Solution of the flyby problem for large space debris at sun-synchronous orbits

the paper considers the flyby problem related to large space debris (LSD) objects at low earth orbits. The data on the overall dimensions of known last and upper stages of launch vehicles makes it possible to single out five compact groups of such objects from the NORAD catalog in the 500–2000 km altitude interval. The orbits of objects of each group have approximately the same inclinations. The features of the mutual distribution of the orbital planes of LSD objects in the group are shown in a portrait of the evolution of deviations of the right ascension of ascending nodes (RAAN). In the case of the first three groups (inclinations of 71°, 74°, and 81°), the straight lines of relative RAAN deviations of object orbits barely intersect each other. The fourth (83°) and fifth (97°–100°) LSD groups include a considerable number of objects whose orbits are described by straight lines (diagonals), which intersect other lines many times. The use of diagonals makes it possible to significantly reduce the temporal and total characteristic velocity expenditures required for object flybys, but it complicates determination of the flyby sequence. Diagonal solutions can be obtained using elements of graph theory. A solution to the flyby problem is presented for the case of group 5, formed of LSD objects at sun-synchronous orbits.     

Large-scale irregularities of the winter polar topside ionosphere according to data from <Emphasis Type="Italic">Swarm</Emphasis> satellites

An analysis of the electron density measurements (Ne) along the flyby trajectories over the high-latitude region of the Northern Hemisphere under winter conditions in 2014 and 2016 has shown that the main large-scale structure observed by Swarm satellites is the tongue of ionization (TOI). At the maximum of the solar cycle (F_10.7 = 160), the average value of Ne in the TOI region at an altitude of 500 km was 8 × 10⁴ cm^–3. Two years later, at F_10.7 = 100, Ne ~ 5 × 10⁴ cm^–3 and Ne ~2.5 × 10⁴ cm^–3 were observed at altitudes of 470 and 530 km, respectively. During the dominance of the azimuthal component of the interplanetary magnetic field, the TOI has been observed mainly on the dawn or dusk side depending on the sign of B _y . Simultaneous observations of the convective plasma drift velocity in the polar cap show the transpolar flow drift to the dawn (B_y < 0) or dusk side (B _y < 0). Observations and numerical simulation of the Ne distribution have confirmed the significant role of the electric field of the magnetospheric convection in the generation of large-scale irregularities in the polar ionosphere.     

Families of periodic solutions in three-dimensional restricted three-body problem

Planar orbits of three-dimensional restricted circular three-body problem are considered as a special case of three-dimensional orbits, and the second-order monodromy matrices M (in coordinate z and velocity v _z ) are calculated for them. Semi-trace s of matrix M determines vertical stability of an orbit. If |s| ≤ 1, then transformation of the subspace (z, v _z ) in the neighborhood of solution for the period is reduced to deformation and a rotation through angle φ, cosφ = s. If the angle ? can be rationally expressed through 2π,φ = 2π·p/q, where p and q are integer, then a planar orbit generates the families of three-dimensional periodic solutions that have a period larger by a factor of q (second kind Poincareé periodic solutions). Directions of continuation in the subspace (z, v _z ) are determined by matrix M. If |s| < 1, we have two new families, while only one exists at resonances 1: 1 (s = 1) and 2: 1 (s = ?1). In the course of motion along the family of three-dimensional periodic solutions, a transition is possible from one family of planar solutions to another one, sometimes previously unknown family of planar solutions.     

Heating and acceleration of charged particles during magnetic dipolarizations

In this paper, we analyzed the thermal and energy characteristics of the plasma components observed during the magnetic dipolarizations in the near tail by the Cluster satellites. It was previously found that the first dipolarization the ratio of proton and electron temperatures (T _p/T _e) was ~6–7. At the time of the observation of the first dipolarization front T _p/T _e decreases by up to ~3–4. The minimum value T _p/T _e (~2.0) is observed behind the front during the turbulent dipolarization phase. Decreases in T _p/T _e observed at this time are associated with an increase in T _e, whereas the proton temperature either decreases or remains unchanged. Decreases of the value T _p/T _e during the magnetic dipolarizations coincide with increase in wave activity in the wide frequency band up to electron gyrofrequency f _ce. High-frequency modes can resonantly interact with electrons causing their heating. The acceleration of ions with different masses up to energies of several hundred kiloelectron-volts is also observed during dipolarizations. In this case, the index of the energy spectrum decreases (a fraction of energetic ions increases) during the enhancement of low-frequency electromagnetic fluctuations at frequencies that correspond to the gyrofrequency of this ion component. Thus, we can conclude that the processes of the interaction between waves and particles play an important role in increasing the energy of plasma particles during magnetic dipolarizations.     

