共查询到20条相似文献，搜索用时 15 毫秒
1.
本文用后－后牛顿近似讨论Ｋｅｒｒ场中缓慢粒子的运动，我们用Ｂｏｙｅｒ－Ｌｉｎｄｑｕｉｓｔ坐标，导出试验粒子的运动方程，把它与有心力场中粒子作二体运动之球坐标形式下的运动方程对比，得出由于Ｋｅｒｒ场的作用而引起的试验粒子的等效摄动加速度，利用球面三角公式把它换算到行星运动摄动方程的形状，对摄动方程进行积分，我们得出了试验粒子绕中心天体运动一周后粒子轨道根数的变化以及单位时间中轨道根数的平均变化，运用 相似文献
2.
Aaron J. Rosengren Daniel J. Scheeres 《Celestial Mechanics and Dynamical Astronomy》2014,118(3):197-220
We consider sets of natural vectorial orbital elements of the Milankovitch type for perturbed Keplerian motion. These elements are closely related to the two vectorial first integrals of the unperturbed two-body problem; namely, the angular momentum vector and the Laplace–Runge–Lenz vector. After a detailed historical discussion of the origin and development of such elements, nonsingular equations for the time variations of these sets of elements under perturbations are established, both in Lagrangian and Gaussian form. After averaging, a compact, elegant, and symmetrical form of secular Milankovitch-like equations is obtained, which reminds of the structure of canonical systems of equations in Hamiltonian mechanics. As an application of this vectorial formulation, we analyze the motion of an object orbiting about a planet (idealized as a point mass moving in a heliocentric elliptical orbit) and subject to solar radiation pressure acceleration (obeying an inverse-square law). We show that the corresponding secular problem is integrable and we give an explicit closed-form solution. 相似文献
3.
The increasing number and variety of extrasolar planets illustrates the importance of characterizing planetary perturbations. Planetary orbits are typically described by physically intuitive orbital elements. Here, we explicitly express the equations of motion of the unaveraged perturbed two-body problem in terms of planetary orbital elements by using a generalized form of Gauss’ equations. We consider a varied set of position and velocity-dependent perturbations, and also derive relevant specific cases of the equations: when they are averaged over fast variables (the “adiabatic” approximation), and in the prograde and retrograde planar cases. In each instance, we delineate the properties of the equations. As brief demonstrations of potential applications, we consider the effect of Galactic tides. We measure the effect on the widest-known exoplanet orbit, Sedna-like objects, and distant scattered disk objects, particularly with regard to where the adiabatic approximation breaks down. The Mathematica code which can help derive the equations of motion for a user-defined perturbation is freely available upon request. 相似文献
4.
Giulio Baù Claudio Bombardelli Jesús Peláez 《Celestial Mechanics and Dynamical Astronomy》2013,116(1):53-78
A formulation of the perturbed two-body problem that relies on a new set of orbital elements is presented. The proposed method represents a generalization of the special perturbation method published by Peláez et al. (Celest Mech Dyn Astron 97(2):131–150, 2007) for the case of a perturbing force that is partially or totally derivable from a potential. We accomplish this result by employing a generalized Sundman time transformation in the framework of the projective decomposition, which is a known approach for transforming the two-body problem into a set of linear and regular differential equations of motion. Numerical tests, carried out with examples extensively used in the literature, show the remarkable improvement of the performance of the new method for different kinds of perturbations and eccentricities. In particular, one notable result is that the quadratic dependence of the position error on the time-like argument exhibited by Peláez’s method for near-circular motion under the $J_{2}$ perturbation is transformed into linear. Moreover, the method reveals to be competitive with two very popular element methods derived from the Kustaanheimo-Stiefel and Sperling-Burdet regularizations. 相似文献
5.
We consider an algorithm to construct averaged motion equations for four-planetary systems by means of the Hori–Deprit method. We obtain the generating function of the transformation, change-variable functions and right-hand sides of the equations of motion in elements of the second Poincaré system. Analytical computations are implemented by means of the Piranha echeloned Poisson processor. The obtained equations are to be used to investigate the orbital evolution of giant planets of the Solar system and various extrasolar planetary systems. 相似文献
6.
Victor R. Bond 《Celestial Mechanics and Dynamical Astronomy》1976,14(3):333-311
A new set of element differential equations for the perturbed two-body motion is derived. The elements are canonical and are similar to the classical canonical Poincaré elements, which have time as the independent variable. The phase space is extended by introducing the total energy and time as canonically conjugated variables. The new independent variable is, to within an additive constant, the eccentric anomaly. These elements are compared to the Kustaanheimo-Stiefel (KS) element differential equations, which also have the eccentric anomaly as the independent variable. For several numerical examples, the accuracy and stability of the new set are equal to those of the KS solution. This comparable accuracy result can probably be attributed to the fact that both sets have the same time element and very similar energy elements. The new set has only 8 elements, compared to 10 elements for the KS set. Both sets are free from singularities due to vanishing eccentricity and inclination. 相似文献
7.
