Stochastic Hill's equations for the study of errant rocket burns in orbit

The problem of errant rocket burns in low Earth orbit is of growing interest, especially in the area of safety analysis of nuclear powered spacecraft. The development of stochastic Hill's equations provides a rigorous mathematical tool for the study of such errant rocket maneuvers. These equations are analyzed within the context of a theory of linear dynamical systems driven by a random white noise. It is established that the trajectories of an errant rocket are realizations of a Gauss-Markov process, whose mean vector is given by the solution of a deterministic rocket problem. The time-dependent covariance matrix of the process is derived in an explicit form.     

Conditions for the Formation and Maintenance of Filaments – (Invited Review)

Observational conditions for the formation and maintenance of filaments are reviewed since 1989 in the light of recent findings on their structure, chirality, inferred magnetic topology, and mass flows. Recent observations confirm the necessary conditions previously cited: (1) their location at a boundary between opposite-polarity magnetic fields (2) a system of overlying coronal loops, (3) a magnetically-defined channel beneath, (4) the convergence of the opposite-polarity network magnetic fields towards their common boundary within the channel and (5) cancellation of magnetic flux at the common polarity boundary. Evidence is put forth for three additional conditions associated with fully developed filaments: (A) field-aligned mass flows parallel with their fine structure (B) a multi-polar background source of small-scale magnetic fields necessary for the formation of the filament barbs and (C) a handedness property known as chirality which requires them to be either of two types, dextral or sinistral. One-to-one relationships have been established between the chirality of filaments and the chirality of their filament channels and overlying coronal arcades. These findings reinforce earlier evidence that every filament magnetic field is separate from the magnetic field of the overlying arcade but both are parts of a larger magnetic field system. The larger system has at least quadrupolar footprints in the photosphere and includes the filament channel and subphotospheric magnetic fields, This ‘systems’ view of filaments and their environment enables new perspectives on why arcades and channels are invariable conditions for their existence. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1005026814076     

In-flight calibration of the HIFI diplexers

HIFI is a heterodyne spectrometer aboard the Herschel Space Observatory, providing high-spectral-resolution capabilities. Of its seven frequency bands, four (bands 3, 4, 6, and 7) employ Martin-Puplett diplexers to combine sky signal and local oscillator at the two linear polarizations H and V, prior to feeding them into the mixers (receivers). The optical path difference in each of these 8 diplexers must be tuned to the observed frequency. The required actuator currents were determined in flight before the start of routine science observations. We here report on regular (roughly quarterly) engineering test observations to validate the repeatability of the HIFI diplexers during the routine phase of Herschel operations. We find the optical path difference to be stable to within 0.4 % of the relevant wavelength, typically at the sub-micron level. We conclude that the repeatability and precision of the diplexer tuning mechanism are so high that science data are in no way negatively affected. With the diplexer calibration established and validated, this line of reasoning can be reversed, and the diplexers can be used as relative spectrometers to measure the local-oscillator frequency, i.e., to check the spectral purity of the local oscillator across the diplexer bands. This was done from before launch out to the last months of cryogenic operations in space.     

The haze and methane distributions on Uranus from HST-STIS spectroscopy

We analyzed a unique, three-dimensional data set of Uranus acquired with the STIS Hubble spectrograph on August 19, 2002. The data covered a full afternoon hemisphere at 0.1 arc-sec spatial resolution between 300 and 1000 nm wavelength at 1 nm resolution. Navigation was accurate to 0.002 arc-sec and 0.02 nm. We tested our calibration with WFPC2 images of Uranus and found good agreement. We constrained the vertical aerosol structure with radiative transfer calculations. The standard types of models for Uranus with condensation cloud layers did not fit our data as well as models with an extended haze layer. The dark albedo of Uranus at near-infrared methane windows could be explained by methane absorption alone using conservatively scattering aerosols. Ultraviolet absorption from small aerosols in the stratosphere was strongest at high southern latitudes. The uppermost troposphere was almost clear, but showed a remarkable narrow spike of opacity centered on the equator to 0.2° accuracy. This feature may have been related to influx from ring material. At lower altitudes, the feature was centered at 1-2° latitude, suggesting an equatorial circulation toward the north. Below the 1.2 bar level, the aerosol opacity increased some 100 fold. A comparison of methane and hydrogen absorptions contradicted the standard interpretation of methane band images, which assumes that the methane mixing ratio is independent of latitude and attributes reflectivity variations to variations in the aerosol opacity. The opposite was true for the main contrast between brighter high latitudes and darker low latitudes, probing the 1-3 bar region. The methane mixing ratio varied between 0.014 and 0.032 from high to low southern latitudes, while the aerosol opacity varied only moderately with latitude, except for an enhancement at −45° latitude and a decrease north of the equator. The latitudinal variation of methane had a similar shape as that of ammonia probed by microwave observations at deeper levels. The variability of methane challenges our understanding of Uranus and requires reconsideration of previous investigations based on a faulty assumption. Below the 2 bar level, the haze was thinning somewhat. Our global radiative transfer models with 1° latitude sampling fit the observed reflectivities to 2% rms. The observed spectra of two discrete clouds could be modeled by using the background model of the appropriate latitude and adding small amounts of additional opacity at levels near 1.2 bar (southern cloud) and levels as high as 0.1 bar (northern cloud). These clouds may have been methane condensation clouds of low optical depth (∼0.2).     

