Changes In Orbital Elements Research Articles

Simple Simulation of Solar System

The article presents a simple derivation of a set of approximate formulas for the rate of change of orbital elements of a planet, perturbed by a time-averaged gravitational force due to the remaining planets of the solar system. The corresponding set of differential equations for long-time development of planetary orbits is then numerically integrated and the results are shown to be consistent with Milankovitch theory of climatic cycles.

A New Approach to Dynamical Evolution of Interplanetary Dust

We introduce the continuity equation written in the coordinate space of the orbital elements (e.g., semimajor axis a versus eccentricity e, etc.). This equation can serve as an effective tool to analyze the transport of interplanetary dust particles as well as their dynamical evolution, and offers a very useful complement to the approach using purely numerical integration of orbits. Using the continuity equation and suitable analytical and numerical approximations, statistically useful results can be achieved very quickly, and new integrals of the motion can be sought to simplify the description of large-scale phenomena. This paper describes the method, illustrates it with a simple example of multiple gravitational scatterings of particles on planets in circular orbits in two dimensions, and outlines the program for further development with more accurate approximations. We describe the particle dynamical evolution due to gravitational by means of the scattering W(a, e, a', e') in the continuity equation. This matrix determines both the probability of transition and the value of the particle's shift from the point a, e to the point a', e'. For purposes of illustration, two cases of the zodiacal particle diffusion due to gravitational are computed, which are characterized by the initial conditions (1) (asteroid case), a0 = 2.5 AU, e0 = 0.4 (resonance 1:3 with Jupiter), and (2) (comet case), a0 = 2.22 AU, e0 = 0.846 (comet Encke). We discuss the approximations of the example and how they might be improved in future work. These include treatments of the Poynting-Robertson drag, interparticle collisions, secular perturbations, three-dimensional orbits, and resonance capture by the planets. For instance, analytical expressions are available for the rates of gradual change of orbital elements due to the Poynting-Robertson and solar wind drags, which can be incorporated easily in the div terms of the continuity equation.

Dynamical Evolution of Interplanetary Dust due to Gravitational Scattering by Jupiter and the Inner Planets

AbstractWe introduce the continuity equation written in the coordinate space of the orbital elements (e.g. large semi-axis a vs. eccentricity e, etc.) to explore the density evolution of the zodiacal cloud. Emphasis is on those terms of the continuity equation which describe ‘jumps’ of particles in the (a, e)-space due to gravitational scattering of the interplanetary dust particles by planets, which represents one of the leading factors in the dynamical evolution of the zodiacal cloud. In the remainder (div-terms of the continuity equation), one can incorporate the known analytical expressions for the rates of gradual change of orbital elements due to the Poynting-Robertson and solar wind drags (Liou et al. 1995).

Interplanetary dust particles: Disintegration and orbital motion

Abrupt or gradual disintegration of the interplanetary dust particle causes increase of its distance from the Sun due to the solar radiation pressure. The problem of the orbital evolution of the interplanetary dust particles under such disintegration processes is discussed. The process of gradual disintegration due to the solar wind particles is calculated in detail. Obtained results represent corrections to the changes of orbital elements for the Poynting-Robertson effect and effect of the solar wind.

Poynting-Robertson effect: ‘Circular’ orbit

Time evolution of the interplanetary dust particle under the action of the solar electromagnetic radiation (Poynting-Robertson effect) is investigated. Evolution of the initially circular orbit in terms of the orbital elements present in the standard equations for their secular changes is considered. It is pointed out that the osculating eccentricity is practically constant during the motion in spite of generally accepted opinion that the standard equations for the secular changes of orbital elements represent time evolution of the osculating elements.

DYNAMICS OF BINARY AND PLANETARY SYSTEM INTERACTION WITH DISKS: ECCENTRICITY CHANGES

ABSTRACT Protostellar and protoplanetary systems, as well as merging galactic nuclei, often interact tidally and resonantly with the astrophysical disks via gravity. Underlying our understanding of the formation processes of stars, planets and some galaxies is a dynamical theory of such interactsion. Its main goals are to determine the geometry of the binary-disk system and, through the torque calculations, the rate of change of orbital elements of the components. We present some recent developments in this field concentrating on eccentricity driving mechanisms in protoplanetary and protobinary systems. In those two types of systems the result of the interaction is opposite. A small body embedded in a disk suffers a decrease_ of orbital eccentricity, whereas newly formed binary stars surrounded by protostellar disks may undergo a significant orbital evolution increasing_ their eccentricities.

Elliptical Hill's problem (large and small impact parameters)

This paper gives analytical formulas to express the changes in orbital elements due to a close encounter between two particles of a ring or between two small satellites of a planet. The study is performed in the frame of the Hill's problem, extended to fully take into account the eccentricities. The Lie's transform method is used to average the Hamiltonian, particularized to two types of encounters: the ones with small impact distance (coorbitals) and those with a large one (shepherds).

