共查询到20条相似文献，搜索用时 31 毫秒
1.
Julien Dufey Anne Lemaître Nicolas Rambaux 《Celestial Mechanics and Dynamical Astronomy》2008,101(1-2):141-157
Two space missions dedicated to Mercury (MESSENGER and BepiColombo) aim at understanding its rotation and confirming the existence of a liquid core. This double challenge requires much more accurate models for the spin-orbit resonant rotation of Mercury. The purpose of this paper is to introduce planetary perturbations on Mercury’s rotation using an analytical method and to analyse the influence of the perturbations on the libration in longitude. Applying a perturbation theory based on the Lie triangle, we were able to re-introduce short periodic terms into the averaged Hamiltonian and to compute the evolution of the rotational variables. The perturbations on Mercury’s forced libration in longitude mainly come from the orbital motion of Mercury (with an amplitude around 41 arcsec that depends on the momenta of inertia). It is completed by various effects from Jupiter (11.86 and 5.93 year-periods), Venus (with a 5.66 year-period), Saturn (14.73 year-period), and the Earth (6.58 year-period). The amplitudes of the oscillations due to Jupiter and Venus are approximately 33% and 10% of those from the orbital motion of Mercury and the amplitudes of the oscillations due to Saturn and the Earth are approximately 3% and 2%. We compare the analytical results with the solution obtained from the spin-orbit numerical model SONYR. 相似文献
2.
The solar radiation effects upon the orbital behaviour of an arbitrarily shaped spacecraft (or a solar sail in particular) in a general fixed orientation with respect to the local coordinate frame are investigated. Through introduction of a quasi-angle in the osculating plane, the motion of the orbital plane becomes uncoupled from the in-plane perturbations. Exact solutions in the form of conic sections and logarithmic spirals can readily be formulated for certain specific initial conditions. An effective out-of-plane spiral transfer trajectory is obtained by reversing the force component normal to the orbital plane at specified positions in the orbit. By choosing the appropriate control angles for the sail orientation, any point in space can be reached eventually. In the case of general initial conditions, the long-term orbital behaviour is assessed asymptotically by means of the two-variable expansion procedure. An implicit expression for the eccentricity is derived and explicit results are established by an iteration scheme. The other orbital elements can be expressed in terms of the eccentricity and their asymptotic series for near-circular initial orbits are also obtained. While equations for the higher-order contributions as well as the periodic parts of their solutions can be formulated readily, their secular terms are determined only for a circular initial orbit. 相似文献
3.
Giacomo Giampieri 《Icarus》2004,167(1):228-230
A planetary body moving on an eccentric orbit around the primary is subject to a periodic perturbing potential, affecting its internal mass distribution. In a previous paper (Rappaport et al., 1997, Icarus 126, 313), we have calculated the periodic modulation of the gravity coefficients of degree 2, for a body on a synchronous orbit. Here, the previous analysis is extended by considering also non-synchronous orbits, and by properly accounting for the apparent motion of the primary due to the non uniform motion along the elliptical orbit. The cases of Titan and Mercury are briefly discussed. 相似文献
4.
Gravity-gradient perturbations of the attitude motion of a tumbling tri-axial satellite are investigated. The satellite center of mass is considered to be in an elliptical orbit about a spherical planet and to be tumbling at a frequency much greater than orbital rate. In determining the unperturbed (free) motion of the satellite, a canonical form for the solution of the torque-free motion of a rigid body is obtained. By casting the gravity-gradient perturbing torque in terms of a perturbing Hamiltonian, the long-term changes in the rotational motion are derived. In particular, far from resonance, there are no long-period changes in the magnitude of the rotational angular momentum and rotational energy, and the rotational angular momentum vector precesses abound the orbital angular momentum vector.At resonance, a low-order commensurability exists between the polhode frequency and tumbling frequency. Near resonance, there may be small long-period fluctuations in the rotational energy and angular momentum magnitude. Moreover, the precession of the rotational angular momentum vector about the orbital angular momentum vector now contains substantial long-period contributions superimposed on the non-resonant precession rate. By averaging certain long-period elliptic functions, the mean value near resonance for the precession of the rotational angular momentum vector is obtained in terms of initial conditions. 相似文献
5.
