共查询到20条相似文献，搜索用时 35 毫秒
1.
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
2.
I. P. Williams 《Celestial Mechanics and Dynamical Astronomy》2003,87(1-2):13-25
The role of tides in deforming and possibly disrupting a secondary body orbiting about a primary body has been known for a considerable time. This was first inspired by the observations of ocean tides on Earth and then seen as playing an important role in the formation and evolution of the Earth–Moon system. Finally, in the beginning of the 20th century it was generally thought to have a significant role in the formation of the solar system through the tidal disruption of the Sun. Here, an overview of the historical developments of the ideas concerned with tidal disruption of a secondary body that can lead to mass loss is given. Some discussion of possible extensions to consider more realistic situations where the secondary body may not be moving on a circular orbit and may not rotate so as to maintain the phase-on configuration to the primary body is also given. 相似文献
3.
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. 相似文献
4.
Christian Circi Ennio Condoleo Emiliano Ortore 《Celestial Mechanics and Dynamical Astronomy》2017,128(2-3):361-382
Taking into consideration a probe moving in an elliptical orbit around a celestial body, the possibility of determining conditions which lead to constant values on average of all the orbit elements has been investigated here, considering the influence of the planetary oblateness and the long-term effects deriving from the attraction of several perturbing bodies. To this end, three equations describing the variation of orbit eccentricity, apsidal line and angular momentum unit vector have been first retrieved, starting from a vectorial expression of the Lagrange planetary equations and considering for the third-body perturbation the gravity-gradient approximation, and then exploited to demonstrate the feasibility of achieving the above-mentioned goal. The study has led to the determination of two families of solutions at constant mean orbit elements, both characterised by a co-planarity condition between the eccentricity vector, the angular momentum and a vector resulting from the combination of the orbital poles of the perturbing bodies. As a practical case, the problem of a probe orbiting the Moon has been faced, taking into account the temporal evolution of the perturbing poles of the Sun and Earth, and frozen solutions at argument of pericentre 0\(^{\circ }\) or 180\(^{\circ }\) have been found. 相似文献
5.
Francois Mignard 《Icarus》1982,49(3):347-366
The dynamics of small dust grains orbiting a planet are investigated when solar radiation pressure forces are added to the planet's gravitational central field. In the first part a set of differential equations is derived in a reference frame linked to the solar motion. The complete solution of these equations is given for particles lying in the planet's orbital plane, and we show that the orbital eccentricity may undergo considerable variation. At the same time the pericenter longitude librates or circulates according to initial conditions. With this result we establish a criterion for any orbiting particle (because of its highly eccentric orbit) to collide with its planet's atmosphere. The case of inclined orbit is studied through a numerical integration and allows us to draw conclusions related to the stability of the orbital plane. All solutions are periodic, with the period being independent of the initial conditions. This last point permits us to investigate the different time scales involved in that problem. Finally, the Poynting-Robertson drag is included, along with the radial radiation pressure forces, and the secular trend is considered. A coupling effect between the two components is ascertained, yielding a systematic behavior in the eccentricity and thus in the pericenter distance. Our solutions generalize the results of S. J. Peale (1966, J. Geophys. Res.71, 911–933) and J. A. Burns, P. Lamy, and S. Soter (1979, Icarus40, 1–48) by allowing eccentricities to be large (of order 1) and inclinations to be nonzero and by considering Poynting-Robertson drag. 相似文献
6.
J. Klačka 《Earth, Moon, and Planets》1993,61(1):57-62
Time evolution of the meteoroid's orbit under the action of the solar electromagnetic radiation is discussed in terms of perihelion and aphelion distances. Perturbation equations for secular changes of orbital elements are written for the most simple case. Initial conditions are formulated for the obtained system of perturbation equations and simple example is presented. 相似文献
7.
Joseph J. F. Liu Philip M. Fitzpatrick 《Celestial Mechanics and Dynamical Astronomy》1975,12(4):463-487
Differential equations are derived for studying the effects of either conservative or nonconservative torques on the attitude motion of a tumbling triaxial rigid satellite. These equations, which are analogous to the Lagrange planetary equations for osculating elements, are then used to study the attitude motions of a rapidly spinning, triaxial, rigid satellite about its center of mass, which, in turn, is constrained to move in an elliptic orbit about an attracting point mass. The only torques considered are the gravity-gradient torques associated with an inverse-square field. The effects of oblateness of the central body on the orbit are included, in that, the apsidal line of the orbit is permitted to rotate at a constant rate while the orbital plane is permitted to precess (either posigrade or retrograde) at a constant rate with constant inclination.A method of averaging is used to obtain an intermediate set of averaged differential equations for the nonresonant, secular behavior of the osculating elements which describe the complete rotational motions of the body about its center of mass. The averaged differential equations are then integrated to obtain long-term secular solutions for the osculating elements. These solutions may be used to predict both the orientation of the body with respect to a nonrotating coordinate system and the motion of the rotational angular momentum about the center of mass. The complete development is valid to first order in (n/w
0)2, wheren is the satellite's orbital mean motion andw
0 its initial rotational angular speed. 相似文献
8.