Multiple impacts in the Earth's cratering history

Post-bombardment periods of increased impact flux on Earth are probably due to the decay of captured Apollo object group orbits. The origin of the Messier binary impact structure on the Moon implies the breakup of a single impactor as the origin of a Cretaceous/Tertiary multiple impact.     

Theoretical Signature of Solar Meridional Flow in Global Seismic Data

Approximate expressions are derived for the perturbations in solar p- and f-mode oscillation eigenfunctions, due to large-scale, meridional flows which are symmetric about the equator. The essential signature of the perturbed eigenfunctions in global helioseismic data is derived and the prospects for detecting meridional flow using global seismic techniques are discussed.     

Climate changes detected through the world's longest sea level series

The sea level series of Stockholm in the Baltic Sea, commencing already in 1774, is analysed in various ways together with contemporary climate data, in order to investigate long-term sea level changes and their relations to climate changes.First, a study of the eustatic rise of sea level, based on annual mean sea levels, is peformed, and compared with other sea level and climate studies. It is concluded that the general climatic rise of sea level has increased significantly (99.9%) from about 0.0 mm/year during the end of the Little Ice Age, to about 1.0 mm/year during the past century, characterized by melting of glaciers. Such sea level changes due to northern hemisphere climate variations since 800 A.D. have (hitherto) probably always kept within −1.5 and +1.5 mm/year, with an average fairly close to zero.Second, an investigation of the sea level variability, also based on annual mean sea levels, is performed together with temperature and wind variabilities. It is found that the interannual sea level variability of the Baltic Sea has decreased significantly (98%) from the end of the 1700s to the beginning of the 1900s; after that it has increased significantly (95%) again. Precisely the same is found to apply to winter climate or, more specifically, to the interannual winter temperature variability and the interannual winter wind variability. The common origin of all these long-term changes turn out to be two consecutive winter wind processes over the North and Baltic Seas, especially the Baltic entrance. From the end of the 1700s to the beginning of the 1900s, there has been a rapidly decreasing number of dominating winter winds from northeast, and after that there has been an increasing number of dominating winter winds from southwest. This may indicate corresponding long-term changes in the North Atlantic Oscillation.Third, using monthly mean sea levels together with corresponding wind data, seasonal variations are investigated. The seasonal sea level variation in the Baltic Sea has increased significantly (99%) since the early 1800s, together with a shift of the maximum from late summer to early winter. It is found that the main origin is a secular change of the winter wind conditions over the Baltic entrance, with increasing southwesterly winds in early winter. This might also be related to a long-term change in the North Atlantic Oscillation.     

Magnetic reconnection as the cause of a photospheric canceling feature and mass flows in a filament

Magnetic reconnection in the temperature minimum region of the solar photosphere can account for the canceling magnetic features on the Sun. Litvinenko (1999a) showed that a reconnection model explains the quiet-Sun features with the magnetic flux cancelation rate of order 10¹⁷ Mx hr⁻¹. In this paper the model is applied to cancelation in solar active regions, which is characterized by a much larger rate of cancelation ∖ ge10¹⁹ Mx hr⁻¹. In particular, the evolution of a photospheric canceling feature observed in an active region on July 2, 1994 is studied. The theoretical predictions are demonstrated to be in reasonable agreement with the measured speed of approaching magnetic fragments, the magnetic field in the fragments, and the flux cancelation rate, deduced from the combined Big Bear Hα time-lapse images and videomagnetograms calibrated against the daily NSO/Kitt Peak magnetogram. Of particular interest is the prediction that photospheric reconnection should lead to a significant upward mass flux and the formation of a solar filament. Hα observations indeed showed a filament that had one of its ends spatially superposed with the canceling feature. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1005284116353