scholarly journals Estimation of the Yarkovsky effect on the example of the asteroid 1685 Toro (1948 OA)

2021 ◽  
Author(s):  
T. N. Sannikova ◽  
Keyword(s):  
Gravitational Field ◽  
Equations Of Motion ◽  
Radius Vector ◽  
Frame Of Reference ◽  
The Sun ◽  
Orbital Elements ◽  
Thermophysical Characteristics ◽  
Yarkovsky Effect ◽  
Averaged Equations ◽  
Central Gravitational Field

On the example of 1685 Toro, secular drifts of orbital elements and the displacement from the unperturbed position were obtained using the analytical solution of the averaged equations of motion of the asteroid in the central gravitational field and additional perturbing acceleration, inversely proportional to the square of the distance to the Sun, in the frame of reference associated with the radius vector. The components of this acceleration are calculated based on the thermophysical characteristics of 1685 Toro within the framework of the Yarkovsky acceleration linear model for spherical asteroids.

Motion of a satellite in the earth’s gravitational field

1960 ◽  
Vol 254 (1276) ◽  
pp. 48-65 ◽  
Keyword(s):  
Gravitational Field ◽  
Spherical Harmonics ◽  
Main Part ◽  
Equations Of Motion ◽  
Orbital Elements ◽  
Partial Derivatives ◽  
Rates Of Change ◽  
Zonal Harmonics ◽  
The Earth ◽  
Secular Terms

The equations of motion of a satellite are given in a general form, account being taken of the precession and nutation of the earth. The main part of the paper deals with the motion arising from the gravitational field of the earth, expressed as a general expansion in spherical harmonics. By evaluating the partial derivatives in Lagrange’s planetary equations, • expressions are obtained for the rates of change of the orbital elements. Particular consideration is given to the form of the expressions for the secular terms arising from the first four zonal harmonics.

The Kepler problem

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Kepler Problem ◽  
Equations Of Motion ◽  
Major Axis ◽  
Radius Vector ◽  
Lagrangian Formalism ◽  
The Sun ◽  
Semi Major Axis ◽  
Johannes Kepler ◽  
Reduced Equations ◽  
Central Forces

This chapter considers Newton’s 1665 explanations of the dynamics in the laws governing the motion of a planet around the Sun, which were established by Johannes Kepler in 1618. The first law states that the motion is planar and the trajectories are ellipses. The second states that the area swept out by the radius vector per unit time is constant. Finally, the cube of the semi-major axis a is proportional to the square of the period P, a3 = (const)P2. The chapter begins with the reduced equations of motion before turning to the ellipses of Kepler. It then illustrates the Kepler problem in the Lagrangian formalism, as well as central forces.

scholarly journals Dynamical evolution of asteroid pairs in the vicinity of resonances

2021 ◽  
Author(s):  
A. E. Potoskuev ◽  
◽  
E. D. Kuznetsov ◽  
Keyword(s):  
Equations Of Motion ◽  
Dynamical Evolution ◽  
Major Axis ◽  
Time Interval ◽  
Orbital Elements ◽  
Semi Major Axis ◽  
Mean Motion Resonances ◽  
Mean Motion ◽  
Yarkovsky Effect ◽  
Numerical Integrations

Dynamical evolution of asteroid pairs in close orbits near Jovian mean motion resonances (3 : 1, 4 : 1, 5 : 2, 7 : 3) has been researched by means of numerical integrations of the equations of motion over 1 Myr time interval in the future. Initial orbital elements’ uncertainty and semi-major axis drift due to the Yarkovsky effect significantly affect orbit modification with time, especially for objects originally situated in the vicinity of resonances. Passing through a resonance generally leads to orbital distance growth.

The post-Newtonian approximation

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Body Problem ◽  
Equations Of Motion ◽  
Two Body Problem ◽  
Newtonian Approximation ◽  
Actual Motion ◽  
Law Of Attraction ◽  
Universal Law ◽  
Two Bodies

This chapter embarks on a study of the two-body problem in general relativity. In other words, it seeks to describe the motion of two compact, self-gravitating bodies which are far-separated and moving slowly. It limits the discussion to corrections proportional to v2 ~ m/R, the so-called post-Newtonian or 1PN corrections to Newton’s universal law of attraction. The chapter first examines the gravitational field, that is, the metric, created by the two bodies. It then derives the equations of motion, and finally the actual motion, that is, the post-Keplerian trajectories, which generalize the post-Keplerian geodesics obtained earlier in the chapter.

scholarly journals New Approach to the Planetary Theory

1979 ◽  
Vol 81 ◽  
pp. 69-72 ◽  
Author(s):  
Manabu Yuasa ◽  
Gen'ichiro Hori
Keyword(s):  
Perturbation Method ◽  
Canonical Form ◽  
Equations Of Motion ◽  
Disturbing Function ◽  
Averaging Principle ◽  
The Sun ◽  
Planetary Theory ◽  
New Approach ◽  
Canonical Perturbation ◽  
Relative Coordinates

A new approach to the planetary theory is examined under the following procedure: 1) we use a canonical perturbation method based on the averaging principle; 2) we adopt Charlier's canonical relative coordinates fixed to the Sun, and the equations of motion of planets can be written in the canonical form; 3) we adopt some devices concerning the development of the disturbing function. Our development can be applied formally in the case of nearly intersecting orbits as the Neptune-Pluto system. Procedure 1) has been adopted by Message (1976).

