Transition methods for stochastic simulation of parametric uncertainty in inverse problems of orbital dynamics

The paper proposes an original nonlinear technique for stochastic simulation of the uncertainty in orbital parameters that arises in inverse problems of dynamical astronomy (orbit determination from observations) due to random observation errors. The technique is based on a vector differential equation describing transition lines from the dynamic state, obtained from observations, to virtual dynamic states of the uncertainty cloud in the space of orbital parameters at a given (initial) epoch. Using some numerical method for solving the differential equation, stochastic simulation for each virtual state is implemented as a sequence of piecewise state transitions. The new technique is tested in strongly nonlinear inverse problems of asteroid dynamics on the examples of one lost and two recently discovered objects. The results by the transition methods are compared with those obtained by the method of disturbed (noisy) observations, also known as the observational Monte Carlo method. A comparative analysis reveals a good agreement of the results, while the amount of calculations by the proposed technique is at least twice less

SPECIAL PERTURBATION THEORY METHODS IN CELESTIAL MECHANICS. II. COMPARATIVE ANALYSIS OF NUMERICAL EFFICIENCY

A comparative analysis of the efficiency of methods in special perturbation theor

Study of the dynamic structure of the near-lunar orbital space

The knowledge of the dynamic features of the near-lunar space is necessary for its optimal mastering. This work is devoted to a study of the special features of the dynamics of the artificial Moon satellites (AMS) with intermediate and high orbits in the range of semimajor axes from 2500 to 26000 km

Orbital structure of the GJ876 extrasolar planetary system, based on the latest Keck and HARPS radial velocity data

We use full available array of radial velocity data, including recently published HARPS and Keck observatory sets, to characterize the orbital configuration of the planetary system orbiting GJ876. First, we propose and describe in detail a fast method to fit perturbed orbital configuration, based on the integration of the sensitivity equations inferred by the equations of the original $N$-body problem. Further, we find that it is unsatisfactory to treat the available radial velocity data for GJ876 in the traditional white noise model, because the actual noise appears autocorrelated (and demonstrates non-white frequency spectrum). The time scale of this correlation is about a few days, and the contribution of the correlated noise is about 2 m/s (i.e., similar to the level of internal errors in the Keck data). We propose a variation of the maximum-likelihood algorithm to estimate the orbital configuration of the system, taking into account the red noise effects. We show, in particular, that the non-zero orbital eccentricity of the innermost planet \emph{d}, obtained in previous studies, is likely a result of misinterpreted red noise in the data. In addition to offsets in some orbital parameters, the red noise also makes the fit uncertainties systematically underestimated (while they are treated in the traditional white noise model). Also, we show that the orbital eccentricity of the outermost planet is actually ill-determined, although bounded by $\sim 0.2$. Finally, we investigate possible orbital non-coplanarity of the system, and limit the mutual inclination between the planets \emph{b} and \emph{c} orbits by $5^\circ-15^\circ$, depending on the angular position of the mutual orbital nodes.Comment: 36 pages, 11 figures, 3 tables; Accepted to Celestial Mechanics and Dynamical Astronom

Determination of area-to-mass ratio of geosynchronous objects using positional observations obtained at Terskol pike

Представлены результаты совместного определения элементов орбит и параметра парусности объекта γ = A/m для группы геосинхронных фрагментов космического мусора на основании позиционных наблюдений, полученных на уникальной научной установке «Цейсс-2000» на Терскольской обсерватории Института астрономии РАН в период 11—25 сентября 2020 г.The results of the joint determination of the orbital elements and the area-to-mass ratio of the object γ = A/m for a group of geosynchronous fragments of space debris based on positional observations obtained at the unique scientific installation Zeiss-2000 at the Terskol Observatory of the Institute of Astronomy of the Russian Academy of Sciences during September 11—25, 2020 are presented.Работа выполнена в рамках государственного задания Министерства науки и высшего образования Российской Федерации (тема № 0721-2020-0049)

Collocation integrator lobbie in orbital dynamics problems

The paper investigates the efficiency of the new collocation integrator Lobbie, presented in (Avdyushev, 2020), in comparison with other integrators widely used in practice, namely, collocation Runge-Kutta, extrapolation Gragg-Bulirsch-Stoer, multistep Adams-Multon-Bashforth integrators, and also with the Everhart integrator, well known in celestial mechanics. The integrators are tested in orbital dynamics problems. In particular, a comparative analysis of efficiency shows that when simulating a complex orbital motion (strongly elliptical or with gravity assist maneuvers), Lobbie excels the other integrators (except Ever-hart) by several times in performance, and by several orders of magnitude in accuracy. A correct comparison of the efficiency of the Everhart integrator and Lobbie is not possible, since they have no common orders: the former has only odd orders on the Radau spacings, while the latter has only even orders on the Lobatto spacings. Nevertheless, if we compare the efficiency of integrators of adjacent orders, then in the strongly elliptic case the Everhart integrator (with a higher order) is one order of magnitude inferior to Lobbie in accuracy. Another advantage of Lobbie is that it allows solving mixed systems of differential equations of the second and first orders, which, for example, are used in celestial mechanics to study dynamic chaos, as well as to linearize, regularize, and stabilize the equations of motion. To use the Everhart integrator to solve such systems, all second-order equations must be reduced to first-order ones. However, as applied to systems of first-order equations, the efficiency of the Everhart integrator becomes noticeably worse

Stochastic simulation of orbital uncertainty of potentially hazardous asteroids observed in one appearance

The paper discusses some features in stochastic simulation of the orbital uncertainty of potentially hazardous asteroids observed in one appearance (opposition). Due to scant observational information, most of these asteroids have huge orbital uncertainties which can be difficult for stochastic simulation because of the strong nonlinearity of the inverse problem. In the paper we present different stochastic methods for simulation of orbital uncertainty and analyze their efficiency; using an original nonlinearity indicator, investigate the nonlinearity for all potentially hazardous asteroids observed in one opposition; consider the conditions that entail strong nonlinearity as well as the causes of falsely strong nonlinearity

Numerical modeling of motion of near-Earth objects in a parallel computing environment

A new version of the numerical model of artificial Earth satellites (AES) motion is presented, which consists of four program blocks intended for 1) predicting the AES motion, 2) studying the chaotic condition in motion of near-Earth space objects, 3) determining the AES motion parameters from the measurement data, and 4) studying the resonance dynamics of near-Earth objects. The main feature of the new version is the use of a new more efficient integrator, which is a further development of the well-known Everhart integrator. It is shown that with the same accuracy, the new integrator has much higher performance. The version intended for use in the parallel computing environment and called the "Numerical model of motion of AES systems" has undergone additional changes related to the optimization of the computation parallelization process. The estimates show that with the new method of parallelization, the integration accuracy is more stable and the integration speed increases several time

Nonlinearity in inverse problems of the dynamics of Jupiter’s outer satellites

This paper presents the results of a study of total and intrinsic nonlinearities in inverse problems of the dynamics of Jupiter’s Outer Satellites, observed on very short orbital arcs. The relationship between nonlinearity and the conditions of satellite observations is revealed. In particular, it is shown that a very strong total nonlinearity occurs when the observation period is less than 0.1 of the orbital period. In addition, it is shown that the intrinsic nonlinearity is rather weak for all the satellites. This indicates the possibility of using nonlinear methods for adequate simulating their orbital uncertaint