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1.
We investigate the Cassini's laws which describe the rotational motion in a 1:1 spin-orbit resonance. When this rotational motion follows the conventional Cassini's laws, the figure axis coincides with the angular momentum axis. In this case we underline the differences between the rotational Hamiltonian for a 'slow rotating' body like the Moon and for a 'fast rotating' body like Phobos. Then, we study a more realistic rotational Hamiltonian where the angle J between the figure axis and the angular momentum axis could be different from zero. This Hamiltonian has not been studied before. We have found a new particular solution for this Hamiltonian which could be seen as an extension of the Cassini's laws. In this new solution the angle J is constant, which is not zero, and the precession of the angular momentum plane is equal to the mean motion of the argument of pericenter of the rotating body. This type of rotational motion is only possible when the orbital eccentricity of the rotating body is not zero. This new law enables describing in particular, the Moon mean rotational motion for which the mean value of the angle J is found to be equal to 103.9±0.7 s of arc. 相似文献
2.
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
3.
An explicit symplectic integrator is constructed for the problem of a rotating planetary satellite on a Keplerian orbit. The
spin vector is fixed perpendicularly to the orbital plane. The integrator is constructed according to the Wisdom-Holman approach:
the Hamiltonian is separated in two parts so that one of them is multiplied by a small parameter. The parameter depends on
the satellite’s shape or the eccentricity of its orbit. The leading part of the Hamiltonian for small eccentricity orbits
is similar to the simple pendulum and hence integrable; the perturbation does not depend on angular momentum which implies
a trivial ‘kick’ solution. In spite of the necessity to evaluate elliptic function at each step, the explicit symplectic integrator
proves to be quite efficient.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
4.
《New Astronomy》2022
In publications presenting analytical results on the non-coplanar motion of a circumbinary planet it was shown that the unperturbed elliptical orbit of the planet undergoes simultaneously two kinds of the precession: the precession of the orbital plane and the precession of the orbit in its own plane. It is also well-known that there is also the relativistic precession of the planetary orbit in its own plane. In the present paper we study a combined effect of the all of the above precessions. For the general case, where the planetary orbit is not coplanar with the stars orbits, we analyzed the dependence of the critical inclination angle ic, at which the precession of the planetary orbit in its own plane vanishes, on the angular momentum L of the planet. We showed that the larger the angular momentum, the smaller the critical inclination angle becomes. We presented the analytical result for ic(L) and calculated the value of L, for which the critical inclination value becomes zero. For the particular case, where the planetary orbit is not coplanar with the stars orbits, we demonstrated analytically that at a certain value of the angular momentum of the planet, the elliptical orbit of the planet would become stationary: no precession. In other words, at this value of the angular momentum, the relativistic precession of the planetary orbit and its precession, caused by the fact that the planet revolves around a binary (rather than single) star, cancel each other out. This is a counterintuitive result. 相似文献
5.
Jeremy Heyl † 《Monthly notices of the Royal Astronomical Society》2007,382(2):915-920
Recent observations of white dwarfs in globular clusters indicate that these stars may get a velocity kick during their time as giants. This velocity kick could originate naturally if the mass loss while on the asymptotic giant branch is slightly asymmetric. If white dwarfs get a kick comparable to the orbital velocity of the binary, the initial Runge–Lenz vector (eccentricity vector) of the orbit is damped to be replaced by a component pointing toward the cross-product of the initial angular momentum and the force. The final eccentricity may be of the order of unity and if the kick is sufficiently large, the system may be disrupted. These results may have important ramifications for the evolution of binary stars and planetary systems. 相似文献
6.
Ballistic capture of spacecraft and celestial bodies by planets of the solar system is studied considering the elliptic restricted
three body model. A preferential region, due to the eccentricity of the planet and the Sun-gravity-gradient effect is found
for the capture phenomenon. An analytical formula is derived which determines the limiting value of the satellite capture
eccentricity ec as a function of the pericenter distance xp and planet’s true anomaly. The analytic values ec are tested by a numerical propagator, which makes use of planetary ephemeris, and only a small difference with respect to
numerical integration is found. It turns out that lower values of ec occur when the planet anomaly is close to zero; that is, capture is easier when the planet is at its perihelion. This fact
is confirmed by the capture of celestial bodies. It is shown that Jupiter comets are generally captured when Jupiter is in
its perihelion region. Ballistic capture is also important in interplanetary missions. The propellant saved using the minimum
ballistic capture eccentricity is evaluated for different missions and compared with respect to the case in which the insertion
orbit is a parabola: a significant saving can be accomplished. 相似文献
7.
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. 相似文献
8.