This paper presents a Hamiltonian approach to modelling spacecraft motion relative to a circular reference orbit based on
a derivation of canonical coordinates for the relative state-space dynamics. The Hamiltonian formulation facilitates the modelling
of high-order terms and orbital perturbations within the context of the Clohessy–Wiltshire solution. First, the Hamiltonian
is partitioned into a linear term and a high-order term. The Hamilton–Jacobi equations are solved for the linear part by separation,
and new constants for the relative motions are obtained, called epicyclic elements. The influence of higher order terms and
perturbations, such as Earth’s oblateness, are incorporated into the analysis by a variation of parameters procedure. As an
example, closed-form solutions for J2-invariant orbits are obtained. 相似文献
6.
7.
Eva Tresaco Jean Paulo S. Carvalho Antonio F. B. A. Prado Antonio Elipe Rodolpho Vilhena de Moraes 《Celestial Mechanics and Dynamical Astronomy》2018,130(2):9
This paper provides a method for finding initial conditions of frozen orbits for a probe around Mercury. Frozen orbits are those whose orbital elements remain constant on average. Thus, at the same point in each orbit, the satellite always passes at the same altitude. This is very interesting for scientific missions that require close inspection of any celestial body. The orbital dynamics of an artificial satellite about Mercury is governed by the potential attraction of the main body. Besides the Keplerian attraction, we consider the inhomogeneities of the potential of the central body. We include secondary terms of Mercury gravity field from \(J_2\) up to \(J_6\), and the tesseral harmonics \(\overline{C}_{22}\) that is of the same magnitude than zonal \(J_2\). In the case of science missions about Mercury, it is also important to consider third-body perturbation (Sun). Circular restricted three body problem can not be applied to Mercury–Sun system due to its non-negligible orbital eccentricity. Besides the harmonics coefficients of Mercury’s gravitational potential, and the Sun gravitational perturbation, our average model also includes Solar acceleration pressure. This simplified model captures the majority of the dynamics of low and high orbits about Mercury. In order to capture the dominant characteristics of the dynamics, short-period terms of the system are removed applying a double-averaging technique. This algorithm is a two-fold process which firstly averages over the period of the satellite, and secondly averages with respect to the period of the third body. This simplified Hamiltonian model is introduced in the Lagrange Planetary equations. Thus, frozen orbits are characterized by a surface depending on three variables: the orbital semimajor axis, eccentricity and inclination. We find frozen orbits for an average altitude of 400 and 1000 km, which are the predicted values for the BepiColombo mission. Finally, the paper delves into the orbital stability of frozen orbits and the temporal evolution of the eccentricity of these orbits. 相似文献
8.
R. Vilhena De Moraes P. A. F. Da Silva 《Celestial Mechanics and Dynamical Astronomy》1989,47(3):225-243
Using Hamiltonian formalism the translational-rotational motion of a satellite is studied near a resonance considering the orbital and rotational motions. A first order perturbation theory is derived by Hori's transformation in order to eliminate short and long periodic terms, preserving in the new Hamiltonian secular and resonant terms. This theory is again applied to study the resonant system whose analysis lead us to a system of equations equivalent to the equations of a simple pendulum which is integrable in terms of elliptical integrals. 相似文献
9.
