Numerical solutions to the problem of charged particel flow around an ionospheric spacecraft

The interaction of a conducting body moving through the ionosphere with the surrounding plasma is treated numerically. The Poisson and Vlasov equations are solved using computer techniques to give information about the redistribution of charged particles in the wake behind the body and the perturbation of the electric potential sheaths around the body. Three cases of interest are studied: body size less than, equal to, and greater than the Debye length in the surrounding plasma. A range of body potentials and ion Mach numbers are considered which are typical of conditions found in the ionosphere. Wake features, such as ion-free wake lengths and angles of propagation of disturbances in the wakes, are investigated for these conditions. Physical pictures of the mechanisms of wake formation behind a plate and a disc are built up for the three classes of body size, and differences due to geometry or size are explained. The smaller bodies are comparable in size to instrument booms, diagnostic probes, antennae, etc. and the larger bodies approach the dimensions of ionospheric satellites and space probes.     

Application of KS-transformation in the problem of investigation of the motion of unusual minor planets and comets

A review is presented of the author's results on application of regularizing and stabilizing KS- transformation in the problem of investigation of the motion of unusual minor planets and comets. Two models of the motion of a minor body are considered, viz. the perturbed two body problem and the perturbed restricted three body problem. The variational equations in KS-variables and transformations for obtaining the matrix of partial derivatives of the instantaneous physical parameters of motion with respect to their initial values are presented. The peculiarities of the implementation of the algorithms developed as programs on a computer are described. The original results of the investigation of the efficiency of the developed algorithms and programs are discussed using as an example the motion of unusual minor planets Icarus and Geographos as well as comets Halley, Honda-Mrkos-Pajdusakova and Gehrels 3.     

Double station and spectroscopic observations of the Quadrantid meteor shower and the implications for its parent body

Object 2003 EH₁ was recently identified as the parent body of the Quadrantid meteor shower. The origin of this body is still uncertain. We use data on 51 Quadrantid meteors obtained from double-station video observations as an insight on the parent body properties. A data analysis shows that the Quadrantids are similar to other meteor showers of cometary origin in some aspects, but in others to Geminid meteors. Quadrantid meteoroids have partially lost volatile component, but are not depleted to the same extent as Geminid meteoroids. In consideration of the orbital history of 2003 EH₁, these results lead us to the conclusion that the parent body is a dormant comet.     

第三体摄动分析解的一种表达式

在太阳系中,大行星、小行星和卫星（包括自然卫星和人造卫星）等对应的运动问题,都可以处理成受摄二体问题,而摄动源又多为第三体,作为第三体的摄动天体,有的比运动天体离中心天体近,有的则相反,前者称为内摄内体,全者则称为外摄天体,对一个具体的运动天体,可以同时出现这两个摄动天体,但是,只要运动天体与摄动天体的轨道都建立在以中心天体（质心）为坐标原点的同一坐标系内,那么在一定条件下（即除运动天体与摄动天体     

Rotational dynamics of a solar system body under solar radiation torques

The rotational dynamics of a small solar system body subject to solar radiation torques is investigated. A set of averaged evolutionary equations are derived as an analytic function of a set of spherical harmonic coefficients that describe the torque acting on the body due to solar radiation. The analysis also includes the effect of thermal inertia. The resulting equations are studied and a set of possible dynamical outcomes for the rotation rate and obliquity of a small body are found and characterized.     

