Application of the integral variation method to satellite orbit prediction

The Integral Variation (IV) method is a technique to generate an approximate solution to initial value problems involving systems of first-order ordinary differential equations. The technique makes use of generalized Fourier expansions in terms of shifted orthogonal polynomials. The IV method is briefly described and then applied to the problem of near Earth satellite orbit prediction. In particular, we will solve the Lagrange planetary equations including the first three zonal harmonics and drag. This is a highly nonlinear system of six coupled first-order differential equations. Comparison with direct numerical integration shows that the IV method indeed provides accurate analytical approximations to the orbit prediction problem.Advanced Systems Studies; Bldg. 254EElectro-Optical Systems Laboratory; Bldg. 201.     

Surface features on glass spherules from the Luna 16 sample

Two ellipsoidal spherules approximately 0.5 mm in diameter were studied in detail using a scanning electron microscope. A variety of surface features were observed: vesicles, mounds, dimples, streaks, ridges, grooves, accretion phenomena, and high-speed impact craters. The diameters of 27 glass-lined pits formed by impact on one spherule range from less than 1m to approximately 50m. Intermediate-sized glass-lined pits surrounded by concentric fractures demonstrate the transition between larger craters that have both a pit and a spall zone and generally smaller craters that have only a pit. Assuming all craters showing evidence of impact-related melting or flow are the result of primary impacts, the differential mass spectrum of impacting meteoroids in the range 10^–11 to 10^–10 g is in good agreement with a spectrum based on satellite-borne particle-detecting experiments.     

A Mössbauer study of pseudotachylytes: redox conditions during seismogenic faulting

The redox conditions during frictional melting provide information on the physical and chemical conditions during seismic slip in the crust. Here we examine frictional melts from five localities by analyzing host rocks and corresponding pseudotachylytes using Mössbauer spectroscopy. The faults examined are located at South Mountain, Arizona; Fort Foster, Maine (two localities); Long Ridge fault, North Carolina; and the Homestake shear zone, Colorado. The main iron-bearing phases in the pseudotachylytes are phyllosilicates (biotite, muscovite and clays) and iron oxides (magnetite and hematite) and minor pyrite. The ferrous/ferric ratios of the phyllosilicates in the host rocks are the same as those in the pseudotachylytes, except for the hematite-bearing pseudotachylyte from the Long Ridge fault, which is more oxidized. The magnetites in the host rocks and the corresponding pseudotachylytes have different ferric and ferrous iron distributions, which is attributed to different cation chemistry, rather than redox conditions. With the exception of the South Mountain locality, the ferric/ferrous ratios of the micas are interpreted to record the primary redox state of the pseudotachylyte melt as the calculated oxygen fugacities are consistent with magnetite and hematite equilibria. Pyrite-bearing pseudotachylytes plot ~0–1 log₁₀ units above the fayalite-magnetite-quartz (FMQ) buffer. Magnetite-bearing pseudotachylytes plot ~2–4 log₁₀ units above the FMQ buffer, and hematite-bearing pseudotachylytes plot 3.5 log₁₀ units above the hematite-magnetite (HM) buffer. Hematite-bearing pseudotachylytes, together with previous oxygen isotope data, are inferred to represent melting in the presence of externally derived pressurized water. Other localities are inferred to represent melting under rock-buffered, closed system, conditions. If the localities studied are representative of seismogenic faulting, the calculated oxygen fugacities indicate that, in the system C–O–H–S, H₂O and CO₂ should be the dominant fluid species. This is the first detailed study of the redox state of pseudotachylytes.     

Long-term dynamical evolution of dusty ejecta from Deimos

We re-assess expected properties of the presumed dust belt of Mars formed by impact ejecta from Deimos. Previous studies have shown that dynamics of Deimos particles are dominated by two perturbing forces: radiation pressure (RP) and Mars’ oblateness (J2). At the same time, they have demonstrated that lifetimes of particles, especially of grains about ten of micrometers in size, may reach more than 10⁴ years. On such timescales, the Poynting-Robertson drag (PR) becomes important. Here we provide a study of the dynamics under the combined action of all three perturbing forces. We show that a PR decay of the semimajor axes leads to an adiabatic decrease of amplitudes and periods of oscillations in orbital inclinations predicted in the framework of the underlying RP+J2 problem. Furthermore, we show that smallest of the long-lived Deimos grains (radius≈5- may reach a chaotic regime, resulting in unpredictable and abrupt changes of their dynamics. The particles just above that size (≈10-) should be the most abundant in the Deimos torus. Our dynamical analysis, combined with a more accurate study of the particle lifetimes, provides corrections to earlier predictions about the dimensions and geometry of the Deimos torus. In addition to a population, appreciably inclined and shifted towards the Sun, the torus should contain a more contracted, less asymmetric, and less tilted component between the orbits of Phobos and Deimos.     