S. Ferraz Mello 《Celestial Mechanics and Dynamical Astronomy》1972,5(1):80-101
In this paper a new mathematical model is proposed for the study of the effects of the direct solar radiation pressure on the orbit of an artificial Earth satellite. The equations for the first order effects become canonical when a different definition for the orders of magnitude is adopted. This enables us the utilization of the method of Von Zeipel to eliminate all periodic terms. The model leads to the non-existence of pure secular perturbations owing to the direct solar radiation pressure on the metric elements: semi-major axis, eccentricity and inclination. Numerical examples built with an approximation for the shadow function show that the secular inequalities on the angle variables—longitude, perigee and node—are very small. 相似文献
9.
D.J. Scheeres 《Icarus》2007,188(2):430-450
A detailed derivation is given of the effect of solar radiation on the rotational dynamics of asteroids, commonly called the YORP effect. The current derivation goes beyond previous discussions published in the literature and provides a comprehensive secular dynamical analysis of the effect of solar radiation torques acting on a uniformly rotating body, and the evolution of its rotation state over time. Our predicted model has the global radiation properties of the asteroid as explicit parameters, and hence can be specified independent of these parameters. The resulting secular equations for the rotation rate and rotation pole are characterized by three parameters of the body's shape and explicitly includes the effect of thermal inertia on the evolution of these rotation state parameters. With this detailed model, in conjunction with estimated asteroid shapes and poles, we compute the expected YORP torques and dynamic response of several asteroids and the change in rotation rate for specific shapes as a function of obliquity. Finally, we define a convenient dimensionless parameter that is only a function of the body geometry and that can be used to characterize the effects of YORP. 相似文献
10.
L. Anselmo B. Bertotti P. Farinella A. Milani A. M. Nobili 《Celestial Mechanics and Dynamical Astronomy》1983,29(1):27-43
We analyze the perturbations due to solar radiation pressure on the orbit of a high artificial satellite. The latter is modelled in a simplified way (axisymmetric body plus despun antenna emitting a radio beam), which seems suitable to describe the main effects for existing telecommunication satellites. We use the regularized general perturbation equations, by expressing the force in the moving Gauss' reference frame and by expanding the results in terms of some small parameters, referring both to the orbit (small eccentricity and inclination) and to the spacecraft's attitude. Some interesting results are derived, which assess the relative importance of different physical effects and of different parts of the spacecraft in determining the long-term evolution of the orbital elements. 相似文献
11.
Harry Dankowicz 《Celestial Mechanics and Dynamical Astronomy》2002,84(1):1-25
This paper presents quantitative estimates of orbital lifetimes for small dust particles in the vicinity of a spherical asteroid orbiting the Sun on a circular orbit. In particular, the modeling accounts for gravitational interactions with the asteroid and the Sun and radiation pressure from the Sun. The analysis focuses on slow drift of particles in a state-space neighborhood of weakly unstable periodic orbits corresponding to the most tightly bound orbits about the asteroid. Through a Hamiltonian normal-form computation, Nekhoroshev-type estimates are derived that yield regions in state space of effective stability, that is, regions in which the grains would remain over significant periods of time in the absence of other depletion and replenishment mechanisms. 相似文献
12.
Pavol Pástor 《Celestial Mechanics and Dynamical Astronomy》2014,120(1):77-104
Circumstellar dust particles can be captured in a mean-motion resonance (MMR) with a planet and simultaneously be affected by non-gravitational effects. It is possible to describe the secular variations of a particle orbit in the MMR analytically using averaged resonant equations. We derive the averaged resonant equations from the equations of motion in near-canonical form. The secular variations of the particle orbit depending on the orientation of the orbit in space are taken into account. The averaged resonant equations can be derived/confirmed also from Lagrange’s planetary equations. We apply the derived theory to the case when the non-gravitational effects are the Poynting–Robertson effect, the radial stellar wind, and an interstellar wind. The analytical and numerical results obtained are in excellent agreement. We found that the types of orbits correspond to libration centers of the conservative problem. The averaged resonant equations can lead to a system of equations which holds for stationary points in a subset of resonant variables. Using this system we show analytically that for the considered non-gravitational effects, all stationary points should correspond to orbits which are stationary in interplanetary space after an averaging over a synodic period. In an exact resonance, the stationary orbits are stable. The stability is achieved by a periodic repetition of the evolution during the synodic period. Numerical solutions of this system show that there are no stationary orbits for either the exact or non-exact resonances. 相似文献
13.
