Thermodynamics and dynamics of pure interfaces

The paper derives, on a coherent postulatory basis, the basic set of equations needed to completely describe the thermodynamics and dynamics of pure interfaces. This set comprises: the equilibrium constitutive equation giving the surface tension as a function of the absolute temperature; the interface balance equations for momentum and internal energy; the non-equilibrium constitutive equations giving the surface transport coefficients (two viscosity coefficients and a thermal conductivity coefficient) as function of the absolute temperature. A discussion of the interface balance equations considered as boundary conditions for the field equations pertaining to the adjoining bulk phases is given and the inadequacies of previous ad hoc formulations pointed out.     

Lorentz-force-perturbed orbits with application to J2-invariant formation

The Lorentz force acting on an electrostatically charged spacecraft in the Earth's magnetic field provides a new propellantless means for controlling a spacecraft's orbit. Assuming that the Lorentz force is much smaller than the gravitational force, the perturbation of a charged spacecraft's orbit by the Lorentz force in the Earth's magnetic field, which is simplified as a titled rotating dipole, is studied in this article. Our research starts with the derivation of the equations of motion in geocentric equatorial inertial Cartesian coordinates using Lagrange mechanics, and then derives the Gauss variational equations involving Lorentz-force perturbation using a set of nodal inertial coordinates as an intermediate step. Subsequently, the approximate averaged changes in classical orbital elements, including single-orbit-averaged and one-day-averaged changes, are obtained by employing orbital averaging. We have found that the approximate analytic one-day-averaged changes in semi-major axis, eccentricity, and inclination are nearly zero, and those in the other three angular orbital elements are affected by J₂ and Lorentz-force perturbations. This characteristic is applied to model bounded relative orbital motion in the presence of the Lorentz force, which is termed Lorentz-augmented J₂-invariant formation. The necessary condition for J₂-invariant formation is derived when the chief spacecraft's reference orbit is either circular or elliptical. It is shown that J₂-invariant formation is easier to implement if the deputy spacecraft is capable of establishing electric charge. All conclusions drawn from the approximate analytic solutions are verified by numerical simulation.     

Mass-, time-, and energy-characteristics of the interstellar flights during the long proper time of astronauts

The existence of extraterrestrial intelligence (ETI) and extraterrestrial scientific-technical civilization (STC) is of principal importance for CETI (communication with extraterrestrial intelligence) and SETI (search for extraterrestrial intelligence). According to Kardashev and Bracewell, the Earth-like STC in their farther development can expand to the nearby planetary systems of the Galaxy, creating galactic community (Bracewell's galactic club).In a previous paper the possibilities of the one-step relativistic rocket interstellar flight during the proper time of life of one-two generations of astronauts were analysed. The realization of such interstellar flights is very improbable, even to the nearest stars. These results could be true for the case of the comparatively short proper time of astronauts, i.e. large acceleration. But flights to the nearest stars could be realized with small and very small accelerations. In the present paper are calculated the proper times t in the reference systems connected with the astronauts (S₂), as well as the times T in the reference systems (S₁)-inertial, velocities v in S₁, mass ratios, powers and energies for various flights, exhaust velocities u and accelerations a. Results are critically discussed.     

Forecasting the velocity of quasi-stationary solar wind and the intensity of geomagnetic disturbances produced by it

A brief review is given of contemporary approaches to solving the problem of medium-term forecast of the velocity of quasi-stationary solar wind (SW) and of the intensity of geomagnetic disturbances caused by it. At the present time, two promising models of calculating the velocity of quasi-stationary SW at the Earth’s orbit are realized. One model is the semi-empirical model of Wang-Sheeley-Arge (WSA) which allows one to calculate the dependence V(t) of SW velocity at the Earth’s orbit using measured values of the photospheric magnetic field. This model is based on calculation of the local divergence f _S of magnetic field lines. The second model is semi-empirical model by Eselevich-Fainshtein-Rudenko (EFR). It is based on calculation in a potential approximation of the area of foot points on the solar surface of open magnetic tubes (sources of fast quasistationary SW). The new Bd-technology is used in these calculations, allowing one to calculate instantaneous distributions of the magnetic field above the entire visible surface of the Sun. Using predicted V(t) profiles, one can in EFR model calculate also the intensity of geomagnetic disturbances caused by quasi-stationary SW. This intensity is expressed through the K _p index. In this paper the EFR model is discussed in detail. Some examples of epignosis and real forecast of V(t) and K _p (t) are discussed. A comparison of the results of applying these two models for the SW velocity forecasting is presented.     