Lin-Sen Li 《Astrophysics and Space Science》2012,340(2):323-330
Perturbative post-Newtonian variations of the standard osculating orbital elements are obtained by using the two-body equations of motion in the parameterized post-Newtonian theoretical framework. The results obtained are applied to the Einstein and Brans–Dicke theories. As a results, the semi-major axis and eccentricity exhibit periodic variation, but no secular changes. The longitude of periastron and mean longitude at epoch experience both secular and periodic shifts. The post-Newtonian effects are calculated and discussed for six extrasolar planets. 相似文献
8.
《Icarus》1987,72(3):593-603
The dynamical behavior of planetary rings is often described in terms of streamline deformations and motions. We argue that the standard formula giving the shape of the streamlines involves geometric elements rather than orbital elements, when the oblateness of the planet is taken into account. We relate the geometric elements to the orbital elements and derive the differential equations which govern the variations with time of the geometric elements. 相似文献
9.
Victor R. Bond 《Celestial Mechanics and Dynamical Astronomy》1974,10(3):303-318
The Newtonian differential equations of motion for the two-body problem can be transformed into four, linear, harmonic oscillator equations by simultaneously applying the regularizing time transformation dt/ds=r and the Kustaanheimo-Stiefel (KS) coordinate transformation. The time transformation changes the independent variable from time to a new variables, and the KS transformation transforms the position and velocity vectors from Cartesian space into a four-dimensional space. This paper presents the derivation of uniform, regular equations for the perturbed twobody problem in the four-dimensional space. The variation of parameters technique is used to develop expressions for the derivatives of ten elements (which are constants in the unperturbed motion) for the general case that includes both perturbations which can arise from a potential and perturbations which cannot be derived from a potential. These element differential equations are slightly modified by introducing two additional elements for the time to further improve long term stability of numerical integration.Originally presented at the AAS/AIAA Astrodynamics Specialists Conference, Vail, Colorado, July 1973 相似文献
10.
Bálint Érdi 《Celestial Mechanics and Dynamical Astronomy》1981,24(4):377-390
An asymptotic solution for the cylindrical coordinates of Trojan asteroids is derived by using a three-variable expansion method in the elliptic restricted three-body problem. The perturbations of the orbital elements are obtained from this solution by applying the formulas of the two-body problem. The main perturbations of the mean motion are studied in detail. 相似文献
11.
F. Mignard 《Earth, Moon, and Planets》1980,23(2):185-201
We present here a model for the tidal evolution of an isolated two-body system. Equations are derived, including the dissipation in the planet as in the satellite, in a frequency dependent lag model. The set of differential equations obtained is still valid for large eccentricity, as well as for all inclinations. The reference plane chosen enables us to study the evolution for both the orbital plane and the equatorial plane.The results obtained show the Moon, after having approached the Earth with small variations for the inclination and the eccentricity, exhibits strong increase for the two parameters in the vicinity of the closest approach. In every case the eccentricity tends towards the value 1, whereas the variations of the in clinations are dependent on the magnitude of the dissipation in the satellite.Some qualitative results are also investigated for the final behaviour of satellites such as Triton and the Galilean satellites. 相似文献
12.
A set of differential equations is derived that has a number of advantages in special perturbation work. In particular, the equations remain valid for all values of the orbital eccentricity and inclination including zero. They are therefore applicable to parabolic- and hyperbolic-type orbits as well as elliptic-type; a scheme for use when the orbit is rectilinear or nearly so is provided. The equations are also much simpler in form than the Lagrange planetary equations and the transformations of the osculating elements to and from the rectangular coordinates are straightforward. 相似文献
13.
14.
P. Pástor 《Celestial Mechanics and Dynamical Astronomy》2012,112(1):23-45
The orbital evolution of a dust particle under the action of a fast interstellar gas flow is investigated. The secular time
derivatives of Keplerian orbital elements and the radial, transversal, and normal components of the gas flow velocity vector
at the pericentre of the particle’s orbit are derived. The secular time derivatives of the semi-major axis, eccentricity,
and of the radial, transversal, and normal components of the gas flow velocity vector at the pericentre of the particle’s
orbit constitute a system of equations that determines the evolution of the particle’s orbit in space with respect to the
gas flow velocity vector. This system of differential equations can be easily solved analytically. From the solution of the
system we found the evolution of the Keplerian orbital elements in the special case when the orbital elements are determined
with respect to a plane perpendicular to the gas flow velocity vector. Transformation of the Keplerian orbital elements determined
for this special case into orbital elements determined with respect to an arbitrary oriented plane is presented. The orbital
elements of the dust particle change periodically with a constant oscillation period or remain constant. Planar, perpendicular
and stationary solutions are discussed. The applicability of this solution in the Solar System is also investigated. We consider
icy particles with radii from 1 to 10 μm. The presented solution is valid for these particles in orbits with semi-major axes
from 200 to 3000 AU and eccentricities smaller than 0.8, approximately. The oscillation periods for these orbits range from
105 to 2 × 106 years, approximately. 相似文献
15.
