Evolution Of Orbital Elements Research Articles

Overlong simulations of the solar system dynamics with two alternating step-lengths

We compare the performance of four symplectic integration methods with leading order symplectic corrector in simulations of the Solar System. These simulations cover 10 Gyr. They are longer than the astrophysical predicted future of the present-day Solar System, thus this work is mainly a study of the integration methods. For the outer Solar System simulation, where the used stepsize was 100 days, the energy errors do not show any secular evolution. The maximum errors show a dependence on the method. The simulations of the full Solar System from Mercury, and including Pluto as a test particle, were calculated with a stepsize of 7 days. The energy errors behave somewhat differently having a small secular behavior. This may due to the short timestep and the short period of the planet Mercury or some small round off error produced by the code. Comparison of the eccentricity evolution’s within simulations show that some planets are dynamically strongly coupled. Venus and Earth form a dynamical pair, also Jupiter and Saturn form a dynamical pair. The FFT of the analysis of the simulations suggests that all the giant planets form a single dynamical quadruple system. The orbit of Mercury is possibly unstable. Each simulation is stopped when Mercury is expelled. All the methods show similar results for times less than 30, Myr in the way that the results for orbital elements are same within plotting precision. Inclusion of Mercury in simulations shortens the Solar System e-folding time to 3.3, Myr. It is clear that chaos has a strong effect in the evolution of orbital elements, especially eccentricities. This is easily seen in Mercury’s orbit when the simulation time exceeds at least 30, Myr. Our low-order simulations seem to match high-order methods over long timescales.

Control of Spacecraft Relative Motion in a Tandem Flight Configuration

The article discusses the problems of controlling the relative motion of spacecraft (SC) in a tandem flight configuration. Flight configurations of two SC that form the so-called ballistically linked group and fly at a relatively small distance from each other are described. The effect of the evolution of orbital elements on the nature of the relative motion of SC in tandem is analyzed. The problems of orbit correction for maintaining the given tandem configuration are considered. Correction energy costs are estimated.

Observational Data and Orbits of the Asteroids Discovered at the Baldone Observatory in 2008–2013

Abstract The paper presents statistics of the asteroids observed and discovered at the Baldone Observatory, Latvia, in 2008–2013 within the project for astrometric observations of the near-Earth objects (NEOs), the main belt asteroids and comets. CCD observations of the asteroids were obtained with the 0.80/1.20 m, f/3 Schmidt telescope and a ST-10XME 15 × 10 mm CCD camera. In the Minor Planet Circulars and the Minor Planet Electronic Circulars (2008–2013) we published 3511 astrometric positions of 826 asteroids. Among them, 43 asteroids were newly discovered at Baldone. For 36 of these asteroids the precise orbits are calculated. Because of short observational arc and small number of observations, a few asteroids have low-precision orbits and their tracks have been lost. For seven objects with poorly known orbits we present their ephemerides for 2015–2016. The orbits and the evolution of orbital elements of two asteroids, (428694) 2008 OS9 from the Apollo group and the Centaur (330836) Orius (2009 HW77), are recalculated including new observations obtained after 2011.

Qualitative studies of orbital elements evolution in the planetary resonance form of the three-body problem in the case of the Rayleigh dissipation

In the planetary form of the three-body problem for first-order resonances the qualitative studies of the evolution of orbital elements of gravitating bodies’ were carried out taking into account the Rayleigh dissipation. The stationary solutions were considered and the phase trajectories were classified. The expressions for the deviation of orbital parameters were obtained.

Modifications of the Schwarzschild null geodesics in effective field theories

In this paper the dynamics of Schwarzschild null geodesics in the context of low-energy effective field theories incorporating some interactions violating the equivalence principle is examined. Nonperturbed geodesics are expressed in terms of a convenient set of constants called orbital elements. The modifications introduced by the effective interactions are treated as small perturbations, then the method of variation of parameters is employed to find the evolution of the orbital elements for the true worldlines. We next focus our discussion on the geometry of nondispersive photon orbits and highlight the importance of different orbital elements in long-term change of the orbit. This calculation shows that nondispersive forces acting on null geodesics drive a secular growth of the positional elements. As an application of our results we examine the evolution of mean orbital elements in the semiclassical theory of quantum gravitational optics and show that the averaged correction terms are within the range of the uncertainty principle.

Dynamics of dust grains with a vaporable icy mantle

We show the effects of solar gravity, electromagnetic radiation and solar wind on the motion of micrometre-sized interplanetary dust grains for initially small eccentric orbits and for heliocentric distances less than 10 au. The traditional approach is that the solar wind effect and the Poynting-Robertson (P-R) effect are simultaneously taken into account through the numerical factor 1 + ηA/C pr , which is multiplied by the P-R effect. In reality, solar wind corpusculae erode the surface of the interplanetary grain. As a consequence, the value of the solar electromagnetic radiation pressure term increases, as it is inversely proportional to the size of the grain. In addition, the radiation pressure efficiency also varies because of the changes to the optical properties of the grain. Both these physical processes are taken into account, and the secular evolution of orbital elements for a Gaussian sphere with a volatile icy coating exhibits a secular increase of the semimajor axis and eccentricity as well as the longitude of perihelion. These secular changes of orbital elements do not exist in the conventional approach for the P-R and solar wind effects. The conventional approach yields 10 4 yr for the lifetime of inspiralling toward the Sun, if the evolution starts from the initial values of the semimajor axis a in = 4 au and eccentricity e in = 0.2. The Gaussian sphere with a volatile icy coating exhibits a semimajor axis greater than 10 au for t > 3 x 10 2 yr for the same initial orbital elements.

Motion of dust near exterior resonances with planet

Motion of non-spherical cosmic dust particle under the action of electromagnetic radiation and gravitational forces of central star and a planet orbiting the star is investigated. The contribution concentrates on the problem if the particle can be trapped in commensurability resonances with the planet (a particle is in resonance with a planet when the ratio of their orbital periods is the ratio of two small integers). Trapping in the circular restricted three-body problem (planetary orbit is circle) with electromagnetic radiation coming from the star is considered. The effect of radiation plays an important role as for the possible capture in exterior resonances (particle's orbital period is larger than that for the planet): particle's optical properties not only define positions of the resonances, but also the capture times and evolution of orbital elements. Results for spherical and non-spherical particles are compared: physical difference between possibilities for resonant captures for spherical and non-spherical dust particles is pointed out.We concentrate on possible trapping of the grain in commensurability resonances – mean motion exterior resonances – with planet Neptune. The orbital evolution of non-spherical dust grains of radius ≈ 2 micrometers is numerically calculated.Capture of spherical grain in a resonance is characterized by decrease of semimajor axis outside the resonance. Non-spherical grain can exhibit also an increase of semimajor axis outside the resonance. This is the first case when a physically justified force – force given by interaction between electromagnetic radiation and non-spherical dust particle – can generate such a behaviour.

New edition of the catalogue of short-period comets

The Institute of Theoretical Astronomy in St. Petersburg and the Astronomical Institute in Bratislava are preparing a new edition of the Catalogue of short-period comets. This edition will be supplemented by short-period comets discovered after the year 1983 and comprises some new features, e. g. the evolution of orbital elements between the years 1750 and 2050, and the perihelion passages of comets within the 1994–2050 years. A new method has been employed for the determination of nongravitational parameters from the osculating elements of a comet based on all its observed returns.