Wave Flow Simulations Over Arctic Leads

We investigate the flow over Arctic leads using a mesoscale numerical model, typical of both summer and winter, under idealised conditions. We find that Arctic leads may be the source of standing atmospheric internal gravity waves during both seasons. The summertime wave may be compared with the wave generated by a small ridge, though with the phase reversed. The mechanism for exciting the wave is found to be the internal boundary layer developing due to horizontal variations in surface temperature and roughness length. During the more exploratory wintertime simulations, with substantial temperature difference between the lead and the ice surface, we find that secondary circulations and intermittent wave-breaking may occur. The effects of the lead appear far downstream.     

Amplitude distributions of solar photospheric fluctuations

Amplitude distributions, which are nearly Gaussian, have been calculated for radial velocity, continuum brightness, spectral line equivalent width and spectral line central residual intensity fluctuations measured from high-dispersion high-resolution spectrograms taken at the center of the solar disk. The RMS and skewness S for each distribution have been calculated in a manner which allows testing of the homogeneity of the granulation pattern (i.e. variations in its statistics across the solar disk and with time). Pattern inhomogeneity across the disk is strongly indicated, and further evidence suggesting appreciable pattern persistence over time intervals 15 minutes is presented. The possibilities for investigations of S and its associated bi-spectrum are discussed. The qualitative values of S obtained are shown not to be due to unusually bright, rising granules (though a statistical tendency towards such granules is possible). An attempt to explain S for continuum brightness fluctuations in terms of the nonlinear effects of Planckian emission and opacity fluctuations in a stratified photosphere, leads to contradiction with the measured amplitude distributions, a contradiction which is probably due to an oversimplified treatment of radiative transfer in an inhomogeneous photosphere.     

Moonquakes and lunar tectonism

With the succesful installation of a geophysical station at Hadley Rille, on July 31, 1971, on the Apollo 15 mission, and the continued operation of stations 12 and 14 approximately 1100 km SW, the Apollo program for the first time achieved a network of seismic stations on the lunar surface. A network of at least three stations is essential for the location of natural events on the Moon. Thus, the establishment of this network was one of the most important milestones in the geophysical exploration of the Moon. The major discoveries that have resulted to date from the analysis of seismic data from this network can be summarized as follows:

1. Lunar seismic signals differ greatly from typical terrestrial seismic signals. It now appears that this can be explained almost entirely by the presence of a thin dry, heterogeneous layer which blankets the Moon to a probable depth of few km with a maximum possible depth of about 20 km. Seismic waves are highly scattered in this zone. Seismic wave propagation within the lunar interior, below the scattering zone, is highly efficient. As a result, it is probable that meteoroid impact signals are being received from the entire lunar surface.
2. The Moon possesses a crust and a mantle, at least in the region of the Apollo 12 and 14 stations. The thickness of the crust is between 55 and 70 km and may consist of two layers. The contrast in elastic properties of the rocks which comprise these major structural units is at least as great as that which exists between the crust and mantle of the earth. (See Toks?zet al., p. 490, for further discussion of seismic evidence of a lunar crust.)
3. Natural lunar events detected by the Apollo seismic network are moonquakes and meteoroid impacts. The average rate of release of seismic energy from moonquakes is far below that of the Earth. Although present data do not permit a completely unambiguous interpretation, the best solution obtainable places the most active moonquake focus at a depth of 800 km; slightly deeper than any known earthquake. These moonquakes occur in monthly cycles; triggered by lunar tides. There are at least 10 zones within which the repeating moonquakes originate.
4. In addition to the repeating moonquakes, moonquake ‘swarms’ have been discovered. During periods of swarm activity, events may occur as frequently as one event every two hours over intervals lasting several days. The source of these swarms is unknown at present. The occurrence of moonquake swarms also appears to be related to lunar tides; although, it is too soon to be certain of this point.

These findings have been discussed in eight previous papers (Lathamet al., 1969, 1970, 1971) The instrument has been described by Lathamet al. (1969) and Sutton and Latham (1964). The locations of the seismic stations are shown in Figure 1.     

Persistent halogenated compounds in black guillemots (Cepphus grylle) from Greenland--levels, compound patterns and spatial trends

Twenty-seven black guillemot eggs and 39 livers were analysed for polychlorinated biphenyls (PCBs), chlorinated pesticides including chlordane-related compounds and toxaphene, and polybrominated diphenylethers (PBDEs). The samples were collected at Qeqertarsuaq (Godhavn, West Greenland) and Ittoqqortoormiit (Scoresbysund, East Greenland). The concentrations of halogenated organic compounds in samples from East Greenland were somewhat higher than the corresponding concentrations from West Greenland. Differences in compound patterns were found between West and East Greenland, with higher percentages of the heavier PCB molecules, p,p(')-DDE and alpha-HCH in the samples from Ittoqqortoormiit. Similarly, different levels and different compositions were observed for eggs and livers. The eggs had generally higher concentrations of all compounds as well as higher percentages of CHB-50, CHB-62 and alpha-HCH than liver samples from the same area. Dividing the liver samples into age groups revealed increasing concentrations with age.