The motion of the Martian satellites

An extensive analysis of the motion of Phobos and Deimos from 1877 to 1973 has been fulfilled. The new values of the parameters of the orbital model first developed by Struve have been determined for both satellites. The new sets of the orbital parameters compete with the solutions of similar accuracy found by Wilkins and Sinclair. A secular acceleration in longitude of Phobos is found to be equal to +(0.107±0.011)×10^?7 deg day^?2. The value of the acceleration is little affected when one or another group of oppositions is omitted. The acceleration of Deimos is determined with great uncertainty: +(0.06±0.34)×10^?9 deg day^?2. Values found for the orbital parameters seem to be in good agreement since the mass, oblateness and coordinates of the pole of Mars inferred from the motion of each satellite have similar values in both cases.     

Analytical direct planetary perturbations on the orbital motion of satellites

An analytical expansion of the disturbing function arising from direct planetary perturbations on the motion of satellites is derived. As a Fourier series, it allows the investigation of the secular effects of these direct perturbations, as well as of every argument present in the perturbation. In particular, we construct an analytical model describing the evection resonance between the longitude of pericenter of the satellite orbit and the longitude of a planet, and study briefly its dynamic. The expansion developed in this paper is valid in the case of planar and circular planetary orbits, but not limited in eccentricity or inclination of the satellite orbit.     

Relative motion of near orbiting satellites

The relative motion of two particles on adjacent orbits about the same primary has been investigated under the condition that both motions have the same period. The geometrical properties of the relative displacement and velocity traces, on representative planes, are studied. A complete state of the motion is given; and, the range and range-rate variations, over one or more orbits, are described.It has been found that cusps appear on some of the traces provided that a proper relationship exists between the eccentricity and inclination. (Here, one particle moves on a circular path while the second moves on an ellipse.) The conditions for which cusps appear are given, and typical traces are shown.     

Influence of the geomagnetic field on the IACT detection technique for possible sites of CTA observatories

We investigate the influence of the geomagnetic field (GF) on the Imaging Air Cherenkov Telescope technique for two northern (Tenerife and San Pedro Martir) and three southern (Salta, Leoncito and Namibia (the H.E.S.S.-site)) site candidates for Cherenkov Telescope Array (CTA) observatories. We use the CORSIKA and sim_telarray programs for Monte Carlo simulations of gamma ray showers, hadronic background and the telescope response. We focus here on gamma ray measurements in the low energy, sub-100 GeV, range. Therefore, we only consider the performance of arrays of several large telescopes. Neglecting the GF effect, we find (in agreement with previous studies) that such arrays have lower energy thresholds, and larger collection areas below 30 GeV, when located at higher altitudes. We point out, however, that in the considered ranges of altitudes and magnetic field intensities, 1800–3600 m a.s.l. and 0–40 μT, respectively, the GF effect has a similar magnitude to this altitude effect. We provide the trigger-level performance parameters of the observatory affected by the GF effect, in particular the collection areas, detection rates and the energy thresholds for all five locations, which information may be useful in the selection of sites for CTA. We also find simple scaling of these parameters with the magnetic field strength, which can be used to assess the magnitude of the GF effect for other sites; in this work we use them to estimate the performance parameters for five sites: South Africa-Beaufort West, USA-Yavapai Ranch, Namibia-Calapanzi, Chile-La Silla and India-Hanle. We roughly investigate the impact of the geophysical conditions on gamma/hadron separation procedures involving image shape and direction cuts. We note that the change of altitude has an opposite effect at the trigger and analysis levels, i.e. gains in triggering efficiency at higher altitudes are partially balanced by losses in the separation efficiency. In turn, a stronger GF spoils both the shape and the direction discrimination of gamma rays, thus its effects at the trigger and analysis levels add up resulting in a significant reduction of the observatory performance. Overall, our results indicate that the local GF strength at a site can be equally important as its altitude for the low-energy performance of CTA.     

Two problems about the motion of low-moon-orbit satellites

A detailed theoretical analysis on the orbital lifetime and frozen orbit of low-moon-orbit satellites (LMOS) is carried out, and their relationships with the orbital inclination, as well as some mutual relationships are presented. Taking account of the main perturbing sources of low-orbit satellites, we carried out numerical simulations under a comprehensive force model, and the results not only confirm the correctness of the theoretical analysis, but also provide some valuable insights on the orbital design of LMOS.     

On the tidal effects in the motion of artificial satellites

The general perturbations in the elliptic and vectorial elements of a satellite as caused by the tidal deformations of the non-spherical Earth are developed into trigonometric series in the standard ecliptical arguments of Hill-Brown lunar theory and in the equatorinal elements ω and Ω of the satellite. The integration of the differential equations for variation of elements of the satellite in this theory is easy because all arguments are linear or nearly linear in time. The trigonometrical expansion permits a judgment about the relative significance of the amplitudes and periods of different tidal ‘waves’ over a long period of time. Graphs are presented of the tidal perturbations in the elliptic elements of the BE-C satellite which illustrate long term periodic behavior. The tidal effects are clearly noticeable in the observations and their comparison with the theory permits improvement of the ‘global’ Love numbers for the Earth.     

Numerical models for the study of motion of lunar satellites

The present study deals with numerical modeling of the elliptic restricted three-body problem as well as of the perturbed elliptic restricted three-body (Earth-Moon-Satellite) problem by a fourth body (Sun). Two numerical algorithms are established and investigated. The first is based on the method of the series solution of the differential equations and the second is based on a 5th-order Runge-Kutta method. The applications concern the solution of the equations and integrals of motion of the circular and elliptical restricted three-body problem as well as the search for periodic orbits of the natural satellites of the Moon in the Earth-Moon system in both cases in which the Moon describes circular or elliptical orbit around the Earth before the perturbations induced by the Sun. After the introduction of the perturbations in the Earth-Moon-Satellite system the motions of the Moon and the Satellite are studied with the same initial conditions which give periodic orbits for the unperturbed elliptic problem.     

