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1.
The Halo orbits originating in the vicinities of both,L 1 andL 2 grow larger, but shorter in period, as they shift towards the Moon. There is in each case a narrow band of stable orbits roughly half-way to the Moon. Nearer to the Moon, the orbits are fairly well-approximated by an almost rectilinear analysis. TheL 2 family shrinks in size as it approaches the Moon, becoming stable again shortly before penetrating the lunar surface. TheL 1-family becomes longer and thinner as it approaches the Moon, with a second narrow band of stable orbits with perilune, however, below the lunar surface.  相似文献   

2.
Quasi-periodic orbits about the translunar libration point   总被引：2，自引：0，他引：2  
Analytical solutions for quasi-periodic orbits about the translunar libration point are obtained by using the method of Lindstedt-Poincaré and computerized algebraic manipulations. The solutions include the effects of nonlinearities, lunar orbital eccentricity, and the Sun's gravitational field. For a small-amplitude orbit, the orbital path as viewed from the Earth traces out a Lissajous figure. This is due to a small difference in the fundamental frequencies of the in-plane and out-of-plane oscillations. However, when the amplitude of the in-plane oscillation is greater than 32 379 km, there is a corresponding value of the out-of-plane amplitude that will produce a path where the fundamental frequencies are equal. This synchronized trajectory describes a halo orbit of the Moon.  相似文献   

3.
Three-dimensional periodic motions of three bodies are shown to exist in the infinitesimal neighbourhood of their collinear equilibrium configurations. These configurations and some characteristic quantities of the emanating three-dimensional periodic orbits are given for many values of the two mass parameters, =m 2/(m 1+m 2) andm 3, of the general three-body problem, under the assumption that the straight line containing the bodies at equilibrium rotates with unit angular velocity. The analysis of the small periodic orbits near the equilibrium configurations is carried out to second-order terms in the small quantities describing the deviation from plane motion but the analytical solution obtained for the horizontal components of the state vector is valid to third-order terms in those quantities. The families of three-dimensional periodic orbits emanating from two of the collinear equilibrium configurations are continued numerically to large orbits. These families are found to terminate at large vertical-critical orbits of the familym of retrograde periodic orbits ofm 3 around the primariesm 1 andm 2. The series of these termination orbits, formed when the value ofm 3 varies, are also given. The three-dimensional orbits are computed form 3=0.1.  相似文献   

4.
The purpose of this paper is to study a transfer strategy from the vicinity of the Earth to a halo orbit around the equilibrium pointL 1 of the Earth-Sun system. The study is done in the real solar system (we use the DE-118 JPL ephemeris in the simulations of motion) although some simplified models, such as the restricted three body problem (RTBP) and the bicircular problem, have been also used in order to clarify the geometrical aspects of the problem. The approach used in the paper makes use of the hyperbolic character of the halo orbits under consideration. The invariant stable manifold of these orbits enables the transfer to be achieved with, theoretically, only one manoeuvre: the one of insertion into the stable manifold. For the total v required, the figures obtained are similar to the ones given by the standard procedures of optimization.  相似文献   

5.
In the three-dimensional restricted three-body problem, it is known that there exists a near one-to-one commensurability ratio between the planar angular frequencies (s 1, 2, 3) and the corresponding angular frequency (S 2) in thez-direction at the three collinear equilibria (L 1, 2, 3), which is significant for small and practically important values of the mass parameter (). When the more massive primary is treated as an oblate spheroid with its equatorial plane coincident with the plane of motion of the primaries, it is established that oblateness induces a one-to-one commensurability at the exterior pointL 3 (to the right of the more massive primary) and at the interior pointL 2 for 01/2 and that atL 1 no such commensurability exists. However, the values of the oblateness coefficient (A 1) involved atL 2 are too high to have any practical significance, while those atL 3 being small for small values of may be useful for generating periodic orbits of the third kind.  相似文献   

6.
We consider periodic halo orbits about artificial equilibrium points (AEP) near to the Lagrange points L 1 and L 2 in the circular restricted three body problem, where the third body is a low-thrust propulsion spacecraft in the Sun–Earth system. Although such halo orbits about artificial equilibrium points can be generated using a solar sail, there are points inside L 1 and beyond L 2 where a solar sail cannot be placed, so low-thrust, such as solar electric propulsion, is the only option to generate artificial halo orbits around points inaccessible to a solar sail. Analytical and numerical halo orbits for such low-thrust propulsion systems are obtained by using the Lindstedt Poincaré and differential corrector method respectively. Both the period and minimum amplitude of halo orbits about artificial equilibrium points inside L 1 decreases with an increase in low-thrust acceleration. The halo orbits about artificial equilibrium points beyond L 2 in contrast show an increase in period with an increase in low-thrust acceleration. However, the minimum amplitude first increases and then decreases after the thrust acceleration exceeds 0.415 mm/s2. Using a continuation method, we also find stable artificial halo orbits which can be sustained for long integration times and require a reasonably small low-thrust acceleration 0.0593 mm/s2.  相似文献   

