首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 778 毫秒
1.
The behaviour of the argument of the pericentre is investigated for the orbit of an artificial satellite which is moving under the potential when the inclination of the orbit is close to thecritical value tan?1 2. The theory is developed to first order and it is applicable to all values of the eccentricity, with the exception of those in the neighbourhood of zero and unity. Four principal types of behaviour are noted and these are illustrated in appropriate phase-plane diagrams. It is shown that the two types which exhibit double libration in the argument of the pericentre are restricted to a relatively small domain in the (a, e)-plane of possible motions. Moreover, it is demonstrated that for double libration to occur it is necessary, but not sufficient, that \(e > \sqrt 6/13\) . The ranges of values of the inclination for which libration of the pericentre is a possibility are given for the more important cases. The general results are applied to the specific case of artificial Earth satellites whose orbits are inclined to the equator at angles close to the value of the critical inclination.  相似文献   

2.
We present a detailed survey of the dynamical structure of the phase space around the new moons of the Pluto–Charon system. The spatial elliptic restricted three-body problem was used as model and stability maps were created by chaos indicators. The orbital elements of the moons are in the stable domain on the semimajor axis, eccentricity and inclination spaces. The structures related to the 4:1 and 6:1 mean motion resonances are clearly visible on the maps. They do not contain the positions of the moons, confirming previous studies. We showed the possibility that Nix might be in the 4:1 resonance if its argument of pericentre or longitude of node falls in a certain range. The results strongly suggest that Hydra is not in the 6:1 resonance for arbitrary values of the argument of pericentre or longitude of node.  相似文献   

3.
In this communication we present an analytical model for the restricted three-body problem, in the case where the perturber is in a parabolic orbit with respect to the central mass. The equations of motion are derived explicitly using the so-called Global Expansion of the disturbing function, and are valid for any eccentricity of the massless body, as well as in the case where both secondary masses have crossing orbits. Integrating the equations of motion over the complete passage of the perturber through the system, we are then able to construct a first-order algebraic mapping for the change in semimajor axis, eccentricity and inclination of the perturbed body.Comparisons with numerical solutions of the exact equations show that the map yields precise results, as long as the minimum distance between both bodies is not too small. Finally, we discuss several possible applications of this model, including the evolution of asteroidal satellites due to background bodies, and simulations of passing stars on extra-solar planets.  相似文献   

4.
I consider a satellite moving around a non-spherical body of mass M and equatorial radius R, and calculate its orbital precessions caused by the body’s octupolar mass moment J 4. I consider only the effects averaged over one orbital period T of the satellite. I give exact formulas, not restricted to any special values of either the eccentricity e or the inclination i of the satellite’s orbit. I do not assume any preferential orientation for the body’s spin axis ${\boldsymbol{\hat{{\mathbf{k}}}}}$ because in many cases of potential interest (exoplanets, neutron stars, black holes) it is poorly known or unknown at all.  相似文献   

5.
The critical inclination is of special interest in artificial satellite theory. The critical inclination can maintain minimal deviations of eccentricity and argument of pericentre from the initial values, and orbits at this inclination have been applied to some space missions. Most previous researches about the critical inclination were made under the assumption that the oblateness term J 2 is dominant among the harmonic coefficients. This paper investigates the extension of the critical inclination where the concept of the critical inclination is different from that of the traditional sense. First, the study takes the case of Venus for instance, and provides some preliminary results. Then for general cases, given the values of argument of pericentre and eccentricity, the relationship between the multiplicity of the solutions for the critical inclination and the values of J 2 and J 4 is analyzed. Besides, when given certain values of J 2 and J 4, the relationship between the multiplicity of the solutions for the critical inclination and the values of semimajor axis and eccentricity is studied. The results show that for some cases, the value of the critical inclination is far away from that of the traditional sense or even has multiple solutions. The analysis in this paper could be used as starters of correction methods in the full gravity field of celestial bodies.  相似文献   

