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1.
This paper studies the stability of infinitesimal motions about the triangular equilibrium points in the elliptic restricted three body problem assuming bigger primary as a source of radiation and the smaller one a triaxial rigid body. The perturbation technique developed by Bennet (Icarus 4:177, 1965b) has been used for determination of characteristic exponents. This technique is based on Floquet’s Theory for determination of characteristic exponents in the system with periodic coefficients. The results of the study are analytical and numerical expressions are simulated for the transition curves bounding the region of stability in the μ–e plane, accurate to O(e 2). The unstable region is found to be divided into three parts. The effect of radiation parameter is significant. For small values of e, the results are in favor with the numerical analysis of Danby (Astron. J. 69:166, 1964), Bennet (Icarus 4:177, 1965b), Alfriend and Rand (AIAA J. 6:1024, 1969). The effect of radiation pressure is significant than the oblateness and triaxiality of the primaries.  相似文献   

2.
The primary poles for (243) Ida and (134340) Pluto and its satellite (134340) Pluto : I Charon were redefined in the IAU Working Group on Cartographic Coordinates and Rotational Elements (WGCCRE) 2006 report (Seidelmann et al. in Celest Mech Dyn Astr 98:155, 2007), and 2009 report (Archinal et al. in Celest Mech Dyn Astr 109:101, 2011), respectively, to be consistent with the primary poles of similar Solar System bodies. However, the WGCCRE failed to take into account the effect of the redefinition of the poles on the values of the rotation angle W at J2000.0. The revised relationships in Table 3 of Archinal et al. 2011) are $$\begin{array}{llll} W & = & 274^{\circ}.05 +1864^{\circ}.6280070\, d\;{\rm for\; (243)\,Ida} \\ W & = & 302^{\circ} .695 + 56^{\circ} .3625225\, d\;{\rm for\; (134340)\,Pluto,\; and}\\ W & = & 122^{\circ} .695 + 56^{\circ} .3625225\, d\;{\rm for\; (134340)\,Pluto : I \,Charon}\end{array}$$ where d is the time in TDB days from J2000.0 (JD2451545.0).  相似文献   

3.
Recursive computation of mutual potential, force, and torque between two polyhedra is studied. Based on formulations by Werner and Scheeres (Celest Mech Dyn Astron 91:337–349, 2005) and Fahnestock and Scheeres (Celest Mech Dyn Astron 96:317–339, 2006) who applied the Legendre polynomial expansion to gravity interactions and expressed each order term by a shape-dependent part and a shape-independent part, this paper generalizes the computation of each order term, giving recursive relations of the shape-dependent part. To consider the potential, force, and torque, we introduce three tensors. This method is applicable to any multi-body systems. Finally, we implement this recursive computation to simulate the dynamics of a two rigid-body system that consists of two equal-sized parallelepipeds.  相似文献   

4.
We study the capture and crossing probabilities in the 3:1 mean motion resonance with Jupiter for a small asteroid that migrates from the inner to the middle Main Belt under the action of the Yarkovsky effect. We use an algebraic mapping of the averaged planar restricted three-body problem based on the symplectic mapping of Hadjidemetriou (Celest Mech Dyn Astron 56:563–599, 1993), adding the secular variations of the orbit of Jupiter and non-symplectic terms to simulate the migration. We found that, for fast migration rates, the captures occur at discrete windows of initial eccentricities whose specific locations depend on the initial resonant angles, indicating that the capture phenomenon is not probabilistic. For slow migration rates, these windows become narrower and start to accumulate at low eccentricities, generating a region of mutual overlap where the capture probability tends to 100 %, in agreement with the theoretical predictions for the adiabatic regime. Our simulations allow us to predict the capture probabilities in both the adiabatic and non-adiabatic cases, in good agreement with results of Gomes (Celest Mech Dyn Astron 61:97–113, 1995) and Quillen (Mon Not RAS 365:1367–1382, 2006). We apply our model to the case of the Vesta asteroid family in the same context as Roig et al. (Icarus 194:125–136, 2008), and found results indicating that the high capture probability of Vesta family members into the 3:1 mean motion resonance is basically governed by the eccentricity of Jupiter and its secular variations.  相似文献   

5.
This paper deals with the existence of libration points and their linear stability when the more massive primary is radiating and the smaller is an oblate spheroid. Our study includes the effects of oblateness of $\bar{J}_{2i}$ (i=1,2) with respect to the smaller primary in the restricted three-body problem. Under combining the perturbed forces that were mentioned before, the collinear points remain unstable and the triangular points are stable for 0<μ<μ c , and unstable in the range $\mu_{c} \le\mu\le\frac{1}{2}$ , where $\mu_{c} \in(0,\frac{1}{2})$ , it is also observed that for these points the range of stability will decrease. The relations for periodic orbits around five libration points with their semimajor, semiminor axes, eccentricities, the frequencies of orbits and periods are found, furthermore for the orbits around the triangular points the orientation and the coefficients of long and short periodic terms also are found in the range 0<μ<μ c .  相似文献   