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.     

Integrated Studies of Electric Propulsion Engines during Flights in the Earth’s Ionosphere

Fifty years ago, on October 1, 1966, the first Yantar satellite laboratory with a gas plasma–ion electric propulsion was launched into orbit as part of the Yantar Soviet space program. In 1966–1971, the program launched a total of four laboratories with thrusters operating on argon, nitrogen, and air with jet velocities of 40, 120, and 140 km/s, respectively. These space experiments were the first to demonstrate the long-term stable operation of these thrusters, which exceed chemical rocket engines in specific impulse by an order of magnitude and provide effective jet charge compensation, under the conditions of a real flight at altitudes of 100–400 km. In this article, we have analyzed the potential modern applications of the scientific results obtained by the Yantar space program for the development of air-breathing electric propulsion that ensure the longterm operation of spacecraft in very low orbits.     

Dynamics of electron fluxes in the slot between radiation belts in November–December 2014 according to data of the <Emphasis Type="Italic">Vernov</Emphasis> satellite

The variations in the spatial structure and time in electron fluxes with E = 235–300 keV in the slot region (2 < L < 3) between the radiation belts in the period of November 1, 2014 through December 8, 2014 during weak and moderate geomagnetic disturbances (Kp < 4, Dst >–60 nT) are analyzed based on the data of the RELEC complex on board the Vernov satellite (the height and inclination of the orbit are from 640 to 830 km and 98.4°, respectively). Irregular increases in the fluxes of such electrons and formation of a local maximum at L ~ 2.2–3.0 were observed. It has been shown that the intensity of this maximum is inversely proportional to the L value and grows with an increase in the geomagnetic activity level. New features discovered for the first time in the dynamics of radiation belt electrons manifest in the variations in the local structure and dynamics of fluxes of subrelativistic electrons in the slot region.     

The use of the Earth’s gravitational potential for interplanetary flights

An efficient scheme of the use of the Earth’s gravity in interplanetary flights is suggested, which opens up new opportunities for exploration of the solar system. The scheme of the gravitational maneuver allows one to considerably reduce the spacecraft mass consumption for a flight and the time of flight. An algorithm of the gravitational maneuver is suggested that takes into account the restriction on the altitude of a planet flyby. Estimates are made of transport capabilities for delivery of a spacecraft to the orbits of Jupiter, Saturn, and Uranus. The spacecraft is based on a middle-class carrier launcher of the Soyuz type and includes chemical and electric plasma jet engines of the SPD-140 type, which use solar energy.     

Effect of reflected ions on the formation of the structure of interplanetary quasi-perpendicular shocks for Mach numbers lower than the first critical mach number

Based on the data of the BMSW instrument installed on the of SPEKTR-R spacecraft, as well as according to the data of instruments of the WIND spacecraft, etc., using two examples, the paper has studied the role of ions reflected from the front and associated structural features of quasi-perpendicular interplanetary shocks (IS) with the Alfvén Mach number М _A lower than the first critical Mach number М _c1 . It has been shown that BSs with the finite parameter 0.1 < β₁ < 1 contain a small fraction of reflected protons, which play a significant role in forming the front structure (β₁ is the ratio of gas-to-magnetic pressure before the shock front). In particular, in the case of a perpendicular shock recorded on August 24, 2013 (the angle between the magnetic field direction and the normal to the front θ_Bn ≈ 85°), an IS with a small Mach number (М_A ≈ 1.4) and small β₁ ≈ 0.2 is shown that the interactions of reflected ions with inflowing solar wind may result in the collisionless heating of ions in front of and behind it. The case of the oblique (θ_Bn = 63°) IS on April 19, 2014 with a small Mach number (М ^A ≈ 1.2) and small β₁ ≈ 0.5 has been investigated. It has been found that, before the front, there is a sequence of trains of magnetosonic waves, the amplitude of which decreases to zero upon increasing their distance from the front. The mechanism of their formation is associated with the development of instability caused by the ions reflected from the front.     