6.
Rodney S. Gomes 《Icarus》2011,215(2):661-668
Numerical integrations of the equations of motion of the giant planets and scattering particles show that there is a possible orbital itinerary that a particle may follow from a scattering mode up to a stable position near the orbit of 2004 XR190. This orbital evolution requires that the particle gets trapped in a mean motion resonance with Neptune coupled with the Kozai resonance. Imposing migration on Neptune while a particle is experiencing both resonances can entail an escape from resonance at a low particle’s eccentricity. This eccentricity and the associated inclination are always similar to those of 2004 XR190. I conclude that 2004 XR190 was most likely a scattered object that went through those resonance processes and was eventually deposited at its current position. By the same argument, it is expected that there must exist several other objects with similar semimajor axis, eccentricity and inclination as those of 2004 XR190.  相似文献   

7.
An astronomical body of mass M and radius R which is non-spherically symmetric generates a free space potential U which can be expanded in multipoles. As such, the trajectory of a test particle orbiting it is not a Keplerian ellipse fixed in the inertial space. The zonal harmonic coefficients J 2,J 3,… of the multipolar expansion of the potential cause cumulative orbital perturbations which can be either harmonic or secular over time scales larger than the unperturbed Keplerian orbital period T. Here, I calculate the averaged rates of change of the osculating Keplerian orbital elements due to the odd zonal harmonic J 3 by assuming an arbitrary orientation of the body’s spin axis \(\hat{\boldsymbol{k}}\) . I use the Lagrange planetary equations, and I make a first-order calculation in J 3. I do not make a-priori assumptions concerning the eccentricity e and the inclination i of the satellite’s orbit.  相似文献   

8.
The focus of this paper is the design and station keeping of repeat-groundtrack orbits for Sun-synchronous satellites. A method to compute the semimajor axis of the orbit is presented together with a station-keeping strategy to compensate for the perturbation due to the atmospheric drag. The results show that the nodal period converges gradually with the increase of the order used in the zonal perturbations up to \(J_{15}\). A differential correction algorithm is performed to obtain the nominal semimajor axis of the reference orbit from the inputs of the desired nodal period, eccentricity, inclination and argument of perigee. To keep the satellite in the proximity of the repeat-groundtrack condition, a practical orbit maintenance strategy is proposed in the presence of errors in the orbital measurements and control, as well as in the estimation of the semimajor axis decay rate. The performance of the maintenance strategy is assessed via the Monte Carlo simulation and the validation in a high fidelity model. Numerical simulations substantiate the validity of proposed mean-elements-based orbit maintenance strategy for repeat-groundtrack orbits.  相似文献   

9.
《Planetary and Space Science》2007,55(10):1388-1397
A new non-singular analytical theory for the motion of near Earth satellite orbits with the air drag effect is developed in terms of the Kustaanheimo and Stiefel (KS) uniformly regular canonical elements, by assuming the atmosphere to be oblate diurnally varying with constant density scale height. The series expansions include up to third-order terms in eccentricity and c (a small parameter dependent on the flattening of the atmosphere). Only two of the nine equations are solved analytically to compute the state vector and change in energy at the end of each revolution, due to symmetry in the equations of motion. Numerical comparisons of the important orbital parameters semimajor axis and eccentricity up to 1000 revolutions, obtained with the present solution, with the third-order analytical theories of Swinerd and Boulton and in terms of the KS elements, with respect to the numerically integrated values, show the superiority of the present solution over the other two theories over a wide range of eccentricity, perigee height and inclination.  相似文献   

10.
The long period dynamics of Sun-synchronous orbits near the critical inclination 116.6° are investigated. It is known that, at the critical inclination, the average perigee location is unchanged by Earth oblateness. For certain values of semimajor axis and eccentricity, orbit plane precession caused by Earth oblateness is synchronous with the mean orbital motion of the apparent Sun (a Sun-synchronism). Sun-synchronous orbits have been used extensively in meteorological and remote sensing satellite missions. Gravitational perturbations arising from an aspherical Earth, the Moon, and the Sun cause long period fluctuations in the mean argument of perigee, eccentricity, inclination, and ascending node. Double resonance occurs because slow oscillations in the perigee and Sun-referenced ascending node are coupled through the solar gravity gradient. It is shown that the total number and infinitesimal stability of equilibrium solutions can change abruptly over the Sun-synchronous range of semimajor axis values (1.54 to 1.70 Earth radii). The effect of direct solar radiation pressure upon certain stable equilibria is investigated.  相似文献   

11.
Hill stability of a triple system with an inner binary of large mass ratio   总被引：1，自引：0，他引：1  
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   