The classical Öpik theory provides an estimate of the collision probability between two bodies on bound, heliocentric or planetocentric orbits under restrictive assumptions of: (i) constant eccentricity and inclination, and (ii) uniform circulation of the longitude of node and argument of pericenter. These assumptions are violated whenever either of the orbits has a large inclination with respect to the local Laplace plane or large eccentricity, and their motion is perturbed by an exterior (tidal) gravitational field of a planet or the Sun. In this situation, known as the Lidov–Kozai regime, the eccentricity and inclination values exhibit large and correlated oscillations. At the same time, the longitude of node and the argument of pericenter may have strongly nonlinear time evolution, with the latter being even bound to a small interval of values. Here we develop a new Öpik-type collision probability theory which is valid even for highly inclined and/or eccentric orbits of the projectile. We assume that the orbit of the target is circular and in the local Laplace plane. Such a generalized setting is necessary, as an example, to correctly estimate the terrestrial impact fluxes of sporadic micrometeoroids on high-inclination orbits (notably those from the toroidal source and the associated helion and anti-helion arcs). 相似文献
9.
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
10.
Richard Greenberg 《Icarus》1974,23(1):51-58
Tides raised by a satellite on a rotating planet dissipate energy and result in an exchange of angular momentum between the orbit and the spin. A set of diagrams is constructed which shows the evolution of the angular momentum vectors. The results are applied to possible histories of the Uranus system. 相似文献
11.
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
12.
M. A. Vashkov’yak 《Astronomy Letters》2001,27(6):404-409
Data on three recently discovered satellites of Uranus are used to determine basic evolutional parameters of their orbits: the extreme eccentricities and inclinations, as well as the circulation periods of the pericenter arguments and of the longitudes of the ascending nodes. The evolution is mainly investigated by analytically solving Hill’s double-averaged problem for the Uranus-Sun-satellite system, in which Uranus’s orbital eccentricity e U and inclination i U to the ecliptic are assumed to be zero. For the real model of Uranus’s evolving orbit with e U≠0 and i U≠0, we refine the evolutional parameters of the satellite orbits by numerically integrating the averaged system. Having analyzed the configuration and dynamics of the orbits of Uranus’s five outer satellites, we have revealed the possibility of their mutual crossings and obtained approximate temporal estimates. 相似文献
13.
An analytical expansion of the disturbing function arising from direct planetary perturbations on the motion of satellites is derived. As a Fourier series, it allows the investigation of the secular effects of these direct perturbations, as well as of every argument present in the perturbation. In particular, we construct an analytical model describing the evection resonance between the longitude of pericenter of the satellite orbit and the longitude of a planet, and study briefly its dynamic. The expansion developed in this paper is valid in the case of planar and circular planetary orbits, but not limited in eccentricity or inclination of the satellite orbit. 相似文献
14.
Mauri J. Valtonen 《Astrophysics and Space Science》1976,42(2):331-347
The distribution of escape energy, escape velocity and final binary eccentricity in the breakup of a three-body system have been studied, using a recent survey of 25 000 numerical experiments. The dependence of these distributions on the initial parameters have been analysed and were found to agree well with analytical predictions in some cases. The escape velocity depends mainly on the total energy and angular momentum of the system, while the eccentricity is markedly different between planar and three-dimensional systems. 相似文献
15.
Using a consistent perturbation theory for collisionless disk-like and spherical star clusters, we construct a theory of slow
modes for systems having an extended central region with a nearly harmonic potential due to the presence of a fairly homogeneous
(on the scales of the stellar system) heavy, dynamically passive halo. In such systems, the stellar orbits are slowly precessing,
centrally symmetric ellipses (2: 1 orbits). Depending on the density distribution in the system and the degree of halo inhomogeneity,
the orbit precession can be both prograde and retrograde, in contrast to systems with 1: 1 elliptical orbits where the precession
is unequivocally retrograde. In the first paper, we show that in the case where at least some of the orbits have a prograde
precession and the stellar distribution function is a decreasing function of angular momentum, an instability that turns into
the well-known radial orbit instability in the limit of low angular momenta can develop in the system. We also explore the
question of whether the so-called spoke approximation, a simplified version of the slow mode approximation, is applicable
for investigating the instability of stellar systems with highly elongated orbits. Highly elongated orbits in clusters with
nonsingular gravitational potentials are known to be also slowly precessing 2: 1 ellipses. This explains the attempts to use
the spoke approximation in finding the spectrum of slow modes with frequencies of the order of the orbit precession rate.
We show that, in contrast to the previously accepted view, the dependence of the precession rate on angular momentum can differ
significantly from a linear one even in a narrow range of variation of the distribution function in angular momentum. Nevertheless,
using a proper precession curve in the spoke approximation allows us to partially “rehabilitate” the spoke approach, i.e.,
to correctly determine the instability growth rate, at least in the principal (O(α
T−1/2) order of the perturbation theory in dimensionless small parameter α
T, which characterizes the width of the distribution function in angular momentum near radial orbits. 相似文献
16.
