Yu. D. Medvedev

A concept of a space hazard counteraction system: Astronomical aspects

The basic science of astronomy and, primarily, its branch responsible for studying the Solar System, face the most important practical task posed by nature and the development of human civilization—to study space hazards and to seek methods of counteracting them. In pursuance of the joint Resolution of the Federal Space Agency (Roscosmos) and the RAS (Russian Academy of Sciences) Space Council of June 23, 2010, the RAS Institute of Astronomy in collaboration with other scientific and industrial organizations prepared a draft concept of the federal-level program targeted at creating a system of space hazard detection and counteraction. The main ideas and astronomical content of the concept are considered in this article.

Using Close Encounters of Minor Planets for the Improvement of Their Masses

The orbits of 6807 numbered minor planets on the time interval 1975–2010 have been integrated. The possibility of determining masses for asteroids with close encounters with each other has been investigated, including several kinds of situations. The importance of the observational time arc, as well as the distribution of observations, for determining the masses are shown. The mass of asteroid (24) Themis from its perturbations on asteroid (2296) Kugultinov, and the mass of (10) Hygiea from its perturbations on (1259) Ogyalla have been determined.

On the accuracy of the orbit of asteroid (99942) APOPHIS at the time of its encounter with the Earth in 2029

We estimate the effect of trajectory measurement errors on the orbital parameters of asteroid Apophis determined from improvements. For this purpose, based on all of the optical and radar observations available to date, we have computed a nominal orbit of the asteroid. The scatter ellipsoid of the initial conditions of motion has been obtained by two methods. In the first, universally accepted method, the scatter ellipsoid is calculated by assuming a linear dependence of the errors in the parameters being determined on observational errors. In the second method, the scatter region of the orbital parameters around the nominal-orbit parameters is determined by the Monte Carlo method. We show that the region determined by the latter method at the initial epoch differs only slightly from the scatter ellipsoid for the linear approximation. We estimate the sizes of the projections of the corresponding regions onto the target plane at the time of the closest encounter of the asteroid with the Earth in 2029. The projections are approximated by ellipses. Our computations have shown that the ellipse has the following sizes: 389.6 km for the semimajor axis and 16.4 km for the semiminor axis in the linear case and 330.0 and 11.1 km, respectively, in the nonlinear case.

Radar observations of the asteroid 2011 UW158

In July 2015 intercontinental bistatic radar observations of the potentially dangerous asteroid 2011 UW158 during its close approach to the Earth were carried out. The asteroid was illuminated at a frequency of 8.4 GHz with the 70-m DSS-14 antenna of the Goldstone Deep Space Communications Complex, while the signal reflected from the asteroid was received with the 32-m radio telescopes of the Quasar VLBI network at the Zelenchukskaya and Badary Observatories. The spectra of the reflected radio signals were obtained. The sizes and rotation period of the asteroid consistent with photometric observations and the ratio of the powers of the reflected signals with left- and right-hand circular polarizations were determined. The derived values suggest that the asteroid has an inhomogeneous surface and a prolate shape. The observations of the Doppler shift of the reflected signal frequency were obtained, which allowed the orbital parameters of the asteroid to be improved.

Method of determining the orbits of the small bodies in the solar system based on an exhaustive search of orbital planes

A universal method of determining the orbits of newly discovered small bodies in the Solar System using their positional observations has been developed. The proposed method suggests determining geocentric distances of a small body by means of an exhaustive search for heliocentric orbital planes and subsequent determination of the distance between the observer and the points at which the chosen plane intersects with the vectors pointing to the object. Further, the remaining orbital elements are determined using the classical Gauss method after eliminating those heliocentric distances that have a fortiori low probabilities. The obtained sets of elements are used to determine the rms between the observed and calculated positions. The sets of elements with the least rms are considered to be most probable for newly discovered small bodies. Afterwards, these elements are improved using the differential method.