12.
The recent discovery of extrasolar planets and planetary systems has raised many new research problems for astronomers. It has become apparent that the newly discovered systems differ significantly from the Solar System. In particular, many massive planets of other stars, in contrast to Jupiter, have large orbital eccentricities. In the present paper, we investigate several dynamic implications of this finding. Numerical integration results show that the orbits of low-mass planets in such systems usually have large evolving eccentricities. If the motion remains regular and no close encounters occur, the orbital evolution can be described analytically by using secular perturbations of Laplace–Lagrange equations. In terms of the Lagrange variables, the trajectories are circles, and the semimajor axis remains constant. The loss of the regularity of motion is normally followed by a nonmonotone synchronous increase in the semimajor axis and eccentricity, and the orbit becomes similar to that of a large-period comet. Narrow resonance-related regions include more complex motions.  相似文献   

13.
Exploring weakly perturbed Keplerian motion within the restricted three-body problem, Lidov (Planet Space Sci 9:719–759, 1962) and, independently, Kozai (Astron J 67:591–598, 1962) discovered coupled oscillations of eccentricity and inclination (the KL cycles). Their classical studies were based on an integrable model of the secular evolution, obtained by double averaging of the disturbing function approximated with its first non-trivial term. This was the quadrupole term in the series expansion with respect to the ratio of the semimajor axis of the disturbed body to that of the disturbing body. If the next (octupole) term is kept in the expression for the disturbing function, long-term modulation of the KL cycles can be established (Ford et al. in Astrophys J 535:385–401, 2000; Naoz et al. in Nature 473:187–189, 2011; Katz et al. in Phys Rev Lett 107:181101, 2011). Specifically, flips between the prograde and retrograde orbits become possible. Since such flips are observed only when the perturber has a nonzero eccentricity, the term “eccentric Kozai–Lidov effect” (or EKL effect) was proposed by Lithwick and Naoz (Astrophys J 742:94, 2011) to specify such behavior. We demonstrate that the EKL effect can be interpreted as a resonance phenomenon. To this end, we write down the equations of motion in terms of “action-angle” variables emerging in the integrable Kozai–Lidov model. It turns out that for some initial values the resonance is degenerate and the usual “pendulum” approximation is insufficient to describe the evolution of the resonance phase. Analysis of the related bifurcations allows us to estimate the typical time between the successive flips for different parts of the phase space.  相似文献   

14.
The formulas for the Poisson bracket of a perturbed two-body problem and a perturbed planetary problem are found in different systems of Keplerian elements. As with canonical parametrization, the Poisson bracket is equal to a linear combination of partial brackets, but it contains coefficients depending on semimajor axis, eccentricity, and inclination. A simple relation between the Poisson brackets and matrices of coefficients of Lagrange-type equations determining the variations of osculating elements is derived. The Poisson bracket of D'Alembertian functions is proved to be a D'Alembertian one by itself.  相似文献   

15.
An analysis is presented of the orbital injection errors for the Lageos III satellite mission. Several methods are introduced for the solution of the Inverse Problem in the Theory of Errors. The novelty of the present approach consists in the use of the full geopotential covariance matrix in the error propagation equations. The GEM-T1 covariance matrix is used. It is found that by properly accounting for the correlation among the even zonal harmonic coefficients the acceptable error bounds increase by an order of magnitude with respect to the case when only the variances are used. The most stringent constraint, even when using the full covariance, is on inclination, whose nominal value must be realized within approximately 0.1° for the recovery of the Lense-Thirring precession to be successful at the 3% level (accounting only for injection errors). The associated tolerance in the semimajor axis is about 30 km while that in eccentricity is approximately 0.2. However, if the errors in semimajor axis and eccentricity can be kept to the routinely achievable levels respectively of 10 km and 0.004, then the tolerance in inclination can be relaxed to 0.2°.  相似文献   