7.
Isentropic oscillations of a star in thermal imbalance are defined as those for which, at every istant, the entropy of each mass element of the configuration in the perturbed motion is equal to that of the same mass element in the unperturbed motion.The solution of the equations describing such isentropic oscillations and written in terms of the infinitesimal displacement r(r 0,t) is presented in terms of asymptotic expansions up to the first order in the parameter /t s where is the adiabatic pulsation period for the fundamental mode andt s , a slow time scale of the order of the Kelvin-Helmholtz time.The solution obtained allows one to define, unambiguously, an isentropic part to the coefficient of vibrational stability of arbitrary stellar models in thermal imbalance, as well as to derive a general formula relating the results of a stability analysis in terms of r and r/r.Application of this general solution to the simple case of homologous motion is also given.  相似文献   

8.
Secondary explosions of the primary ice fragments ejected in the explosion of the electrolyzed massive ice envelopes of the Galilean satellites are capable of imparting velocities of up to ~5km s–1 to the secondary fragments. As a result, the secondary fragments can enter the orbits of the irregular satellites (Agafonova and Drobyshevski, 1984b) and the Trojan libration orbits. In the latter case a perturbation velocity of V 0.3–2 km s–1 is sufficient.The primary fragments ejected by the gravitational perturbations due to the Galilean satellites sunward from Jupiter's sphere of action move faster relative to the Sun than Jupiter does and therefore reach their first aphelion ahead of Jupiter in the neighborhood of L 4. At the same time the fragments propelled from Jupiter's sphere of action beyond the planet's orbit approach it again in their perihelia behind Jupiter in the region of L 5. The concentration of the fragments and, hence, the frequency of their collisions and explosions at L 4 turn out to be much greater than those at L 5. As a result, the number of the secondary fragments of diameter 15 km captured into libration orbits ahead of Jupiter can be as high as many hundreds and should exceed by more than a factor 3.5 that captured behind Jupiter.Since the icy mix of the fragments contains hydrocarbons and particulate material (silicates and the like), after ice sublimation from the surface layers the Trojans should reveal type C and RD spectra typical for Jupiter's irregular satellites, comet nuclei and other distant ice bodies of similar origin. Among the Trojans there cannot be rocky or metallic objects which are known to exist in the main asteroid belt.It is shown that a velocity perturbation of 150–200 m s–1 resulting from a purely mechanical impact of two bodies may be sufficient to move collision fragments from the orbits of the Trojans to horseshoe-shaped trajectories with a subsequent transfer to the cometary orbits of Jupiter's family.  相似文献   

9.
A number of Jupiter family comets such as Otermaand Gehrels 3make a rapid transition from heliocentric orbits outside the orbit of Jupiter to heliocentric orbits inside the orbit of Jupiter and vice versa. During this transition, the comet can be captured temporarily by Jupiter for one to several orbits around Jupiter. The interior heliocentric orbit is typically close to the 3:2 resonance while the exterior heliocentric orbit is near the 2:3 resonance. An important feature of the dynamics of these comets is that during the transition, the orbit passes close to the libration points L 1and L 2, two of the equilibrium points for the restricted three-body problem for the Sun-Jupiter system. Studying the libration point invariant manifold structures for L 1and L 2is a starting point for understanding the capture and resonance transition of these comets. For example, the recently discovered heteroclinic connection between pairs of unstable periodic orbits (one around the L 1and the other around L 2) implies a complicated dynamics for comets in a certain energy range. Furthermore, the stable and unstable invariant manifold tubes associated to libration point periodic orbits, of which the heteroclinic connections are a part, are phase space conduits transporting material to and from Jupiter and between the interior and exterior of Jupiter's orbit.  相似文献   