In the following paper we argue that each wind-driving star in relative motion with respect to the ambient interstellar medium experiences a force exerted on its central wind-generating body. The exact magnitude of this force depends on the actual geometry of the counterflow configuration of stellar and interstellar winds for a particular kinematic situation which is especially sensitive to whether the interstellar flow is subsonic or supersonic. It will, however, be demonstrated here that this force is of an accelerating nature, i.e., it operates like a rocket-motor, as long as the peculiar motion of the wind-driving star with respect to the ambient interstellar medium remains subsonic.Here we use a specific analytical model to describe theoretically the specific counterflow configuration for the case of the solar system in a subsonic peculiar motion with respect to the local interstellar medium assuming irrotational and incompressible flows. We can work out a quantitative number for the accelerating force governing the Sun's motion at present. The net reaction force exerted on the solar body is then mediated by the asymmetric boundary conditions to which the distant solar wind field has to adapt.Next we study the indirect action of such a force on orbiting Keplerian objects like planets, planetesimals and comets. Since this force only influences the central solar body, but not the planets themselves, the problem is different from the treatment of a constant perturbation force perturbing the Keplerian orbits. We present a perturbation analysis treating the action of a corresponding position-dependent perturbation force resulting in secular changes of the orbital elements of Keplerian objects. It is found that changes are accumulating more rapidly in time the closer to the sun the orbiting bodies are. Main axis and perihelion distances are systematically increasing. Especially pronounced are changes in the perihelion position angle of the objects. For solar wind mass losses larger than the Sun's present value by a factor of 1000 (T-Tauri phase of the Sun,) the migration periods calculated for the planet Mercury are of the same order of magnitude as that for corresponding general relativistic migration. 相似文献
10.
《Chinese Astronomy and Astrophysics》2022,46(4):346-390
The 1:1 mean motion resonance may be referred to as the lowest order mean motion resonance in restricted or planetary three-body problems. The five well-known libration points of the circular restricted three-body problem are five equilibriums of the 1:1 resonance. Coorbital motion may take different shapes of trajectory. In case of small orbital eccentricities and inclinations, tadpole-shape and horseshoe-shape orbits are well-known. Other 1:1 libration modes different from the elementary ones can exist at moderate or large eccentricities and inclinations. Coorbital objects are not rare in our solar system, for example the Trojans asteroids and the coorbital satellite systems of Saturn. Recently, dozens of coorbital bodies have been identified among the near-Earth asteroids. These coorbital asteroids are believed to transit recurrently between different 1:1 libration modes mainly due to orbital precessions, planetary perturbations, and other possible effects. The Hamiltonian system and the Hill’s three-body problem are two effective approaches to study coorbital motions. To apply the perturbation theory to the Hamiltonian system, standard procedures involve the development of the disturbing function, averaging and normalization, theory of ideal resonance model, secular perturbation theory, etc. Global dynamics of coorbital motion can be revealed by the Hamiltonian approach with a suitable expansion. The Hill’s problem is particularly suitable for the studies on the relative motion of two coorbital bodies during their close encounter. The Hill’s equation derived from the circular restricted three-body problem is well known. However, the general Hill’s problem whose equation of motion takes exactly the same form applies to the non-restricted case where the mass of each body is non-negligible, namely the planetary case. The Hill’s problem can be transformed into a “canonical shape” so that the averaging principle can be applied to construct a secular perturbation theory. Besides the two analytical theories, numerical methods may be consulted, for example the approach of periodic orbit, the surface of section, and the computation of invariant manifolds carried by equilibriums or periodic orbits. 相似文献
11.
12.
V. M. Fedorov 《Solar System Research》2012,46(2):170-176
It can be concluded from the calculations performed of interannual variations of the distance between the Sun and the Earth
in the moments of the Earth’s position in the equinoctial and solstitial points that the mean amplitude (approximately the
same for all the equinoctial and solstitial points) is determined to be equal to 5700 km (at the maximum values being approximately
equal to 15000 km). The values of the solar constant have been calculated on the basis of the data of varying distances, and
the values of its interannual variability (for the period from 1900 up to 2050) have determined. Based on the analysis of
the series, new periodic characteristics of a long-term variation of the solar constant, related to the celestial-mechanical
process, namely, to the perturbed orbital motion of the Earth, are obtained. A three-year cycle is distinguished in the interannual
variability of the solar constant, which alternates with a two-year cycle every eight and eleven years. The amplitude of the
interannual variability in the series of equinoctial and solstitial points is on average about 0.1 W/m2 (about 0.008% of the solar constant value). This is comparable to the interannual variability of the solar constant in the
eleven-year cycle of the solar activity. The series obtained can be represented by alternation of eleven-year and eight-year
cycles. The eleven-year cycle is composed of three three-year cycles and one two-year cycle, and the eight-year cycle is composed
of two three-year cycles and one two-year cycle. 相似文献
13.