Exact analytic solutions for the rotation of an axially symmetric rigid body subjected to a constant torque

New exact analytic solutions are introduced for the rotational motion of a rigid body having two equal principal moments of inertia and subjected to an external torque which is constant in magnitude. In particular, the solutions are obtained for the following cases: (1) Torque parallel to the symmetry axis and arbitrary initial angular velocity; (2) Torque perpendicular to the symmetry axis and such that the torque is rotating at a constant rate about the symmetry axis, and arbitrary initial angular velocity; (3) Torque and initial angular velocity perpendicular to the symmetry axis, with the torque being fixed with the body. In addition to the solutions for these three forced cases, an original solution is introduced for the case of torque-free motion, which is simpler than the classical solution as regards its derivation and uses the rotation matrix in order to describe the body orientation. This paper builds upon the recently discovered exact solution for the motion of a rigid body with a spherical ellipsoid of inertia. In particular, by following Hestenes’ theory, the rotational motion of an axially symmetric rigid body is seen at any instant in time as the combination of the motion of a “virtual” spherical body with respect to the inertial frame and the motion of the axially symmetric body with respect to this “virtual” body. The kinematic solutions are presented in terms of the rotation matrix. The newly found exact analytic solutions are valid for any motion time length and rotation amplitude. The present paper adds further elements to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.     

Dynamic Elastic Tides

This is an exploration of dynamic tides on elastic bodies. The body is thought of as a dynamical system described by its modes of oscillation. The dynamics of these modes are governed by differential equations that depend on the rheology. The modes are damped by dissipation. Tidal friction occurs as exterior bodies excite the modes and the modes act back on the tide raising body. The whole process is governed by a closed set of differential equations. Standard results from tidal theory are recovered in a two-timescale approximation to the solution of these differential equations.     

Perturbations in satellite orbits due to variations in rotation of the central body

Variations in satellite orbital elements are derived due to perturbations in the external gravitational field of the central body caused by mass deformations of the body occurring from variations in its rotation; the central body is assumed to be perfectly elastic. General theory derived is applied to the actual Earth, as an example; possible resonances are discussed.     

Analytical study of the swing-by maneuver in an elliptical system

The objective of the present paper is to derive a set of analytical equations that describe a swing-by maneuver realized in a system of primaries that are in elliptical orbits. The goal is to calculate the variations of energy, velocity and angular momentum as a function of the usual basic parameters that describe the swing-by maneuver, as done before for the case of circular orbits. In elliptical orbits the velocity of the secondary body is no longer constant, as in the circular case, but it varies with the position of the secondary body in its orbit. As a consequence, the variations of energy, velocity and angular momentum become functions of the magnitude and the angle between the velocity vector of the secondary body and the line connecting the primaries. The “patched-conics” approach is used to obtain these equations. The configurations that result in maximum gains and losses of energy for the spacecraft are shown next, and a comparison between the results obtained using the analytical equations and numerical simulations are made to validate the method developed here.     

The impact origin of Eunomia and Themis families

Abstract— Criteria for finding asteroid families (Zappala et al. 1995) are applied to a large (205,770 member) data set of asteroid orbital elements. The cases of the Eunomia and Themis families are considered as examples. This is combined with the cratering criteria for catastrophic disruption of small bodies in the solar system (Leliwa‐Kopystyński et al. 2008). We find that the Eunomia parent body itself was not catastrophically disrupted in the family‐generating impact event; after impact, the current body contains as much as 70% of its primordial mass. However, by contrast with Eunomia, the present mass of 24 Themis is only about 21% of that of its primordial body. Limits are placed on the sizes of the impactors in both examples, and for the case of Eunomia, the radius of the just sub‐critical crater (which may be present on 15 Eunomia) is predicted as <58 km.     

Secular orbit variation due to solar radiation effects: a detailed model for BYORP

A detailed derivation of the effect of solar radiation pressure on the orbit of a body about a primary orbiting the Sun is given. The result is a set of secular equations that can be used for long-term predictions of changes in the orbit. Solar radiation pressure is modeled as a Fourier series in the body’s rotation state, where the coefficients are based on the shape and radiation properties of the body as parameters. In this work, the assumption is made that the body is in a synchronous orbit about the primary and rotates at a constant rate. This model is used to write explicit variational equations of the energy, eccentricity vector, and angular momentum vector for an orbiting body. Given that the effect of the solar radiation pressure and the orbit are periodic functions, they are readily averaged over an orbit. Furthermore, the equations can be averaged again over the orbit of the primary about the Sun to give secular equations for long-term prediction. This methodology is applied to both circular and elliptical orbits, and the full equations for secular changes to the orbit in both cases are presented. These results can be applied to natural systems, such as the binary asteroid system 1999 KW4, to predict their evolution due to the Binary YORP effect, or to artificial Earth orbiting, nadir-pointing satellites to enable more precise models for their orbital evolution.     