6.
This paper studies the motion of an infinitesimal mass around triangular equilibrium points in the elliptic restricted three body problem assuming bigger primary as a source of radiation and the smaller one a triaxial rigid body. A practical application of this case could be the study of motion of a satellite under the effect of Sun and Earth. We have exploited the method of averaging used by Grebnikov (Nauka, Moscow, revised 1986) throughout the analysis of stability of the system. The critical mass ratio depends on the radiation pressure, oblateness, eccentricity and semi major axis of the elliptic orbits and the range of stability decreases as the radiation parameter increases.  相似文献   

7.
Based on many planetary observations between the years 1971 and 2003, Krasinsky and Brumberg (Celest. Mech. Dyn. Astron. 90:267–288, 2004) have estimated a rate of increase in the mean Sun-Earth distance of (15±4) m per century. Together with other anomalous observations in the solar system, this increase appears to be unexplained (Lämmerzahl et al. in Astrophys. Space Sci. Lib., vol. 349, pp. 75–101, 2008). We explain these findings by invoking a recently proposed gravitational impact model (Wilhelm et al. in Astrophys. Space Sci. 343:135–144, 2013) that implies a secular mass increase of all massive bodies. This allows us to formulate a quantitative understanding of the effect within the parameter range of the model with a mass accumulation rate of the Sun of (6.4±1.7)×1010 kg?s?1.  相似文献   

8.
The symmetric trace free (STF) tensor formalism, developed by Hartmann et al. (Celest Mech Dyn Astron 60:139–159. doi:10.1007/BF00693097, 1994), is a nice tool, not much used in Celestial Mechanics. It is fully equivalent to the usual spherical harmonics but permits more elegant and compact formulations. The coupling between the gravitational fields of extended bodies with this formalism has been used in Mathis and Le Poncin-Lafitte (Astron Astrophys 497:889–910. doi:10.1051/0004-6361/20079054, 2009) for binary stars or planetary systems, but not yet applied to binary asteroids. However, binary asteroids are common in the Solar System and usually their study requires a full two rigid body approach. The formulation of the two-body interaction potential in the STF formalism in the full two rigid body problem is detailed and completed in this article. An application to the binary asteroid (66391) 1999 KW4 is presented with a comparison of our results with other results of the literature for validation.  相似文献   

9.
The Cassini spacecraft collects high resolution images of the Saturnian satellites and reveals the surface of these new worlds. Tiscareno et?al. succeeded to determine the Epimetheus rotation from the Cassini Imaging Science Subsystem data, initiating studies on the rotation of Epimetheus and its companion Janus (Tiscareno et?al., Icarus 204:254?C261, 2009; Noyelles, Icarus 207:887?C902, 2010; Robutel et?al., Icarus 211:758?C769, 2011). Especially, Epimetheus is characterized by its horseshoe shape orbit and the presence of the swap has to be introduced explicitly into rotational models. During its journey in the Saturnian system, Cassini spacecraft accumulates the observational data of the other satellites and it will be possible to determine the rotational parameters of several of them. To prepare these future observations, we built rotational models of the coorbital (also called Trojan) satellites Telesto, Calypso, Helene, and Polydeuces, in addition to Janus and Epimetheus. Indeed, Telesto and Calypso orbit around the L 4 and L 5 Lagrange points of Saturn-Tethys while Helene and Polydeuces are coorbital of Dione. The goal of this study is to understand how the departure from the Keplerian motion induced by the perturbations of the coorbital body, influences the rotation of these satellites. To this aim, we introduce explicitly the perturbation in the rotational equations by using the formalism developed by érdi (Celest Mech 15:367?C383, 1977) to represent the coorbital motions, and so we describe the rotational motion of the coorbitals, Janus and Epimetheus included, in compact form.  相似文献   

10.
We have examined the effects of oblateness up to J 4 of the less massive primary and gravitational potential from a circum-binary belt on the linear stability of triangular equilibrium points in the circular restricted three-body problem, when the more massive primary emits electromagnetic radiation impinging on the other bodies of the system. Using analytical and numerical methods, we have found the triangular equilibrium points and examined their linear stability. The triangular equilibrium points move towards the line joining the primaries in the presence of any of these perturbations, except in the presence of oblateness up to J 4 where the points move away from the line joining the primaries. It is observed that the triangular points are stable for 0 < μ < μ c and unstable for \(\mu_{\mathrm{c}} \le \mu \le \frac {1}{2},\) where μ c is the critical mass ratio affected by the oblateness up to J 4 of the less massive primary, electromagnetic radiation of the more massive primary and potential from the belt, all of which have destabilizing tendencies, except the coefficient J4 and the potential from the belt. A practical application of this model could be the study of motion of a dust particle near a radiating star and an oblate body surrounded by a belt.  相似文献   