10.
We have investigated an improved version of the classic restricted three-body problem where both primaries are considered oblate and are enclosed by a homogeneous circular planar cluster of material points centered at the mass center of the system. In this dynamical model we have examined the effect on the number and on the linear stability of the equilibrium locations of the small particle due to both, the primaries’ oblateness and the potential created by the circular cluster. We have drawn the zero-velocity surfaces and we have found that in addition to the usual five Lagrangian equilibrium points of the classic restricted three-body problem, there exist two new collinear points L n1,L n2 due to the potential from the circular cluster of material points. Numerical investigations reveal that with the increase in the mass of the circular cluster of material points, L n2 comes nearer to the more massive primary, while L n1 moves away from it. Owing to oblateness of the bodies, L n1 comes nearer to the more massive primary, while L n2 moves towards the less massive primary. The collinear equilibrium points remain unstable, while the triangular points are stable for 0<μ<μ c and unstable for $\mu_{c} \le \mu \le \frac{1}{2}$ , where μ c is the critical mass ratio influenced by oblateness of the primaries and the potential from the circular cluster of material points. The oblateness and the circular cluster of material points have destabilizing tendency.  相似文献   

11.
Study of evolution of galaxies, of transient events such as supernovae and large scale structures at redshifts greater than unity implies observing in a small sky area with a dedicated telescope. A fixed primary mirror aimed at the celestial pole seems the best way to yearly accumulate enough observation time. After earlier proposals made by Soviet and American astronomers, an European group intends to use an existing 3.50m Italian mirror to build a specialized, spectroscopic, polar telescope named POST.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.  相似文献   

12.
The minimum-propellant deterministic guidance law for bounded-thrust, constant jetexhaust velocity, spacecrafts is developed using the neighboring extremal theory. Minimization of the first-order variation in cost between a multi-burn nominal extremal and the perturbed trajectory eliminates all correction strategies except small changes in the nominal thrust-on, thrust-off times and small rotations of the thrust vector. Optimal values of these corrective controls for fixed values of initial state deviations, x 0, are found by minimizing the second variation in cost subject to the variational state and adjoint equations — an accessory minimum problem. The solution takes the linear feedback form u=A –1 22 A 21x 0, where the matricesA 22 andA 21 are functions only of transition matrices calculated along the nominal trajectory. The solution is applied to a three-burn Earth-Mars transfer.  相似文献   

13.
We report results from long term numerical integrations and analytical studies of particular orbits in the circular restricted three-body problem. These are mostly high-inclination trajectories in 1 : 1 resonance starting at or near the triangular Lagrangian L5 point. In some intervals of inclination these orbits have short Lyapunov times, from 100 to a few hundred periods, yet the osculating semi-major axis shows only relatively small fluctuations and there are no escapes from the 1 : 1 resonance. The eccentricity of these chaotic orbits varies in an erratic manner, some of the orbits becoming temporarily almost rectilinear. Similarly the inclination experiences large variations due to the conservation of the Jacobi constant. We studied such orbits for up to 109 periods in two cases and for 106 periods in all others, for inclinations varying from 0° to 180°. Thus our integrations extend from thousands to 10 million Lyapunov times without escapes of the massless particle. Since there are no zero-velocity curves restricting the motion this opens questions concerning the reason for the persistence of the 1 : 1 resonant motion. In the theory sections we consider the mechanism responsible for the observed behavior. We derive the averaged 1 : 1 resonance disturbing function, to second order in eccentricity, to calculate a critical inclination found in the numerical experiment, and examine motion close to this inclination. The cause of the chaos observed in the numerical experiments appears to be the emergence of saddle points in the averaged disturbing potential. We determine the location of several such saddle points in the (, ) plane, with being the mean longitude difference and the argument of pericentre. Some of the saddle points are illustrated with the aid of contour plots of the disturbing function. Motion close to these saddles is sensitive to initial conditions, thus causing chaos.This revised version was published online in October 2005 with corrections to the Cover Date.  相似文献   

14.
The type IV burst phenomenon consists of at least five physically distinct components or phases. Concerning the spectral and polarization characteristics of the radio emission, the X-ray emission and the association of energetic particle emission, two main classes of type IV burst components can be distinguished. The first class associated with energetic particle events comprises the (especially hard) X-ray burst, the type IV and mA1 components. With respect to the dynamics of the burst source a quasistationary mA1-phase can be distinguished from a moving mA2-phase. The general tendencies of the development of large type IV events have been discussed with regard to the possibility of the occurrence of neutral points of the magnetic field in greater coronal heights.  相似文献   

15.
We consider the system of neutrino-antineutrino – plasma taking into account theirweak Fermi interaction, when the density of neutrinos andthe plasma particles are rather high and their collective interactionplays a vital role. New fluid instabilities driven by strong neutrino flux in aplasma are observed. It is shown that a bunch of neutrinos, drifting witha constant velocity across a homogeneous plasma, can also induce emission oflower energy neutrinos due to scattering, i.e. the decay of a heavy neutrinoH into a heavy and a light neutrino L(HHL) in a plasma. Furthermore we find thatthe neutrino production in stars does not lead in general to energy lossesfrom the neutron stars.  相似文献   