We investigate the secular dynamics of three-body circumbinary systems under the effect of tides. We use the octupolar non-restricted approximation for the orbital interactions, general relativity corrections, the quadrupolar approximation for the spins, and the viscous linear model for tides. We derive the averaged equations of motion in a simplified vectorial formalism, which is suitable to model the long-term evolution of a wide variety of circumbinary systems in very eccentric and inclined orbits. In particular, this vectorial approach can be used to derive constraints for tidal migration, capture in Cassini states, and stellar spin–orbit misalignment. We show that circumbinary planets with initial arbitrary orbital inclination can become coplanar through a secular resonance between the precession of the orbit and the precession of the spin of one of the stars. We also show that circumbinary systems for which the pericenter of the inner orbit is initially in libration present chaotic motion for the spins and for the eccentricity of the outer orbit. Because our model is valid for the non-restricted problem, it can also be applied to any three-body hierarchical system such as star–planet–satellite systems and triple stellar systems. 相似文献
14.
Carolin Früh Thomas M. Kelecy Moriba K. Jah 《Celestial Mechanics and Dynamical Astronomy》2013,117(4):385-404
The orbital and attitude dynamics of uncontrolled Earth orbiting objects are perturbed by a variety of sources. In research, emphasis has been put on operational space vehicles. Operational satellites typically have a relatively compact shape, and hence, a low area-to-mass ratio (AMR), and are in most cases actively or passively attitude stabilized. This enables one to treat the orbit and attitude propagation as decoupled problems, and in many cases the attitude dynamics can be neglected completely. The situation is different for space debris objects, which are in an uncontrolled attitude state. Furthermore, the assumption that a steady-state attitude motion can be averaged over data reduction intervals may no longer be valid. Additionally, a subset of the debris objects have significantly high area-to-mass ratio (HAMR) values, resulting in highly perturbed orbits, e.g. by solar radiation pressure, even if a stable AMR value is assumed. Note, this assumption implies a steady-state attitude such that the average cross-sectional area exposed to the sun is close to constant. Time-varying solar radiation pressure accelerations due to attitude variations will result in un-modeled errors in the state propagation. This work investigates the evolution of the coupled attitude and orbit motion of HAMR objects. Standardized pieces of multilayer insulation (MLI) are simulated in a near geosynchronous orbits. It is assumed that the objects are rigid bodies and are in uncontrolled attitude states. The integrated effects of the Earth gravitational field and solar radiation pressure on the attitude motion are investigated. The light curves that represent the observed brightness variations over time in a specific viewing direction are extracted. A sensor model is utilized to generate light curves with visibility constraints and magnitude uncertainties as observed by a standard ground based telescope. The photometric models will be needed when combining photometric and astrometric observations for estimation of orbit and attitude dynamics of non-resolved space objects. 相似文献
15.
J. Klačka 《Earth, Moon, and Planets》1994,64(2):125-132
The problem of the action of the solar radiation on the motion of interplanetary dust particle is discussed. Differences between the action of electromagnetic solar radiation and that of the solar wind are explained not only from the point of view of the physical nature of these phenomena but also from the point of view of dust particle's orbital evolution. As for the electromagnetic solar radiation, general equation of motion for the particle is written and the most important consequences are: (i) the process of inspiralling toward the Sun is not the only possible motion - even spiralling from the Sun is also possible, and, (ii) the orbital plane of the particle (its inclination) may change in time. As for the solar wind, the effect corresponding to the fact that solar wind particles spread out from the Sun in nonradial direction causes that the process of inspiralling toward the Sun is in more than 50% less effective than for radial spread out; in the region of the asteroid belt (long period orbits) the process of inspiralling is changed into offspiralling. Also shift in the perihelion of dust particle's orbit exists. 相似文献
16.
A previous theory by the authors for detailed modeling of the binary YORP effect is reviewed and expanded to accommodate doubly-synchronous binary systems, as well as a method for non-dimensionalizing the coefficients for application to binary systems where a shape model to compute its own coefficients is not available. The theory is also expanded to account for the effects of primary J2 and the Sun’s 3rd body perturbation on the secular orbit evolution. The newly expanded theory is applied to the binary near-Earth Asteroid 1999 KW4, for which a detailed shape model is available. The result of simulation of the secular evolutionary equations shows that the KW4 orbit will be double in size in approximately 22,000 years, and will reach the Hill radius in approximately 54,000 years. The simulation also shows that the eccentricity will alternate growing and shrinking in magnitude, depending on the location of the solar node in the body-fixed frame. Therefore the eccentricity is not fixed to evolve in the opposite sign as the semi-major axis unless the circulation of the node (with a period of 500 years) is averaged out as well. The current orbit expansion rate for KW4 of 7 cm per year is shown to be detectable with observations of the mean anomaly which grows quadratically in time with an expanding orbit. Finally, the KW4 results are scaled for application to a number of other binary systems for which detailed shape models are not available. This application shows that the orbits considered can expand to their Hill radius in the range of 104-106 years. This implies rapid formation of binary systems is necessary to support the large percentage of binaries observed in the NEA population. 相似文献
17.