<Emphasis Type="Italic">Luna-5</Emphasis> (1965): Some Results of a Failed Mission to the Moon

Luna-5 was the second Soviet spacecraft to reach the Moon. During the first decade of space exploration of the Moon, the Luna probe series was the main part of the Soviet scientific program. The tasks of the Luna-5 probe launched to the Moon in May 1965 were to land softly on the lunar surface, take photos, and study the surface. Before the Luna-5 landing, the prospective coordinates of the landing site were telegraphed to observatories so that they would observe the event. However, during its descent, the braking engine failed and the probe crash landed at 22 h 13 min on May 12, 1965. Later, new supposed coordinates of the impact were reported. All the experiments were undoubtedly lost; nevertheless, successive television images of the failed landing made at the Abastumani Astrophysical Observatory (AbAO) of the Georgian Academy of Sciences can be considered a specific scientific result of the mission. In the images, a changeable object was detected near the large Lansberg crater; for obscure secrecy reasons, almost nothing was reported to specialists about this object. It has been identified as a small, gradually spreading impact cloud. An analysis of the reprocessed images taken at the AbAO has revealed the exact coordinates of the Luna-5 impact for the first time to be 1.35° S, 25.48° W, which differ substantially the calculation data published earlier. Some properties of the regolith at the Luna-5 impact site are compared to the results of the Lunar Crater Observation and Sensing Satellite (LCROSS) related to the region near the south pole of the Moon and reported in 2010.     

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.     

Design of Interplanetary Transfers with Passive Gravity Assists and Deep Space Maneuvers

In the paper, the problem of designing interplanetary trajectories with several swing-bys and deep-space maneuvers is solved using the method of virtual trajectories developed by the authors. The algorithms for the calculation of both heliocentric and planetocentric trajectory arcs are presented, including the case of resonant trajectories. The results of applying the method of virtual trajectories to the problem of designing an interplanetary transfer to Jupiter are given and compared with the baseline trajectories for the Juno, Europa Clipper, and Laplace missions.     

Plasma flow disturbances in the magnetospheric plasma sheet during substorm activations

We have considered variations in fields and particle fluxes in the near-Earth plasma sheet on the THEMIS-D satellite together with the auroral dynamics in the satellite-conjugate ionospheric part during two substorm activations on December 19, 2014 with K _p = 2. The satellite was at ~8.5R_E and MLT = 21.8 in the outer region of captured energetic particles with isotropic ion fluxes near the convection boundary of electrons with an energy of ~10 keV. During substorm activations, the satellite recorded energetic particle injections and magnetic field oscillations with a period of ~90 s. In the satellite-conjugate ionospheric part, the activations were preceded by wavelike disturbances of auroral brightness along the southern azimuthal arc. In the expansion phase of activations, large-scale vortex structures appeared in the structure of auroras. The sudden enhancements of auroral activity (brightening of arcs, auroral breakup, and appearance of NS forms) coincided with moments of local magnetic field dipolarization and an increase in the amplitude Pi2 of pulsations of the B_z component of the magnetic field on the satellite. Approximately 30–50 s before these moments, the magnetosphere was characterized by an increased rate of plasma flow in the radial direction, which initiated the formation of plasma vortices. The auroral activation delays relative to the times when plasma vortices appear in the magnetosphere decreased with decreasing latitude of the satellite projection. The plasma vortices in the magnetosphere are assumed to be responsible for the observed auroral vortex structures and the manifestation of the hybrid vortex instability (or shear flow ballooning instability) that develops in the equatorial magnetospheric plane in the presence of a shear plasma flow in the region of strong pressure gradients in the Earthward direction.     

Fluxes of Quasi-trapped Electrons with Energies >0.08 MeV in the Near-Earth Space on Drift Shells <Emphasis Type="Italic">L</Emphasis> < 2

We study the characteristics of fluxes of electrons with energy >80 keV in the near-Earth space regions corresponding to the drift shells L = 1.7, 1.4, and 1.1 observed during the entire period of the GRIF experiment onboard the Spectr module of the Mir orbital station from October 1995 to June 1997. The obtained geographic maps of the distribution of electron fluxes at the height of the station flight (400 km) and, also, the estimates of the spectra indicate that the South-Atlantic Anomaly provides for a mechanism of stable replenishment for shells with L < 1.5. The mechanism of stable replenishment of shells with L < 1.5 may be due to the scattering, in the residual atmosphere, of electrons from the inner radiation belt precipitating into the region of the South-Atlantic Anomaly.     

