributed parameter modeling of repeated truss structures

A new approach to find homogeneous models for beam-like repeated flexible structures is proposed which conceptually involves two steps. The first step involves the approximation of 3-D non-homogeneous model by a 1-D periodic beam model. The structure is modeled as a 3-D non-homogeneous continuum. The displacement field is approximated by Taylor series expansion. Then, the cross sectional mass and stiffness matrices are obtained by energy equivalence using their additive properties. Due to the repeated nature of the flexible bodies, the mass, and stiffness matrices are also periodic. This procedure is systematic and requires less dynamics detail. The first step involves the homogenization from a 1-D periodic beam model to a 1-D homogeneous beam model. The periodic beam model is homogenized into an equivalent homogeneous beam model using the additive property of compliance along the generic axis. The major departure from previous approaches in literature is using compliance instead of stiffness in homogenization. An obvious justification is that the stiffness is additive at each cross section but not along the generic axis. The homogenized model preserves many properties of the original periodic model.

Wang, Han-Ching↗

NASA NTRS2010

Infrared Spectroscopy of Parent Volatiles in Comets: Implications for Astrobiology

Current cometary orbits provide information on their recent dynamical history. However, determining a given comet's formation region from its current dynamical state alone is complicated by radial migration in the proto-planetary disk and by dynamical interactions with the growing giant planets. Because comets reside for long periods of time in the outer Solar System, the ices contained in their nuclei (native ices) retain a relatively well-preserved footprint of when and where they formed, and this in turn can provide clues to conditions in the formation epoch. As a comet approaches the Sun, sublimation of its native ices releases parent volatiles into the coma where they can be measured spectroscopically. The past to - 15 years have seen the advent of infrared spectrometers with high sensitivity between about 2.8 and 5.0 micron, enabling a taxonomy among comets based on abundances of parent volatiles (e.g., H2O, CO, CH4, C2H6, HCN, CH30H, H2CO, NH3). Such molecules are of keen interest to Astrobiology, as they include important pre-biotic species that likely were required for the emergence of life on Earth and perhaps elsewhere. Approximately 20 comets have thus far been characterized, beginning with C/1996 82 (Hyakutake) in 1996. Molecular production rates are established through comparison of observed emission line intensities with those predicted by quantum mechanical fluorescence models. Abundances of parent volatiles (relative to H2O) vary among even the relatively small number of comets sampled, with the most volatile species (CO and CH4) displaying the largest variations. Techniques developed for measuring parent volatile abundances in comets will be discussed, as will possible implications for their formation.

DiSanti, Michael A.↗

NASA NTRS1960

Analog Techniques for Measuring the Frequency Response of Linear Physical Systems Excited by Frequency-Sweep Inputs

Data-reduction methods using general-purpose analog computer equipment and compatible testing techniques for determining the frequency response of linear physical systems are examined. The techniques considered may be classed as steady state or transient depending on the method of excitation. The relative merits of periodic, slow sweep, and transient (rapid sweep) forcing functions are discussed and applications are given that relate to dynamic-response tests of aeroelastic systems. Two frequency-sweep-input methods are considered in detail. one case the sweep rate is sufficiently slow that the response is approximately the same as that for steady-state conditions. With this input the frequency response can be evaluated and displayed in real time while the test is in progress. Errors due to treating sweep data as steady state can be eliminated, when desired, by reanalyzing tape-recorded time histories of the input and output as transient rather than as periodic data. In the second method the frequency-response function is deter- mined from the system's transient response to a very rapid sweep input. The purpose of frequency sweep in this case is to provide sufficient harmonic content in the input to overcome noise while keeping the test time as short as possible. tests and limited flight-test data presented herein, it appears that a transient-type rapid-sweep forcing function offers a considerable saving in test time while preserving the accuracy possible with steady-state sinusoidal inputs.

Wilmer H. Reed III↗

NASA NTRS1963

Space Flight Handbooks. Volume 3- Planetary Flight Handbook: Supplementary Trajectory Data: Venus to Earth and Mars to Earth - Part 2

Parts 2 and 3 present tabulations of trajectory data for scheduling flights to and from Venus and Mars during the period 1960-2000. Part 2 contains information for outbound flights to these planets; Part 3 contains information for trajectories returning from the planets to Earth. Each Part contains data for single-plane transfers, as well as for broken-plane transfers which employ a midcourse plane-change to eliminate the high speed "ridges." The mathematical analyses employed for all calculations are described in Part 1 of this handbook. To facilitate the construction of round-trip trajectories, the date at the target planet is held fixed while the trip duration is varied in 10-day increments from zero days to the length of that planet's synodic period with Earth. Dates of arrival at the target planet are presented in the extreme right-hand column of Part 2, and dates of departure from the target planet are presented in the extreme left-hand column of Part 3. Thus, by holding Part 2 directly to the left of Part 3, the analyst may easily and rapidly scan all trip possibilities which involve any desired stopover time at the target planet. Within approximately 200 days of each conjunction or opposition, data are presented in 10-day increments at the target planet. Only those trips are listed for which the hyperbolic excess speeds at either or both ends of the trajectory do not exceed 0.6 EMOS (Earth Mean Orbital Speed). For the remaining mission regions, the requirements are so smoothly varying that a 50-day interval in dates at the target planet may be employed; the 10-day interval in trip times is, however, preserved here. In these regions, only those trips are listed for which either or both speeds do not exceed 0.3 EMOS.

INTERPLANETARY FLIGHT↗