Giacomo Lari 《Celestial Mechanics and Dynamical Astronomy》2018,130(8):50
The Galilean satellites’ dynamics has been studied extensively during the last century. In the past it was common to use analytical expansions in order to get simple models to integrate, but with the new generation of computers it became prevalent the numerical integration of very sophisticated and almost complete equations of motion. In this article we aim to describe the resonant and secular motion of the Galilean satellites through a Hamiltonian, depending on the slow angles only, obtained with an analytical expansion of the perturbing functions and an averaging operation. In order to have a model as near as possible to the actual dynamics, we added perturbations and we considered terms that in similar studies of the past were neglected, such as the terms involving the inclinations and the Sun’s perturbation. Moreover, we added the tidal dissipation into the equations, in order to investigate how well the model captures the evolution of the system. 相似文献
14.
Piotr Wąż 《Celestial Mechanics and Dynamical Astronomy》2006,96(3-4):159-167
The dynamics of planetary and star systems including perturbing forces due to the flattering and quadrupole distortion of the bodies is studied. The analytical model describing the perturbations which influence on the orbital motion of extrasolar planetary systems is presented. The calculations of the secular evolution of the mean orbital elements have shown that the effects related to the shape of the body are more important than the ones due to the quadrupole distortion. 相似文献
15.
The time series of total solar irradiance (TSI) satellite observations since 1978 provided by ACRIM and PMOD TSI composites are studied. We find empirical evidence for planetary-induced forcing and modulation of solar activity. Power spectra and direct data pattern analysis reveal a clear signature of the 1.09-year Earth-Jupiter conjunction cycle, in particular during solar cycle 23 maximum. This appears to suggest that the Jupiter side of the Sun is slightly brighter during solar maxima. The effect is observed when the Earth crosses the Sun-Jupiter conjunction line every 1.09 years. Multiple spectral peaks are observed in the TSI records that are coherent with known planetary harmonics such as the spring, orbital and synodic periods among Mercury, Venus, Earth and Jupiter: the Mercury-Venus spring-tidal cycle (0.20 year); the Mercury orbital cycle (0.24 year); the Venus-Jupiter spring-tidal cycle (0.32 year); the Venus-Mercury synodic cycle (0.40 year); the Venus-Jupiter synodic cycle (0.65 year); and the Venus-Earth spring tidal cycle (0.80 year). Strong evidence is also found for a 0.5-year TSI cycle that could be driven by the Earth’s crossing the solar equatorial plane twice a year and may indicate a latitudinal solar-luminosity asymmetry. Because both spring and synodic planetary cycles appear to be present and the amplitudes of their TSI signatures appear enhanced during sunspot cycle maxima, we conjecture that on annual and sub-annual scales both gravitational and electro-magnetic planet-sun interactions and internal non-linear feedbacks may be modulating solar activity. Gravitational tidal forces should mostly stress spring cycles while electro-magnetic forces could be linked to the solar wobbling dynamics, and would mostly stress the synodic cycles. The observed statistical coherence between the TSI records and the planetary harmonics is confirmed by three alternative tests. 相似文献
16.
Noboru Takeichi 《Celestial Mechanics and Dynamical Astronomy》2010,108(4):405-416
The parametric excitation of a gravity gradient stabilized spacecraft induced by the periodic solar pressure torque is discussed.
The solar pressure torque in the linearized equations of motion appears as linear terms with periodic coefficients. The attitude
stability is analyzed numerically through the calculation of the Floquet multiplier. The perturbation method is also applied
to identify the instability condition analytically. It is made clear that the periodic solar pressure torque can destabilize
the coupled roll and yaw attitude motion of the spacecraft. It is also shown that the conditions of parametric resonance are
included in the gravity gradient stability condition. Nonlinear simulations are also carried out to verify the effect of the
parametric resonance. The numerical simulation using actual parameters shows that the spacecraft inevitably experiences a
large amplitude attitude motion due to the periodic solar pressure torque even if the gravity gradient stability condition
is satisfied. 相似文献
17.