András Pál 《Monthly notices of the Royal Astronomical Society》2009,396(3):1737-1742
In this paper, we present a framework which provides an analytical (i.e. infinitely differentiable) transformation between spatial coordinates and orbital elements for the solution of the gravitational two-body problem. The formalism omits all singular variables which otherwise would yield discontinuities. This method is based on two simple real functions for which the derivative rules are only required to be known, all other applications – e.g. calculating the orbital velocities, obtaining the partial derivatives of radial velocity curves with respect to the orbital elements – are thereafter straightforward. As it is shown, the presented formalism can be applied to find optimal instants for radial velocity measurements in transiting explanatory systems to constrain the orbital eccentricity as well as to detect secular variations in the eccentricity or in the longitude of periastron. 相似文献
16.
J. F. Ling 《Astrophysics and Space Science》1991,185(1):51-61
The stellar three-body problem has been approached by directly integrating the equations of motion in the orbital elements. The problem is set up in a barycentric chain with the orbits as perturbed ellipses.The integration was performed using the semi-analytical stroboscopic method, which is particularly useful for solving differential systems that depend on several slow variables and one fast, angular variable. Perturbation theory is applied and the solution for a particular order is obtained by way of successive approximations on the fundamental period of the fast variable. 相似文献
17.
Victor R. Bond 《Celestial Mechanics and Dynamical Astronomy》1976,14(3):333
A new set of element differential equations for the perturbed two-body motions is derived. The elements are canonical and are similar to the classical canonical Poincaré elements, which have time as the independent variable. The phase space is extended by introducing the total energy and time as canonically conjugated variables. The new independent variable is, to within an additive constant, the eccentric anomaly. These elements are compared to the Kustaanheimo-Stiefel (KS) element differential equations, which also have the eccentric anomaly as the independent variable. For several numerical examples, the accuracy and stability of the new set are equal to those of the KS solution. This comparable accuracy result can probably be attributed to the fact that both sets have the same time element and very similar energy elements. The new set has only 8 elements, compared to 10 elements for the KS set. Both sets are free from singularities due to vanishing eccentricity and inclination.This paper is published in its entirety inCelest. Mech.
13 (1976), 287–311. 相似文献
18.
《Icarus》1987,70(2):319-333
The present nearly resonant orbital periods of the planets are explained in terms of past two-body resonance capture of planetesimals in the solar nebula. Planetary formation then occurs sequentially starting with Jupiter for the outer planets and Venus for the inner planets and propagates outward due to two-body orbital resonances. It might now be possible to reconstruct the evolutionary history of the planets from their nearly commensurable orbital periods and, hence, provide an explanation for the Titius-Bode law. 相似文献
19.
Theory of the motion of an artificial Earth satellite 总被引：1，自引：0，他引：1
Felix R. Hoots 《Celestial Mechanics and Dynamical Astronomy》1981,23(4):307-363
An improved analytical solution is obtained for the motion of an artificial Earth satellite under the combined influences of gravity and atmospheric drag. The gravitational model includes zonal harmonics throughJ
4, and the atmospheric model assumes a nonrotating spherical power density function. The differential equations are developed through second order under the assumption that the second zonal harmonic and the drag coefficient are both first-order terms, while the remaining zonal harmonics are of second order.Canonical transformations and the method of averaging are used to obtain transformations of variables which significantly simplify the transformed differential equations. A solution for these transformed equations is found; and this solution, in conjunction with the transformations cited above, gives equations for computing the six osculating orbital elements which describe the orbital motion of the satellite. The solution is valid for all eccentricities greater than 0 and less than 0.1 and all inclinations not near 0o or the critical inclination. Approximately ninety percent of the satellites currently in orbit satisfy all these restrictions. 相似文献
20.
John D. Hadjidemetriou 《Astrophysics and Space Science》1969,3(1):31-45
The effects of non-isotropic ejection of mass from either component of a binary system on the orbital elements are studied, for the case of a small initial eccentricity of the relative orbit, when all the ejected mass falls on the other component. The problem is transformed to an equivalent two-body problem with isotropic variation of mass, plus a perturbing force which is a function of the intial conditions of ejection of the particles and their final, positions and velocities when they fall on the surface of the other star. The variation of the orbital elements are derived. It is shown that, to first-order terms in the eccentricity, the secular change of the semimajor axis is equal to the one corresponding to the case of zero initial eccentricity. On the contrary, the secular change of the eccentricity is smaller and it depends on the variations of mass ejection due to the finite eccentricity. 相似文献