Dynamical evolution of the Oort cloud: I. A Monte Carlo simulation

We have studied the long-time dynamical evolution of a population of comets surrounding the Solar System at a large distance. Orbital changes are caused by random passing stars. We first emphasize the need for a new simulation because of the lack of completeness of previous analytical and numerical studies. Then the solar neighborhood is modeled by a sphere of 1 pc in radius, which stars cross at random in direction and distance. The geometry of the encounters allows us to compute the impulse gained by the star and the Sun, in the context of an impact approximation. Then we determine the change of orbital elements for a population of comets and follow the evolution of the frequency distribution for the five Keplerian elements. Clouds are selected in such a way that we test the two main hypotheses for the origin of the Oort cloud, and also the regions of stability in an aphelion-eccentricity diagram. We show that stellar perturbations randomize the cloud and prevent one from inferring the initial cloud configuration from the current distribution. Clouds are depleted by the diffusion of comets into the planetary regions, where they become planet-influenced comets or are ejected from the Solar System. The diffusion of aphelion toward interstellar regions proves to be the major source of cometary loss. Direct ejection to hyperbolic orbits amounts to 9% of the originally population over the age of the Solar System. Finally the current and original cloud populations are estimated at 1.8 × 10 12 and 2 × 10 13 comets and we discuss these results.

Exospheric perturbations by radiation pressure: II. Solution for orbits in the ecliptic plane

An earlier paper gave solutions for the mean time rates of change of orbital elements of satellite atoms in an exosphere influenced by solar radiation pressure. Each element was assumet to beahve independently. Here the instantaneous rates of change for three elements (e, ω, and θ = ω + Ω) are integrated simultaneously for the case of the inclination i = 0. The results (a) confirm the validity of using mean rates when the orbits are tightly bound to the planet and (b) serve as examples to be reproduced by the complicated numerical solutions required for arbitrary inclination. Strongly bound hydrogen atoms perturbed in Earth orbit by radiation pressure do not seem a likely cause of the geotail extending in the anti-Sun direction. Instead, radiation pressure wil cause those particles' orbits to form a broad fan-shaped tail and to deteriorate into the Earth's atmosphere. Whether loosely bound H atoms are plentiful enough to create the geotail depends on their source function versus r; that question is beyond the scope of this paper.

Influence of the interplanetary magnetic field on cometary and primordial dust orbits: Applications of Lorentz scattering

The equations describing the change in orbital elements of interplanetary dust due to Lorentz-force accelerations are presented in a simplified form. Such accelerations depend on the charge state of the dust; results of theoretical calculations for five possible dust materials are presented. Under present-day conditions, it is possible that semiconducting material such as graphite might carry a net voltage near zero, compared with a roughly 10-V charge expected for other grains. The scattering of dust by a randomly changing magnetic field can be viewed analogously to the dust diffusing in space; the equations presented thus can be used to interpret observations of the present distribution of dust in terms of its possible sources and sinks. The stronger magnetic fields of the early solar system would have led to more vigorous scattering of the dust; particles as large as 1 mm could have been significantly transported by Lorentz scattering during this time.

Planetary Systems and Stellar Multiplicity

AbstractIn this paper we have discussed the origin of planetary systems on one hand and binary and multiple stars on the other. First we show that phenomenological differences between these two kinds of celestial objects are due to their genetic difference. The basic point is that formation of a planetary system around a star has to be a minor event in the life history of the star while formation of a binary or multiple system has to be an event that is important equally to all components of the system. Thus the planetary system evolves from a rotating disk of gaseous and dust particles that comes into being after the star has already been there. It is therefore reasonable to suggest that the rotating disk results from transfer of angular momentum from the central star to the surrounding medium which is likely a residue left over in the process of formation of the central star.Binary and multiple systems cannot be formed in this way because they do not show the characteristics of having come out of a rotating disk. The dominant mechanism of their formation is that they were formed naturally as they are, each from perhaps a single condensation in the interstellar medium. However such a single mechanism of formation cannot satisfactorily explain the observed spread of binaries in mean separations between two components (or equivalently orbital periods). But the disagreement may be removed by including a small number of binaries formed by other processes and by considering the change of orbital elements of binaries after their formation. Trapezia were likely formed also by more than one mechanism.That several stars could be formed, from a single condensation requires the” existence oí pre-stellar nuclei which are briefly: discussed at the end of the paper.

Tidal Interactions in Compact Binary Systems

An analytic model has been constructed for the change of orbital elements because of tidal drag in a binary system where one of the components is compact (Lecar et al., 1976). The basic assumptions are (i) tides on the compact object are neglected (ii) only P2 deformations of the non-compact star are considered (iii) the lag angle is linearly proportional to the difference between the instantaneous orbital angular velocity and the spin angular velocity of the non-compact star (iv) the semi major axis a and eccentricity e do not change significantly in a single orbit. The results are exact solutions for a and ė as a function of e and the ratio of primary star to orbital angular velocity, Ω/ω.Tidal instability in this model is manifest by the dynamical inability to attain or sustain synchronism. An analysis to second order in e and first order in (Ω/ω−1) shows that the criterion for instability is the same as in the work of Counselman (1973), namely ma2 > I where m is the reduced mass and I the moment of inertia of the primary star. This criterion is shown to apply to eccentric orbits and is thus more general than the criterion derived from the energetics of circular orbits. Stable systems may overshoot the condition of synchronism before settling into the final circular synchronous orbit.

Effects of Resonant Tesseral Gravity Coefficients on Viking-Type Orbits

A special perturbation technique has been developed for the long-period and secular motion of a Viking-type orbiter. The technique uses a method of singly averaging the perturbations over the mean anomaly to determine changes in orbital elements due to atmospheric drag, solar radiation pressure, solar gravity, and the asymmetrical Mars gravitational field. The technique has been specialized to treat resonant tesseral gravity effects resulting from the commensiirability of the satellite orbit period with the rotational period of the primary. Results are presented which indicate that orbiter lifetimes can be significantly reduced by resonant tesserals for orbits near the critical inclination. Conversely, it is shown that lifetimes can be extended via capture in resonant orbits which are stable against small drag forces.