Galactic cosmic rays and parameters of the interplanetary medium near solar activity minima

The time behavior of intensity of cosmic rays with relatively low (~1–6 GeV) and high (>10 GeV) energies are considered together with characteristics influencing the modulation of cosmic rays in the heliosphere. The periods under study are close to solar activity minima in cycles 21/22, 22/23, and 23/24. Diffusion and convection in small-scale magnetic fields of the heliosphere are demonstrated to play some role only at sufficiently weak disturbances of the field (B/δB > 1.3). In this case, a negative correlation is observed between B/δB and a tilt of the surface of the heliospheric current sheet. The analysis of characteristics of the interplanetary medium in periods of solar activity minima shows that the energy anomaly of cosmic rays in the minimum of cycles 23/24 is caused by deficit of high energy particles rather than by an excess of particles of relatively small energies.     

A method of calculation of vertical cutoff rigidity in the geomagnetic field

On the basis of generalization of the results of extensive trajectory calculations for trial charged particles moving in the geomagnetic field the method of calculation of effective vertical cutoff rigidity, taking into account the values of K _p -index and local time, is developed. The IGRF and Tsyganenko-89 models are used for the geomagnetic field. A comparison of the results of model simulations with the experimental data on penetration of charged particles into near-Earth space is made, and penetration functions for typical spacecraft orbits are calculated.     

Manifold dynamics in the Earth–Moon system via isomorphic mapping with application to spacecraft end-of-life strategies

Recently, manifold dynamics has assumed an increasing relevance for analysis and design of low-energy missions, both in the Earth–Moon system and in alternative multibody environments. With regard to lunar missions, exterior and interior transfers, based on the transit through the regions where the collinear libration points L₁ and L₂ are located, have been studied for a long time and some space missions have already taken advantage of the results of these studies. This paper is focused on the definition and use of a special isomorphic mapping for low-energy mission analysis. A convenient set of cylindrical coordinates is employed to describe the spacecraft dynamics (i.e. position and velocity), in the context of the circular restricted three-body problem, used to model the spacecraft motion in the Earth–Moon system. This isomorphic mapping of trajectories allows the identification and intuitive representation of periodic orbits and of the related invariant manifolds, which correspond to tubes that emanate from the curve associated with the periodic orbit. Heteroclinic connections, i.e. the trajectories that belong to both the stable and the unstable manifolds of two distinct periodic orbits, can be easily detected by means of this representation. This paper illustrates the use of isomorphic mapping for finding (a) periodic orbits, (b) heteroclinic connections between trajectories emanating from two Lyapunov orbits, the first at L₁, and the second at L₂, and (c) heteroclinic connections between trajectories emanating from the Lyapunov orbit at L₁ and from a particular unstable lunar orbit. Heteroclinic trajectories are asymptotic trajectories that travels at zero-propellant cost. In practical situations, a modest delta-v budget is required to perform transfers along the manifolds. This circumstance implies the possibility of performing complex missions, by combining different types of trajectory arcs belonging to the manifolds. This work studies also the possible application of manifold dynamics to defining suitable, convenient end-of-life strategies for spacecraft orbiting the Earth. Seven distinct options are identified, and lead to placing the spacecraft into the final disposal orbit, which is either (a) a lunar capture orbit, (b) a lunar impact trajectory, (c) a stable lunar periodic orbit, or (d) an outer orbit, never approaching the Earth or the Moon. Two remarkable properties that relate the velocity variations with the spacecraft energy are employed for the purpose of identifying the optimal locations, magnitudes, and directions of the velocity impulses needed to perform the seven transfer trajectories. The overall performance of each end-of-life strategy is evaluated in terms of time of flight and propellant budget.     