Observations of electromagnetic emissions inside the Earth’s plasmasphere from the <Emphasis Type="Italic">Interball-1</Emphasis> satellite

The spectrum analyzer AKR-X onboard the Interball-1 satellite at the beginning (August–October 1995) and at the end (August–October 2000) of satellite operation in perigees of its orbital motion recorded and analyzed electromagnetic emissions of the inner regions of the Earth’s plasmasphere in the frequency band 100–1500 kHz at distances of 1.1–1.8 R _E. The observations have shown that the electromagnetic modes (the Z and LO modes escaping the magnetosphere) which are formed at the altitudes 600–4000 km are associated with the subauroral nonthermal continuum and with the recently discovered kilometric continuum. There are noticeable differences in the spectral character of these emissions during the minimum (1996) and maximum (2000) solar activity, when, as a rule, the LO mode escaping the plasmaphere and the continua are not present.     

Experiments with the DAKON-M convection sensor

We have described an express technique for processing the results of experiments with a DAKON-M convection sensor on board the Service Module of the International Space Station (ISS) in 2011. The technique uses a certain rule to compare the sensor measurements with the calculated data on the quasistatic component of microacceleration at the point of installation. The sensor experiments have been conducted during shuttle docking and undocking, when low-frequency microaccelerations on the ISS were significant. The microaccelerations have been calculated using measurement data of the MAMS low-frequency accelerometer installed in the Lab module and the telemetry data on the ISS rotational motion. This has made it possible to convert the MAMS measurement data to the DAKON-M convection sensor installation point. A comparison of sensor readings with calculated microaccelerations has revealed fairly good agreement between them.     

Calculation and Study of Limited Orbits around the <Emphasis Type="Italic">L</Emphasis><Subscript>2</Subscript> Libration Point of the Sun–Earth System

A procedure has been proposed for calculating limited orbits around the L₂ libration points of the Sun–Earth system. The motion of a spacecraft in the vicinity of the libration point has been considered a superposition of three components, i.e., decreasing (stable), increasing (unstable), and limited. The proposed procedure makes it possible to correct the state vector of the spacecraft so as to neutralize the unstable component of the motion. Using this procedure, the calculation of orbits around various types of libration points has been carried out and the dependence on the orbit type on the initial conditions has been studied.     

Quasiperiodic oscillations of the sub-mHz band in near-sun plasma according to the coherent radio occultation data

In 2013 and 2015, investigations of the internal solar wind were carried out using the method of two-frequency radio sounding by signals from the Mars Express European spacecraft. The values of the S- and X-bands’ frequency and the differential frequency were registered with a sampling rate of 1s at the American and European networks of ground-based tracking stations. The spatial distribution of the frequency fluctuation’s level has been studied. It has been shown that the intensity of frequency fluctuation considerably decreases at high heliolatitudes. In some radio sounding sessions, quasiperiodic oscillations of sub-mHz band have been observed in the temporal spectra of frequency fluctuations; they are supposed to be associated with the density inhomogeneities, the sizes of which are close to the turbulence outer scale.     

Geochronology and monitoring of cosmic rays for accumulating cosmogenic isotopes <Superscript>53</Superscript>Mn and <Superscript>10</Superscript>Be in terrestrial rocks

The paper is devoted to discussing the method of measuring the accumulation of radioactive isotopes ⁵³Mn (with a half-life T = 3.7 million years) and ¹⁰Be (T = 2.5 million years) in iron-bearing rocks. Knowledge of the dynamics of the accumulation of these isotopes would allow us to estimate the variations in the intensity of cosmic rays, periods of glaciations and geological changes, as well as climatic processes on the Earth in retrospect of 0.1–10 million years. For an operative study of a large number of samples, it has been proposed to use a low-cost neutron activation method with the implementation of the ⁵³Mn(n, γ)⁵⁴Mn reaction in a slow neutron reactor. As has been shown, using the 10Be isotope together with ⁵³Mn makes it possible to simultaneously determine both the cosmic-ray fluxes and the shielding time of the corresponding region from cosmic radiation. To obtain the reliable data on cosmic rays, it has been proposed to study rock samples from the lunar surface.