16.
The restricted three-body problem describes the motion of a massless particle under the influence of two primaries of masses 1− μ and μ that circle each other with period equal to 2π. For small μ, a resonant periodic motion of the massless particle in the rotating frame can be described by relatively prime integers p and q, if its period around the heavier primary is approximately 2π p/q, and by its approximate eccentricity e. We give a method for the formal development of the stable and unstable manifolds associated with these resonant motions. We prove the validity of this formal development and the existence of homoclinic points in the resonant region. In the study of the Kirkwood gaps in the asteroid belt, the separatrices of the averaged equations of the restricted three-body problem are commonly used to derive analytical approximations to the boundaries of the resonances. We use the unaveraged equations to find values of asteroid eccentricity below which these approximations will not hold for the Kirkwood gaps with q/p equal to 2/1, 7/3, 5/2, 3/1, and 4/1. Another application is to the existence of asymmetric librations in the exterior resonances. We give values of asteroid eccentricity below which asymmetric librations will not exist for the 1/7, 1/6, 1/5, 1/4, 1/3, and 1/2 resonances for any μ however small. But if the eccentricity exceeds these thresholds, asymmetric librations will exist for μ small enough in the unaveraged restricted three-body problem.  相似文献   

17.
The averaged spin-orbit resonant motion of Mercury is considered, with e the orbital eccentricity, and i o the orbital inclination introduced as very slow functions of time, given by any secular planetary theory. The basis is our Hamiltonian approach (D’Hoedt, S., Lemaître, A.: Celest. Mech. Dyn. Astron. 89:267–283, 2004) in which Mercury is considered as a rigid body. The model is based on two degrees of freedom; the first one is linked to the 3:2 resonant spin-orbit motion, and the second one to the commensurability of the rotational and orbital nodes. Mercury is assumed to be very close to the Cassini equilibrium of the model. To follow the motion of rotation close to this equilibrium, which varies with respect to time through e and i o , we use the adiabatic invariant theory, extended to two degrees of freedom. We calculate the corrections (remaining functions) introduced by the time dependence of e and i o in the three steps necessary to characterize the frequencies at the equilibrium. The conclusion is that Mercury follows the Cassini equilibrium (stays in the Cassini forced state), in an adiabatic behavior: the area around the equilibrium does not change by more than ${\varepsilon}$ for times smaller than ${\frac{1}{\varepsilon}}$ . The role of the inclination and the eccentricity can be dissociated and measured in each step of the canonical transformation.  相似文献   

18.
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   

19.
The heating of a spinning artificial satellite by natural radiation sources such as the Sun and the Earth results in temperature gradients arising across the satellite's surface. The corresponding anisotropic emission of thermal radiation leads to a recoil force, commonly referred to as “thermal force”. A quantitative theory of this effect is developed, based on more general assumptions than used so far, to model such radiation forces on spherically symmetric LAGEOS-like satellites. In particular, the theory holds for any ratio of the three basic timescales of the problem: the rotation period of the satellite, the orbital period around the Earth, and the relaxation time for the thermal processes. Thus, the simplifying assumption of a comparatively fast rotational motion is avoided, which will fail for LAGEOS within the next decade, owing to magnetic dissipation effects. A number of predictions about the future behaviour of non-gravitational long-term orbital perturbations of LAGEOS become possible with the new theory. In particular the Yarkovsky-Schach thermal force effects are studied arising as a consequence of the solar radiation flux onto the satellite, periodically interrupted by eclipses. Starting on about year 2005, the orbital perturbation effects predicted by the new theory are substantially different from those inferred in the fast-rotation case. This holds not only for the long-term semimajor axis effects, but also for eccentricity and inclination perturbations.  相似文献   

20.
A theory of galactic morphology results from the consideration of isoplethic surfaces in states of geometric equilibrium within the theory of general relativity. In the linearized case, one solves ?2ψ+ρ2ψ=0 on the surface of an oblate spheroid with unit semimajor axis and eccentricity ε. The surface defined by $$x^2 + y^2 + z^2 /(1 - \varepsilon ^2 ) = {\text{exp (}}\psi {\text{)}}$$ are then equilibrium isopleths. The resulting morphological system contains two continuous parameters (ε and the norm of ψ) and an integer-valued parametern. The system includes the ellipticals as special cases, and the various available profiles are given for a variety of values of the parameters. The forms are sufficiently varied as to represent NGC 3115, 128, 7332, and IC 3973. These forms cease to be enigmatic for they fit into an orderly sequence progressing out of the ellipticals and have equilibrium interpretations as previously obtained only for the ellipticals.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号