Observation of narrow energy spectrum electron flows on <Emphasis Type="Italic">the INTERBALL Tail Probe</Emphasis> and their possible relation with the spacecraft charging

The paper describes cases of observations of narrow energy spectrum electron flows up to 500 eV on the INTERBALL Tail Probe. About 30 events were registered in 1996 on the night side of the Earth predominantly in 03^h–06^h local time sector. Quasimonochromatic electrons (QME) were registered by all 8 spectrometer channels oriented along the spacecraft meridian with angles of the field of view centers relative to sunward direction from 11° to 169°. Quasimonochromatic electrons were observed simultaneously with large fluxes of high temperature magnetospheric electrons. The dependences of QME energy on both fluxes and energy of high-energy magnetospheric electrons were observed in every event. The ratio of full width at half height (FWHH) to mean energy of QME was ~20%. This electron component with quasimonochromatic energy probably was originated on the spacecraft surface. The registered energy of QME was apparently due to difference of potentials between spacecraft surface from which electron beam originated and the location of electron spectrometer.     

On Saturn’s rotation relative to a center of mass under the action of the gravitational moments of the Sun and Jupiter

Saturn’s rotation relative to a center of mass is considered within an elliptic restricted three-body problem. It is assumed that Saturn is a solid under the action of gravity of the Sun and Jupiter. The motions of Saturn and Jupiter are considered elliptic with small eccentricities e_S and e_J, respectively; the mean motion of Jupiter n_J is also small. We obtain the averaged Hamiltonian function for a small parameter of ε = n_J and integrals of evolution equations. The main effects of the influence of Jupiter on Saturn’s rotation are described: (α) the evolution of the constant parameters of regular precession for the angular momentum vector I₂; (β) the occurrence of new libration zones of oscillations I₂ near the plane of the celestial equator parallel to the plane of the Jupiter’s orbit; (γ) the occurrence of additional unstable equilibria of vector I₂ at the points of the north and south poles of the celestial sphere and, as a result, the existence of homoclinic trajectories; and (δ) the existence of periodic trajectories with arbitrarily large periods near the homoclinic trajectory. It is shown that the effects of (β), (γ), and (δ) are caused by the eccentricity e of the Jupiter’s orbit and are practically independent of Jupiter’s mass (within satellite approximation).     

An inversion approach for lunar regolith layer thickness using optical albedo data and microwave emission simulation

An approach to inversion of the lunar regolith layer thickness by using multi-channel brightness temperature observation in passive microwave remote sensing is developed. To first make simulation of brightness temperature from the lunar layered media, the lunar regolith layer thickness (d) is proposed being constructed by available lunar DEM (digital elevation mapping) and on site measurements. The physical temperature distribution (T) over the lunar surface is also empirically assumed as a monotonic function of the latitude. Optical albedo of the lunar nearside from the telescopic observation is employed to construct the spatial distribution of the FeO+TiO₂ content (S) in the lunar regolith layer. A statistic relationship between the DEM and S of the lunar nearside is further extended to construction of S of the lunar farside. Thus, the dielectric permittivity (ε) of global lunar regolith layer can then be determined. Based on all these conditions (d,T,ε), brightness temperature of the lunar regolith layer in passive microwave remote sensing, which is planned for China's Chang-E lunar project, is numerically simulated by a parallel layering model using the strong fluctuation theory of random media.Then, taking these simulations with random noise as observations, an inversion method of the lunar regolith layer thickness is developed by using three- or two-channels brightness temperatures. When the S is low, and the four channels brightness temperatures in China's Chang-E project are well distinguishable, the regolith layer thickness and physical temperature of the underlying lunar rock media can be inverted by the three-channels approach. When the S becomes high that the brightness temperature at high frequency channels such as 19.35, 37 GHz are saturated, the regolith layer thickness is alternatively inverted only by the two-channels approach.Numerical simulation and inversion approach in this paper make an evaluation of the performance for lunar passive microwave remote sensing, and for future data calibration and validation.     

Estimation of the soil composition by IR observation of the Earth by satellites

A number of missions are in progress for Earth resources satellites to perform soil diagnosis by observing the bare soil thermal response to the heat input from the surrounding atmosphere. Heat capacity missions (and similar missions) are accomplished by measuring the soil temperature at the times of the satellite passes over the soil site.The models which are usually adopted assume that, for atmospheric conditions periodically changing during the day, the surface temperature time dependence is a function of the soil thermal inertia alone (for a dry soil).The present author has shown elsewhere that a more appropriate, two dimensional finite element modelling of the thermal behaviour of the soil, exhibits a dependence of the surface temperature time evolution on both the thermal conductivity (k) and on the volume heat capacity (?c) (for no evaporation at the interface). At least two independent temperature measurements are necessary in order to get information about k and ?c. It is shown that, within the range of values of k and ?c of the usual soils, temperature measurements taken at two successive satellite passes may yield the necessary information on the soil thermophysical properties. Charts can be constructed which will provide information on k and ?c when two soil temperatures are measured at proper times.     