I. V. Tupikova 《Celestial Mechanics and Dynamical Astronomy》2009,104(1-2):129-144
A new mathematically correct approach to construct an averaging procedure for the motion of a massless body around the central body perturbed by fully interacting planets is developed and the errors of the standard solution are discussed. The new technique allows to combine the advantages of the Hamiltonian representation with the usage of standard osculating elements in combination with all the standard expansions of the perturbing functions. The main idea is to introduce new additional variables conjugate to all the standard elements and to work in a corresponding super phase space. In this way, the number of variables is doubled at first, but one has to deal with only one Hamiltonian. The artificially introduced variables disappear from the final averaged equations as well as from the transformation formulae connecting the osculating and the mean elements. 相似文献
18.
M. M. Koval’chuk M. B. Hirnyak O. A. Baran M. I. Stodilka Ye. B. Vovchyk A. I. Bilinsky Ya. T. Blahodyr N. V. Virun S. V. Apunevych 《Kinematics and Physics of Celestial Bodies》2017,33(6):295-301
The investigation of the solar wind and geomagnetic activity parameters' effect on variations of the orbital motion periods of artificial satellites has been continued. The periods of orbital motion of uncontrolled satellites from the database of the Ukrainian network of optical stations (UNOS) for 2012–2014 was used. The data have been compared with the values of geomagnetic planetary index K and the energy spectra of protons and electrons obtained by the GEOS satellites in events during which the orbital periods have changed. It is shown that, in the energy spectra of the proton and electron fluxes, there is no effect of softening the spectrum with time at the time of the flare appearance. This indicates the possibility of particle accumulation above the active region (AR), which entails further continuous energy emission of the solar flare from AR. Dependences have been obtained between the geomagnetic activity and the solar wind speed at a given interplanetary magnetic field strength during the periods under study for the changes in the orbital motion periods of satellites. The corresponding correlation coefficients are 0.93–0.96. 相似文献
19.
The magnetic field of Mercury and the structure and dynamics of Mercury's magnetosphere, which will be studied by the spacecraft orbiting Mercury, are strongly influenced by the interaction of the solar wind with Mercury. In order to understand the internal magnetic field, it will be necessary to correct the observations of the external field for the distortions produced by the solar wind. Understanding of the solar wind interaction with Mercury is essential for understanding the structure and dynamics of the magnetosphere and phenomena such as magnetic storms. Helios 1 and 2 made a number of passes in the region traversed by the orbit of Mercury, and each pass provided a sample of the solar wind environment of Mercury. This paper reviews the plasma and magnetic field observations from Helios that provide a general basis for interpreting the observations of Mercury that will be made by orbiting spacecraft. The variables that govern the structure and dynamics of the magnetospheres of Mercury and Earth are approximately 5–10 times larger at Mercury than at Earth. Thus, the solar wind interaction with Mercury will be much stronger than the interaction with Earth. Moreover, the solar wind at Mercury is probably more variable than that at Earth. There is a clear need for measurements of the solar wind during the approach of spacecraft to Mercury and while they are in orbit around Mercury. 相似文献
20.
Using specialized codes for the search of periodic and linear components we show that direct solar radiation leads to short-period
variations of all the orbital elements of geosynchronous satellites. The variation period of the semimajor axis a, orbit inclination i and the longitude of the ascending node Ω is 1 day. Eccentricity e, the argument of perigee ω and the mean anomaly M vary with a period of 0.5 days. Direct solar radiation also leads to long-period variations in e, ω and M with a period of 1 year. The elements a, i and Ω undergo variations only in the amplitude of diurnal variations with a period of 1 or 0.5 years. Secular variability
(linear components) are not detected. To obtain the initial value array of the orbital elements we used the Lagrange equations
of perturbed motion in the form of a Gaussian with their subsequent integration via a special method of harmonics: the values
of the derived orbital elements, obtained from the Lagrange equations, were presented through the periodic functions that
are easy to integrate. 相似文献