17.
《New Astronomy》2021
In our previous paper (hereafter, paper I) we presented analytical results on the non-planar motion of a planet around a binary star for the cases of the circular orbits of the components of the binary. We found that the orbital plane of the planet (the plane containing the “unperturbed” elliptical orbit of the planet), in addition to precessing about the angular momentum of the binary, undergoes simultaneously the precession within the orbital plane. We demonstrated that the analytically calculated frequency of this additional precession is not the same as the frequency of the precession of the orbital plane about the angular momentum of the binary, though the frequencies of both precessions are of the same order of magnitude. In the present paper we extend the analytical results from paper I by relaxing the assumption that the binary is circular – by allowing for a relatively small eccentricity ε of the stars orbits in the binary. We obtain an additional, ε-dependent term in the effective potential for the motion of the planet. By analytical calculations we demonstrate that in the particular case of the planar geometry (where the planetary orbit is in the plane of the stars orbits), it leads to an additional contribution to the frequency of the precession of the planetary orbit. We show that this additional, ε-dependent contribution to the precession frequency of the planetary orbit can reach the same order of magnitude as the primary, ε-independent contribution to the precession frequency. Besides, we also obtain analytical results for another type of the non-planar configuration corresponding to the linear oscillatory motion of the planet along the axis of the symmetry of the circular orbits of the stars. We show that as the absolute value of the energy increases, the period of the oscillations decreases. 相似文献
18.
We have performed a numerical simulation to analyze the energy spectra of escaping planetary O+ and O2+ ions at Mars. The simulated time-energy spectrograms were generated along orbit no. 555 (June 27, 2004) of Mars Express when its Ion Mass Analyzer (IMA)/ASPERA-3 ion instrument detected escaping planetary ions. The simulated time-energy spectrograms are in general agreement with the hypothesis that planetary O+ and O2+ ions far from Mars are accelerated by the convective electric field. The HYB-Mars hybrid model simulation also shows that O+ ions originating from the ionized hot oxygen corona result in a high-energy (E>1 keV) O+ ion population that exists very close to Mars. In addition, the simulation also results in a low-energy (E<0.1 keV) planetary ion population near the pericenter. In the analyzed orbit, IMA did not observe a clear high-energy planetary ion or a clear low-energy planetary ion population near Mars. One possible source for this discrepancy may be the Martian magnetic crustal anomalies because MEX passed over a strong crustal field region near the pericenter, but the hybrid model does not include the magnetic crustal anomalies. 相似文献
19.
M. A. Vashkov’yak 《Solar System Research》2017,51(4):315-326
The well-known twice-averaged Hill problem is considered by taking into account the oblateness of the central body. This problem has several integrable cases that have been studied qualitatively by many scientists, beginning with M.L. Lidov and Y. Kozai. However, no rigorous analytical solution can be obtained in these cases due to the complexity of the integrals. This paper is devoted to studying the case where the equatorial plane of the central body coincides with the plane of its orbital motion relative to the perturbing body, while the satellite itself moves in a polar orbit. A more detailed qualitative study is performed, and an approximate constructive-analytical solution of the evolution system in the form of explicit time dependences of the eccentricity and pericenter argument of the satellite orbit is proposed. The methodical accuracy for the polar orbits of lunar satellites has been estimated by comparison with the numerical solution of the system. 相似文献
20.
R. Brasser 《Monthly notices of the Royal Astronomical Society》2002,332(3):723-728
We determine the maximum dimensionless pericentre distance a third body can have to the barycentre of an extreme mass ratio binary, beyond which no exchange or ejection of any of the binary components can occur. We calculate this maximum distance, q '/ a , where q ' is the pericentre of the third mass to the binary barycentre and a is the semimajor axis of the binary, as a function of the critical value of L 2 E of the system, where L is the magnitude of the angular momentum vector and E is the total energy of the system. The critical value is obtained by calculating L 2 E for the central configuration of the system at the collinear Lagrangian points. In our case we can make approximations for the system when one of the masses is small. We compare the calculated values of the pericentre distance with numerical scattering experiments as a function of the eccentricity of the inner orbit, e , the mutual inclination i and the eccentricity of the outer orbit, e '. These show that the maximum observed value of q '/ a is indeed the critical q '/ a , as expected. However, when e '→1 , the maximum observed value of q '/ a is equal to the critical value calculated when e '=0 , which is contrary to the theory, which predicts exchange distances several orders of magnitude larger for nearly parabolic orbits. This does not occur because changes in the binding energy of the binary are exponentially small for distant, nearly parabolic encounters. 相似文献