Robust attitude stabilization of spacecraft subject to actuator failures

A robust nonlinear control scheme is developed to stabilize the 3-axis attitude of the spacecraft for cases where there is no control available on either roll or yaw axis. The stability conditions for robustness against unmatched uncertainties and disturbances are derived to establish the regions of asymptotic 3-axis attitude stabilization. The properties of the proposed sliding surface are investigated to obtain the domains of sliding mode for the closed-loop system. Several numerical simulations are presented to demonstrate the efficacy of the proposed controller and validate the theoretical results. The control algorithm is shown to compensate for time-varying external disturbances including solar radiation pressure, aerodynamic forces, and magnetic disturbances; and uncertainties in the spacecraft inertia parameters. The numerical results also establish the robustness of the proposed control scheme to negate disturbances caused by orbit eccentricity.     

Distortions of rectangular pulse with linear frequency modulation during trans-ionospheric sounding of the Martian surface

Specific features of propagation of a wideband rectangular pulse along the route spacecraft-Martian surface-spacecraft caused by the influence of the planetary ionosphere are considered as applied to the problem of radio pulse sounding of the subsurface Martian soil from the Mars-Express satellite. The night Martian ionosphere considerably reduces the energy of the pulse, but does not lead to degradation of its envelope or uncertainty function. When sounding a two-layer surface, the influence of the ionosphere is also manifested in limitation from below of the thickness of the upper layer accessible for measurement, which is more essential than when sounding with the use of a wideband Gaussian pulse. It is demonstrated that the surface sounding is possible through the dayside planet ionosphere at the parameters of operating pulse of the MARSIS radar.     

The heliospheric magnetic field and its relation to the temperature,density, and velocity of solar plasma: Experimental evidence

Using daily and hourly data on solar plasma parameters at the Ulysses spacecraft orbit and at 1 AU it is demonstrated that there is a simple relationship between plasma temperature and density with the heliospheric magnetic field (HMF). A mathematical expression connecting HMF with plasma temperature and density is suggested. Correlation coefficients and regression equations for measured and calculated magnetic fields are presented for the 1990–2009 period according to Ulysses spacecraft data and for 2003–2010 at 1 AU (OMNI database). The roles played by density, temperature, and high-speed solar wind streams in forming the magnetic-field peaks are demonstrated using hourly data of OMNI2 and Ulysses.     

Frequency fluctuations of coherent signals from spacecraft observed during dual-frequency radio sounding of the circumsolar plasma in 2004–2008

We have performed spectral processing of the data of experiments on radio sounding of circumsolar plasma by coherent S- and X-band signals from the spacecraft Ulysses, Mars Express, Rosetta, and Venus Express carried out from 1991 to 2009. The experiments were realized in the mode of coherent response, when a signal stabilized by the hydrogen standard is transmitted from the ground station to a spacecraft, received by the onboard systems, and retransmitted to the Earth with conserved coherence. Thus, the signal sounding the coronal plasma passes twice through the medium: on the propagation path ground station — spacecraft and on the same path in the opposite direction. The spectra of frequency fluctuations in both the bands are obtained and, using them, the radial dependences of fluctuation intensities are found, which can be approximated by a power law. It is shown that the ratio of intensities of frequency fluctuations in the S- and X-bands is comparable with the theoretical value and characterizes the degree of correlation of irregularities of the electron density along the propagation path ground station — spacecraft and back. Analysis of the correlation of frequency fluctuations on the two paths allows one to get a lower estimate of the outer scale of the circumsolar plasma turbulence. For heliocentric distances R = 10 solar radii (R _S ) the outer scale is larger than 0.25R _S .     