On a non-symmetric theory of the pure gravitational field

1958 ◽  
Vol 54 (1) ◽  
pp. 72-80 ◽  
Author(s):  
D. W. Sciama
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Symmetric Tensor ◽  
Momentum Tensor ◽  
Unified Field Theory ◽  
Field Equations ◽  
Metric Tensor ◽  
Unified Field

ABSTRACTIt is suggested, on heuristic grounds, that the energy-momentum tensor of a material field with non-zero spin and non-zero rest-mass should be non-symmetric. The usual relationship between energy-momentum tensor and gravitational potential then implies that the latter should also be a non-symmetric tensor. This suggestion has nothing to do with unified field theory; it is concerned with the pure gravitational field.A theory of gravitation based on a non-symmetric potential is developed. Field equations are derived, and a study is made of Rosenfeld identities, Bianchi identities, angular momentum and the equations of motion of test particles. These latter equations represent the geodesics of a Riemannian space whose contravariant metric tensor is gij–, in agreement with a result of Lichnerowicz(9) on the bicharacteristics of the Einstein–Schrödinger field equations.

Consistent section-averaged equations of quasi-one-dimensional laminar flow

2010 ◽  
Vol 656 ◽  
pp. 337-341 ◽  
Author(s):  
PAOLO LUCHINI ◽  
FRANÇOIS CHARRU
Keyword(s):  
Equations Of Motion ◽  
Stability Result ◽  
Momentum Equation ◽  
Dissipation Function ◽  
Dimensional Solution ◽  
First Order ◽  
Averaged Equations ◽  
Classical Stability ◽  
Momentum Integral ◽  
Free Falling

Section-averaged equations of motion, widely adopted for slowly varying flows in pipes, channels and thin films, are usually derived from the momentum integral on a heuristic basis, although this formulation is affected by known inconsistencies. We show that starting from the energy rather than the momentum equation makes it become consistent to first order in the slowness parameter, giving the same results that have been provided until today only by a much more laborious two-dimensional solution. The kinetic-energy equation correctly provides the pressure gradient because with a suitable normalization the first-order correction to the dissipation function is identically zero. The momentum equation then correctly provides the wall shear stress. As an example, the classical stability result for a free falling liquid film is recovered straightforwardly.

Numerical modelling of swirling momentumless turbulent wake dynamics

2018 ◽  
pp. 37-48
Author(s):  
Андрей Геннадьевич Деменков ◽  
Геннадий Георгиевич Черных
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Equations Of Motion ◽  
Turbulent Wake ◽  
The Body ◽  
Jet Flows ◽  
Reynolds Stresses ◽  
Bodies Of Revolution ◽  
Averaged Equations

С применением математической модели, включающей осредненные уравнения движения и дифференциальные уравнения переноса нормальных рейнольдсовых напряжений и скорости диссипации, выполнено численное моделирование эволюции безымпульсного закрученного турбулентного следа с ненулевым моментом количества движения за телом вращения. Получено, что начиная с расстояний порядка 1000 диаметров от тела течение становится автомодельным. На основе анализа результатов численных экспериментов построены упрощенные математические модели дальнего следа. Swirling turbulent jet flows are of interest in connection with the design and development of various energy and chemical-technological devices as well as both study of flow around bodies and solving problems of environmental hydrodynamics, etc. An interesting example of such a flow is a swirling turbulent wake behind bodies of revolution. Analysis of the known works on the numerical simulation of swirling turbulent wakes behind bodies of revolution indicates lack of knowledge on the dynamics of the momentumless swirling turbulent wake. A special case of the motion of a body with a propulsor whose thrust compensates the swirl is studied, but there is a nonzero integral swirl in the flow. In previous works with the participation of the authors, a numerical simulation of the initial stage of the evolution of a swirling momentumless turbulent wake based on a hierarchy of second-order mathematical models was performed. It is shown that a satisfactory agreement of the results of calculations with the available experimental data is possible only with the use of a mathematical model that includes the averaged equations of motion and differential equations for the transfer of normal Reynolds stresses along the rate of dissipation. In the present work, based on the above mentioned mathematical model, a numerical simulation of the evolution of a far momentumless swirling turbulent wake with a nonzero angular momentum behind the body of revolution is performed. It is shown that starting from distances of the order of 1000 diameters from the body the flow becomes self-similar. Based on the analysis of the results of numerical experiments, simplified mathematical models of the far wake are constructed. The authors dedicate this work to the blessed memory of Vladimir Alekseevich Kostomakha.

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