16.
In the bounds of the totally nonmetric model of gravitational interaction theory (gravidynamics) the strong field of a compact object (a collapsar) — an analogue to the black hole in general relativity — is investigated. In the case of utmost strong (for gravidynamics) collapsar, field a region filled, by matter (a bag) must have the radius equal tor *=GM/c 2 10 km at the total collapsar massM7M . Only half of the collapsar mass is contained in the bag, the other one of its total energy (Mc 2 ) is distributed in the space surrounding the bag in the form of a coat, i.e., in the form of continuous medium (a relativistic gas) of virtual gravitons. The object must have the surface (the bag surface) with absolutely definite physical properties. The potential of such a surface is finite (+=-c 2/2) and the particle mass finding itself in a bound state on the bag surface is two times less than the mass of the same particle in a totally free state. The bag surface can perform periodic oscillations (pulsations) with the periodGM/c 2 3×10–5 s. An energy density inside the bag with the utmost strong gravitational field or with an utmost dense coat shrouding the bag is determined by gravitation theory constants only and depends on the distance to the bag centerr in the following way: (r)=(c 5 /8G)r –2. The bag matter in the case is most probably in the state of quark-gluon plasma.  相似文献   

17.
A largely numerical study was made of families of three-dimensional, periodic, halo orbits near the collinear libration points in the restricted three-body problem. Families extend from each of the libration points to the nearest primary. They appear to exist for all values of the mass ratio , from 0 to 1. More importantly, most of the families contain a range of stable orbits. Only near L1, the libration point between the two primaries, are there no stable orbits for certain values of . In that case the stable range decreases with increasing , until it disappears at =0.0573. Near the other libration points, stable orbits exist for all mass ratios investigated between 0 and 1. In addition, the orbits increase in size with increasing .  相似文献   

18.
Small perturbations of spherical star clusters around massive black holes are studied. The presence of a black hole gives rise to peculiar distributions that have no stars with low angular momenta (falling into the so-called “loss cone”). The stability of such a distribution has been found to depend significantly on whether it monotonically increases with angular momentum L (from the loss cone up to L = L circ in circular orbits) or has a maximum at some intermediate L = L *. In the case of spherical systems under consideration, the loss-cone instability is shown to be possible only for nonmonotonic distributions.  相似文献   

19.
Six neutral atomic oxygen Fraunhofer multiplets were observed at nine disk positions at Sacramento Peak Observatory. I filtered the data, corrected them for the instrumental profile and obtained equivalent widths.The equation of transfer for a plane-parallel atmosphere is solved to yield an expression for the equivalent width of a line or multiplet as a function of disk position; line source function, S L, and relative population of the lower energy level of the transition. Comparison with the observations gives the abundance, average levels of formation of the lines and S L.The numerical results show that the weak lines are formed either in L.T.E. or pure scattering (i.e., S L B v (T e) J c), but for 7770 Å S L/B (T e) 0.6 ± 0.1 at c = 0.1. An analysis of the central intensities of 7770 Å yields essentially the same results. The results for 8446 Å are not reliable due to a possible blend with an iron line. The abundance of oxygen in the photosphere may be slightly less than that found by previous investigators.The results are consistent with the assumption that all levels of photospheric oxygen are populated as in L.T.E. with the exception of 35S, which is overpopulated by approximately 50% at c = 0.1. The overpopulation may be due to the metastability of this level.Based on National Center for Atmospheric Research Cooperative Thesis No. 9.  相似文献   

20.
Lunar frozen orbits, characterized by constant orbital elements on average, have been previously found using various dynamical models, incorporating the gravitational field of the Moon and the third-body perturbation exerted by the Earth. The resulting mean orbital elements must be converted to osculating elements to initialize the orbiter position and velocity in the lunar frame. Thus far, however, there has not been an explicit transformation from mean to osculating elements, which includes the zonal harmonic \(J_2\), the sectorial harmonic \(C_{22}\), and the Earth third-body effect. In the current paper, we derive the dynamics of a lunar orbiter under the mentioned perturbations, which are shown to be dominant for the evolution of circumlunar orbits, and use von Zeipel’s method to obtain a transformation between mean and osculating elements. Whereas the dynamics of the mean elements do not include \(C_{22}\), and hence does not affect the equilibria leading to frozen orbits, \(C_{22}\) is present in the mean-to-osculating transformation, hence affecting the initialization of the physical circumlunar orbit. Simulations show that by using the newly-derived transformation, frozen orbits exhibit better behavior in terms of long-term stability about the mean values of eccentricity and argument of periapsis, especially for high orbits.  相似文献   

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