Improvement of the position of planet X based on the motion of nearly parabolic comets

Based on the motion of nearly parabolic comets, we have improved the position of planet X in its orbit obtained by Batygin and Brown (2016). By assuming that some of the comets discovered to date could have close encounters with this planet, we have determined the comets with a small minimum orbit intersection distance with the planet. Five comets having hyperbolic orbits before their entry into the inner Solar system have been separated out from the general list. By assuming that at least one of them had a close encounter with the planet, we have determined the planet’s possible position. The planet’s probable ephemeris positions at the present epoch have been obtained by assuming the planet to have prograde and retrograde motions. In the case of a prograde motion, the planet is currently at a distance Δ whose value belongs to the interval Δ ∈ (1110, 1120) AU and has a right ascension α and declination δ within the intervals α ∈ (83◦, 90◦) and δ ∈ (8◦, 10◦); the true anomaly υ belongs to the interval υ ∈ (176◦, 184◦). In the case of a retrograde motion: α ∈ (48◦, 58◦), δ ∈ (−12◦, −6◦), Δ ∈ (790, 910) AU, and υ ∈ (212◦, 223◦). It should be noted that in the case of a retrograde motion of the planet, its ephemeris position obtained from the motion of comets agrees with the planet’s position obtained byHolman and Payne (2016) from highly accurate Cassini observations and is consistent with the results of Fienga et al. (2016).

Asymmetric outgassing of short-periodic comets with respect to perihelion

The asymmetric model accounting for nongravitational effects is applied to improve orbits of a number of short-periodic comets that have shifts of maximum brightness with respect to their perihelions. Shifts of maximum gas productivity have been obtained for 20 short-periodic comets using photometric and dynamic methods. When using the photometric method, the maximum gas productivity is supposed to coincide with the maximum brightness of the comet, while, in the dynamic approach, it is believed to correspond to the maximum nongravitational acceleration. An analysis and evaluation of the results have been carried out.

Determination of the orbits of near-Earth asteroids from observations at the first opposition

Observations at the first opposition are used to determine the orbits of 16 near-Earth asteroids with two or more observed oppositions. The orbits are improved by the differential method. This paper considers two modifications of the improvement technique, which are compared to the classical method based on the principle of the least square method (LSM). The first modification uses the principle of least absolute deviations (LAD). In the second modification, the differences O - C (between the observed and calculated positions) are transformed to fit into a new coordinate system whereby the axes go parallel and perpendicular to the asteroid’s apparent path (the modified differential method (MDM)). The orbits determined from one opposition by the classical LSM, LAD, and MDM are compared to a more accurate orbit calculated by the LSM from all the available oppositions. The calculations show that in 13 cases out of 16, the asteroid orbits calculated by LAD are more accurate than those calculated by the classical LSM. The improvement by the modified differential method, which includes the O - C transformation, does not produce any perceptible increase in accuracy when compared to the orbits calculated by the classical method.

Long-term numerical theories of comet motion

We propose a method of constructing numerical theories of comet motion that cover long time intervals. The method involves the determination of individual values of the constants A1, A2, and A3 (radial, transversal, and normal components of nongravitational acceleration) and photocenter shifts for each appearance with the presence of a sufficient quantity of observations. Moreover, in the case of close planetary approaches, bursts of brightness, or heavy shifts in the cometary gas production maxima against the perihelion when standard models of nongravitational acceleration cannot provide an accurate presentation of the observations, we propose the use of instant velocity measurements. This method was used to construct a unified numerical theory of motion of the Kopff comet in the interval of 1906–2002. The theory encompassed 16 appearances of the comet with the mean error of unit weight σ = 1.40.

Restricted four-body problem. The case of a central configuration: Libration points and their stability

We consider the problem of the motion of a zero-mass body in the vicinity of a system of three gravitating bodies forming a central configuration.We study the case where two gravitating bodies of equal mass lie on the same straight line and rotate around the central body with the same angular velocity. Equations for calculating the equilibrium positions in this system have been derived. The stability of the equilibrium points for a system of three gravitating bodies is investigated. We show that, as in the case of libration points for two bodies, the collinear points are unstable; for the triangular points, there exists a ratio of the mass of the central body to the masses of the extreme bodies, 11.720349, at which stability is observed.