Alexander Wittig Camilla Colombo Roberto Armellin 《Celestial Mechanics and Dynamical Astronomy》2017,128(4):435-452
This paper introduces and combines for the first time two techniques to allow long-term density propagation in astrodynamics. First, we introduce an efficient method for the propagation of phase space densities based on differential algebra (DA) techniques. Second, this DA density propagator is used in combination with a DA implementation of the averaged orbital dynamics through semi-analytical methods. This approach combines the power of orbit averaging with the efficiency of DA techniques. While the DA-based method for the propagation of densities introduced in this paper is independent of the dynamical system under consideration, the particular combination of DA techniques with averaged equations of motion yields a fast and accurate technique to propagate large clouds of initial conditions and their associated probability density functions very efficiently for long time. This enables the study of the long-term behavior of particles subjected to the given dynamics. To demonstrate the effectiveness of the proposed approach, the evolution of a cloud of high area-to-mass objects in Medium Earth Orbit is reproduced considering the effects of solar radiation pressure, the Earth’s oblateness and luni-solar perturbations. The method can propagate 10,000 random fragments and their density for 1 year within a few seconds on a common desktop PC. 相似文献
18.
Daniel J. Scheeres Sepidehsadat Mirrahimi 《Celestial Mechanics and Dynamical Astronomy》2008,101(1-2):69-103
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. 相似文献
19.
R. A. Lyttleton 《Astrophysics and Space Science》1976,44(1):119-140
Revised equations of motion are formulated on more general assumptions than hitherto making allowance for some reflection of sunlight by a dust-particle, and from these the secular rates of change of the orbital elements of the particle are obtained. The equation for the eccentricity yields numerical results for the time taken for given changes in this element to occur. Other elements turn out to be expressible in terms of the eccentricity and thence are effectively also known in terms of the time. More general forms of earlier results are found, and some new mathematical results in the theory of the process are derived. The time of infall to the Sun associated with almost circular initial motion of a particle is calculated, and also the time from an orbit of initially high eccentricity. In this latter case, infall takes place much more rapidly than from a circular orbit of radius comparable with the average distance in the eccentric orbit. The effect on a particle of a long-period comet during a single return is negligible compared with the change in its binding-energy to the Sun that will in general result from planetary action. The possible history of a dust-particle from original capture by the Sun to final infall to the solar surface is briefly considered. 相似文献
20.
The simulated Doppler shifts of the solar Mg I Fraunhofer line produced by scattering on the solar light by asteroidal, cometary, and trans-neptunian dust particles are compared with the shifts obtained by Wisconsin H-Alpha Mapper (WHAM) spectrometer. The simulated spectra are based on the results of integrations of the orbital evolution of particles under the gravitational influence of planets, the Poynting-Robertson drag, radiation pressure, and solar wind drag. Our results demonstrate that the differences in the line centroid position in the solar elongation and in the line width averaged over the elongations for different sizes of particles are usually less than those for different sources of dust. The deviation of the derived spectral parameters for various sources of dust used in the model reached maximum at the elongation (measured eastward from the Sun) between 90° and 120°. For the future zodiacal light Doppler shifts measurements, it is important to pay a particular attention to observing at this elongation range. At the elongations of the fields observed by WHAM, the model-predicted Doppler shifts were close to each other for several scattering functions considered. Therefore the main conclusions of our paper do not depend on a scattering function and mass distribution of particles if they are reasonable. A comparison of the dependencies of the Doppler shifts on solar elongation and the mean width of the Mg I line modeled for different sources of dust with those obtained from the WHAM observations shows that the fraction of cometary particles in zodiacal dust is significant and can be dominant. Cometary particles originating inside Jupiter's orbit and particles originating beyond Jupiter's orbit (including trans-neptunian dust particles) can contribute to zodiacal dust about 1/3 each, with a possible deviation from 1/3 up to 0.1-0.2. The fraction of asteroidal dust is estimated to be ∼0.3-0.5. The mean eccentricities of zodiacal particles located at 1-2 AU from the Sun that better fit the WHAM observations are between 0.2 and 0.5, with a more probable value of about 0.3. 相似文献