Project Icarus: A review of local interstellar medium properties of relevance for space missions to the nearest stars

I review those properties of the interstellar medium within 15 light-years of the Sun, which will be relevant for the planning of future rapid (v≥0.1c) interstellar space missions to the nearest stars. As the detailed properties of the local interstellar medium (LISM) may only become apparent after interstellar probes have been able to make in situ measurements, the first such probes will have to be designed conservatively with respect to what can be learned about the LISM from the immediate environment of the Solar System. It follows that studies of interstellar vehicles should assume the lowest plausible density when considering braking devices, which rely on transferring momentum from the vehicle to the surrounding medium, but the highest plausible densities when considering possible damage caused by the impact of the vehicle with interstellar material. Some suggestions for working values of these parameters are provided. This paper is a submission of the Project Icarus Study Group.     

Equilibrium attitude and stability of a spacecraft on a stationary orbit around an asteroid

The stationary orbits around an asteroid, if exist, can be used for communication and navigation purposes just as around the Earth. The equilibrium attitude and stability of a rigid spacecraft on a stationary orbit around a uniformly-rotating asteroid are studied. The linearized equations of attitude motion are obtained under the small motion assumption. Then, the equilibrium attitude is determined in both cases of a general and a symmetrical spacecraft. Due to the higher-order inertia integrals of the spacecraft, the equilibrium attitude is slightly away from zero Euler angles. Then necessary conditions of stability of this conservative system are analyzed based on the linearized equations of motion. The effects of different parameters, including the harmonic coefficients C₂₀ and C₂₂ of the asteroid and higher-order inertia integrals of the spacecraft, on the stability are assessed and compared. Due to the significantly non-spherical shape and rapid rotation of the asteroid, the effects of the harmonic coefficients C₂₀ and C₂₂ are very significant, while effects of the third- and fourth-order inertia integrals of the spacecraft can be neglected. Considering a spacecraft on a stationary orbit around an example asteroid, we show that the classical stability domain predicted by the Beletskii–DeBra–Delp method on a circular orbit in a central gravity field is modified due to the non-spherical mass distribution of the asteroid. Our results are confirmed by a numerical simulation.     

Short increases of the fluxes of electrons with energies > 0.08 MeV at low-latitude (<Emphasis Type="Italic">L</Emphasis> < 2) regions of near-Earth space

We present the characteristics of short (duration less than 1 min) increases of the counting rate of electrons with energies >0.08 MeV observed in low-latitude (L < 2.0) regions of near-Earth space in the course of the GRIF experiment on the Spektr module of the Mir orbital station. The measurements were carried out using a set of instruments including X-ray and gamma-ray spectrometers, as well as detectors of electrons, protons, and nuclei with large and small geometrical factors, which allowed one to detect the fluxes of charged particles both in the region of the Earth’s radiation belts and in regions close to the geomagnetic equator. As a result of more than 1.5 years of observation, it is demonstrated that short increases in the intensity of electrons of subrelativistic energies are detected not only in the regions of the near-Earth space known as “precipitation zones” (1.7 < L < 2.5), but in high-latitude regions (up to the geomagnetic equator, L < 1.1) as well. Two types of increases of the electron counting rate are found: either fairly regular increases repeating on successive orbits or increases local in time. The latter type of increases can be caused by a short enhancement of electron flux on a given drift shell. The results of our measurements have shown that the duration of the detected increases in intensity can be rather short, as little as 20–30 s. Therefore, in the case of large amplitudes, such increases of the counting rate of electrons can imitate astrophysical events of the type of cosmic gamma-ray bursts in the detectors of hard X-ray and gamma radiation.     

Reconstruction of spacecraft rotational motion using a Kalman filter

Quasi-static microaccelerations of four satellites of the Foton series (nos. 11, 12, M-2, M-3) were monitored as follows. First, according to measurements of onboard sensors obtained in a certain time interval, spacecraft rotational motion was reconstructed in this interval. Then, along the found motion, microacceleration at a given onboard point was calculated according to the known formula as a function of time. The motion was reconstructed by the least squares method using the solutions to the equations of satellite rotational motion. The time intervals in which these equations make reconstruction possible were from one to five orbital revolutions. This length is increased with the modulus of the satellite angular velocity. To get an idea on microaccelerations and satellite motion during an entire flight, the motion was reconstructed in several tens of such intervals. This paper proposes a method for motion reconstruction suitable for an interval of arbitrary length. The method is based on the Kalman filter. We preliminary describe a new version of the method for reconstructing uncontrolled satellite rotational motion from magnetic measurements using the least squares method, which is essentially used to construct the Kalman filter. The results of comparison of both methods are presented using the data obtained on a flight of the Foton M-3.