The geomagnetic effects on the motion of an electrically charged artificial satellite

The orbital effects of the Lorentz force on the motion of an electrically charged artificial satellite moving in the Earth's magnetic field are determined. The geomagnetic field is considered as a multipole potential field and the satellite electrical charge is supposed to be constant. The relativistic perturbations of the main geomagnetic field are discussed briefly. The results are concentrated on the determination of the secular changes, and numerical values are computed for the case of the LAGEOS satellite. The results are discussed in the context of a possible detection of the Lense-Thirring effect analyzing the orbital perturbations of the LAGEOS and LAGEOS X satellites.     

On a semi-inverse problem in the motion of gyrostat satellites

In this paper we study the equilibrium orientation of a gyrostat satellite in the gravity field of a point mass. Direct problem is to find all possible equilibrium orientation when the relative angular momentum vector is given. Inverse problem is to find this relative angular momentum in order to obtain equilibrium in a given orientation. Semi-inverse problem is solved here when some parameters (but not all) giving orientation of the satellite are chosen arbitrarily, giving for what choices real solutions occur.     

Artificial oscillations of geomagnetic field line

Forced oscillations of a geomagnetic field tube are theoretically studied. The oscillation source is the ionosphere the conductivity of which is modulated artificially. The amplitude-frequency characteristics of the tube are calculated in the Pc3–5 frequency range.     

Interplanetary magnetic field polarity and low-latitude geomagnetic field

The relationship between the low latitude magnetic field and the polarity of the interplanetary magnetic field, inferred by Svalgaard for a period of about 4 solar cycles, is derived and discussed for low and high solar activity conditions. The field reacts differently during the passage of A (away) and C (toward) sectors and, during the passage of sector boundary, the response is substantially different depending upon the nature of the change, i.e.A to C or C to A; a change of sector from A to C is found to be associated with a large depression in the field. It is also observed that the night-time field in low latitudes is best correlated with the AC index and that the correlation, observed throughout the period of 1929–1957, breaks down after 1962. The results computed from Alibag observations are confirmed by an examination of the data from Hermanus and San Juan.     

The galilean satellites and the Jovian magnetic field

Alfvén and Arrhenius have proposed that satellites may form from the condensation of plasma suspended in the dipole magnetic field of a central body. Further, they predict that the condensed material will appear at an orbit distance of two-thirds the distance of the plasma. Recent spacecraft measurements have defined the radial extent of the stable quasi-dipole Jovian magnetic field. In support of the Alfvén and Arrhenius hypothesis, we note that all the Galilean satellites lie within two-thirds of this distance.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May 1978.     

Some particularities in motion of retrograde satellites of Jupiter

Some peculiarities in the motion of retrograde satellites of Jupiter have been investigated. The intermediate orbits were obtained by approximated solution of differential equations before transformation by the Zeipel's method. These orbits are non-keplerian ellipses. For their construction the secular motion of nodes, perijoves, and essential periodic perturbations were taken into account.The eccentricities and inclinations of all the retrograte satellites change in a large range. The motion may happen in a region, which is located very near to the limit cases of our theory. For some satellites the sign of the constant, which characterizes the type of orbit, librating or circular, may change. In some cases the value of this constant may be close to zero. Then the motion of the longitude of perijove will reduce the speed and in some moment the circular orbit may change its direction.     

Night-time geomagnetic variations at low latitudes

Using hourly values of the magnetic elements H, D and Z for 1964, 1965, their variation during night-time hours is examined from both their monthly means and from a previously used harmonic analysis method. The data set used represents quiet magnetic conditions. Consistent changes during the night are often found. Seasonal changes are also examined and it seems necessary to modify the Malin—Isikara hypothesis of a moving ring current by including a seasonal modulation of ring current strength with equinoctial maximum and a local time-varying component or partial ring current. The night-time D component shows considerable asymmetry between North and South hemispheres and this might be due to field-aligned current structure. There is a small amount of evidence for a night-time westward equatorial electrojet enhancement.     

Lines of force of the geomagnetic field in space

The lines of force of the geomagnetic field at various latitudes and longitudes in the northern hemisphere are approximately traced to their intersections with the earth's surface in the southern hemisphere, using an electronic computer and the first nine Gauss coefficients. Those lines leaving the average northern auroral zone are traced to their intersection of the geomagnetic field with the earth's surface. These points of intersection are found to be very nearly at the average southern auroral zone deduced from auroral observations and from magnetic measurements of disturbance. It is concluded, therefore, that the geomagnetic field has stability and a simple character even at distances as great as about 6 earth radii above the earth, measured in the equatorial plane, even during auroral displays. It is also concluded that solar streams at such times do not seriously distort the field lines connecting the auroral zones.     

Nonlinear theory of low frequency geomagnetic pulsations

The nonlinear equations for Alfvén waves in magnetospheric plasma are studied taking the influence of hot particles into account. It is shown that oscillations are localized in regions where the pressure of hot ions has local minima. The theoretical results are applied to the problem of generation of geomagnetic pulsations in the magnetospheric plasma.     

On the vertical electric component of the geomagnetic pulsation field

The existence of a close correlation between the atmospheric electric field and geomagnetic pulsations in the range of Pc 2–4 is demonstrated experimentally and theoretically (from the horizontal propagation of pulsations). The need to take this into account in any geological-geophysical interpretation of experimental data is stressed.