Dynamical evolution of two associated galactic bars

We study the dynamical interactions of mass systems in equilibrium under their own gravity that mutually exert and ex‐perience gravitational forces. The method we employ is to model the dynamical evolution of two isolated bars, hosted within the same galactic system, under their mutual gravitational interaction. In this study, we present an analytical treatment of the secular evolution of two bars that oscillate with respect to one another. Two cases of interaction, with and without geometrical deformation, are discussed. In the latter case, the bars are described as modified Jacobi ellipsoids. These triaxial systems are formed by a rotating fluid mass in gravitational equilibrium with its own rotational velocity and the gravitational field of the other bar. The governing equation for the variation of their relative angular separation is then numerically integrated, which also provides the time evolution of the geometrical parameters of the bodies. The case of rigid, non‐deformable, bars produces in some cases an oscillatory motion in the bodies similar to that of a harmonic oscillator. For the other case, a deformable rotating body that can be represented by a modified Jacobi ellipsoid under the influence of an exterior massive body will change its rotational velocity to escape from the attracting body, just as if the gravitational torque exerted by the exterior body were of opposite sign. Instead, the exchange of angular momentum will cause the Jacobian body to modify its geometry by enlarging its long axis, located in the plane of rotation, thus decreasing its axial ratios. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

VUGS IN ORDINARY CHONDRITES

Large vugs occur in the ordinary chondrite, Farmington. They contain the same phases present in the body of the meteorite, either as vug wall lining or as crystals attached to linings. The morphologies of these phases indicate a history of melting and vapor deposition. These vugs are compared with vugs in the ordinary chondrites, Orvinio and Tadjera, and with published reports of vugs in Rose City and Shaw. It is concluded that although shock events may not cause heating above the liquidus for the body of the meteorite, local pockets of melting and vapor formation do occur due to inhomogenieties in the shock wave pattern. Vugs represent such pockets. Vug formation, as a consequence of shock processing, is widespread among ordinary chondrites and shows no correlation with the average temperature of shock heating, subsequent average cooling rate (as indicated by metallurgical criteria), or blackening of body color.     

A computer aided analysis of the Sitnikov Problem

We deal with the problem of a zero mass body oscillating perpendicular to a plane in which two heavy bodies of equal mass orbit each other on Keplerian ellipses. The zero mass body intersects the primaries plane at the systems barycenter. This problem is commonly known as theSitnikov Problem. In this work we are looking for a first integral related to the oscillatory motion of the zero mass body. This is done by first expressing the equation of motion by a second order polynomial differential equation using a Chebyshev approximation techniques. Next we search for an autonomous mapping of the canonical variables over one period of the primaries. For that we discretize the time dependent coefficient functions in a certain number of Dirac Delta Functions and we concatenate the elementary mappings related to the single Delta Function Pulses. Finally for the so obtained polynomial mapping we look for an integral also in polynomial form. The invariant curves in the two dimensional phase space of the canonical variables are investigated as function of the primaries eccentricity and their initial phase. In addition we present a detailed analysis of the linearized Sitnikov Problem which is valid for infinitesimally small oscillation amplitudes of the zero mass body. All computations are performed automatically by the FORTRAN program SALOME which has been designed for stability considerations in high energy particle accelerators.     

Quasi-Tangency Points on the Orbits of a Small Body and a Planet at the Low-Velocity Encounter

We propose a method for selecting a low-velocity encounter of a small body with a planet from the evolution of the orbital elements. Polar orbital coordinates of the quasi-tangency point on the orbit of a small body are determined. Rectangular heliocentric coordinates of the quasi-tangency point on the orbit of a planet are determined. An algorithm to search for low-velocity encounters in the evolution of the orbital elements of small bodies is described. The low-velocity encounter of comet 39P/Oterma with Jupiter is considered as an example.     

数值历表对动力系统参数的偏导数

本文推导了天体运动方程的数值解对积分初始条件、天体质量等动力系统参数的偏导数所满足的微分方程和初始条件。     

Coupled organic synthesis and mineral alteration on meteorite parent bodies

Abstract— The hypothesis that the soluble fraction of the organic compounds present in carbonaceous chondrite meteorites was formed during aqueous alteration of the parent body was tested with mass‐transfer, reaction‐path calculations. In these calculations, we start with likely compositions of the original parent body and asteroidal fluids that are far from thermodynamic equilibrium, and metastable and stable equilibrium constraints are imposed as the total Gibbs free energy of the parent body environment is minimized. The results of these calculations suggest that the classes of soluble organic compounds present in carbonaceous chondrite meteorites could have formed during relatively low temperature aqueous alteration of the meteorite parent body or bodies. The main controls on the potential for synthesis and transformation of organic compounds were the oxidation state of the rock/fluid system, the bulk composition of that system, and the temperatures that were achieved during the alteration event or events. It also appears that the alteration mineral assemblages were influenced by the presence of soluble organic compounds and reaction among them.     

Thermal consequences of impacts in the early solar system

Collisions between planetesimals were common during the first approximately 100 Myr of solar system formation. Such collisions have been suggested to be responsible for thermal processing seen in some meteorites, although previous work has demonstrated that such events could not be responsible for the global thermal evolution of a meteorite parent body. At this early epoch in solar system history, however, meteorite parent bodies would have been heated or retained heat from the decay of short‐lived radionuclides, most notably ²⁶Al. The postimpact structure of an impacted body is shown here to be a strong function of the internal temperature structure of the target body. We calculate the temperature–time history of all mass in these impacted bodies, accounting for their heating in an onion‐shell–structured body prior to the collision event and then allowing for the postimpact thermal evolution as heat from both radioactivities and the impact is diffused through the resulting planetesimal and radiated to space. The thermal histories of materials in these bodies are compared with what they would be in an unimpacted, onion‐shell body. We find that while collisions in the early solar system led to the heating of a target body around the point of impact, a greater amount of mass had its cooling rates accelerated as a result of the flow of heated materials to the surface during the cratering event.     

Mutual gravitational potential,force, and torque of a homogeneous polyhedron and an extended body: an application to binary asteroids

Binary systems are quite common within the populations of near-Earth asteroids, main-belt asteroids, and Kuiper belt asteroids. The dynamics of binary systems, which can be modeled as the full two-body problem, is a fundamental problem for their evolution and the design of relevant space missions. This paper proposes a new shape-based model for the mutual gravitational potential of binary asteroids, differing from prior approaches such as inertia integrals, spherical harmonics, or symmetric trace-free tensors. One asteroid is modeled as a homogeneous polyhedron, while the other is modeled as an extended rigid body with arbitrary mass distribution. Since the potential of the polyhedron is precisely described in a closed form, the mutual gravitational potential can be formulated as a volume integral over the extended body. By using Taylor expansion, the mutual potential is then derived in terms of inertia integrals of the extended body, derivatives of the polyhedron’s potential, and the relative location and orientation between the two bodies. The gravitational forces and torques acting on the two bodies described in the body-fixed frame of the polyhedron are derived in the form of a second-order expansion. The gravitational model is then used to simulate the evolution of the binary asteroid (66391) 1999 KW4, and compared with previous results in the literature.