11.
Spin-orbit coupling is often described in an approach known as ??the MacDonald torque??, which has long become the textbook standard due to its apparent simplicity. Within this method, a concise expression for the additional tidal potential, derived by MacDonald (Rev Geophys 2:467?C541, 1994), is combined with a convenient assumption that the quality factor Q is frequency-independent (or, equivalently, that the geometric lag angle is constant in time). This makes the treatment unphysical because MacDonald??s derivation of the said formula was, very implicitly, based on keeping the time lag frequency-independent, which is equivalent to setting Q scale as the inverse tidal frequency. This contradiction requires the entire MacDonald treatment of both non-resonant and resonant rotation to be rewritten. The non-resonant case was reconsidered by Efroimsky and Williams (Cel Mech Dyn Astron 104:257?C289, 2009), in application to spin modes distant from the major commensurabilities. In the current paper, we continue this work by introducing the necessary alterations into the MacDonald-torque-based model of falling into a 1-to-1 resonance. (The original version of this model was offered by Goldreich (Astron J 71:1?C7, 1996). Although the MacDonald torque, both in its original formulation and in its corrected version, is incompatible with realistic rheologies of minerals and mantles, it remains a useful toy model, which enables one to obtain, in some situations, qualitatively meaningful results without resorting to the more rigorous (and complicated) theory of Darwin and Kaula. We first address this simplified model in application to an oblate primary body, with tides raised on it by an orbiting zero-inclination secondary. (Here the role of the tidally-perturbed primary can be played by a satellite, the perturbing secondary being its host planet. A planet may as well be the perturbed primary, its host star acting as the tide-raising secondary). We then extend the model to a triaxial primary body experiencing both a tidal and a permanent-figure torque exerted by an orbiting secondary. We consider the effect of the triaxiality on both circulating and librating rotation near the synchronous state. Circulating rotation may evolve toward the libration region or toward a spin faster than synchronous (the so-called pseudosynchronous spin). Which behaviour depends on the orbit eccentricity, the triaxial figure of the primary, and the mass ratio of the secondary and primary bodies. The spin evolution will always stall for the oblate case. For libration with a small amplitude, expressions are derived for the libration frequency, damping rate, and average orientation. Importantly, the stability of pseudosynchronous spin hinges upon the dissipation model. Makarove and Efroimsky (Astrophys J, 2012) have found that a more realistic tidal dissipation model than the corrected MacDonald torque makes pseudosynchronous spin unstable. Besides, for a sufficiently large triaxiality, pseudosynchronism is impossible, no matter what dissipation model is used.  相似文献   

12.
One of the most interesting features in the libration domain of co-orbital motions is the existence of secondary resonances. For some combinations of physical parameters, these resonances occupy a large fraction of the domain of stability and rule the dynamics within the stable tadpole region. In this work, we present an application of a recently introduced ‘basic Hamiltonian model’ \(H_\mathrm{b}\) for Trojan dynamics (Páez and Efthymiopoulos in Celest Mech Dyn Astron 121(2):139, 2015; Páez et al. in Celest Mech Dyn Astron 126:519, 2016): we show that the inner border of the secondary resonance of lowermost order, as defined by \(H_\mathrm{b}\), provides a good estimation of the region in phase space for which the orbits remain regular regardless of the orbital parameters of the system. The computation of this boundary is straightforward by combining a resonant normal form calculation in conjunction with an ‘asymmetric expansion’ of the Hamiltonian around the libration points, which speeds up convergence. Applications to the determination of the effective stability domain for exoplanetary Trojans (planet-sized objects or asteroids) which may accompany giant exoplanets are discussed.  相似文献   

13.
The location and the stability in the linear sense of the libration points in the restricted problem have been studied when there are perturbations in the potentials between the bodies. It is seen that if the perturbing functions satisfy certain conditions, there are five libration points, two triangular and three collinear. It is further observed that the collinear points are unstable and for the triangular points, the range of stability increases or decreases depending upon whetherP> or <0 wherep depends upon the perturbing functions. The theory is verified in the following four cases:
  1. There are no perturbations in the potentials (classical problem).
  2. Only the bigger primary is an oblate spheroid whose axis of symmetry is perpendicular to the plane of relative motion (circular) of the primaries.
  3. Both the primaries are oblate spheroids whose axes of symmetry are perpendicular to the plane of relative motion (circular) of the primaries.
  4. The primaries are spherical in shape and the bigger is a source of radiation.
  相似文献   

14.
Within the frame work of the circular restricted three-body problem (CR3BP) we have examined the effect of axis-symmetric of the bigger primary, oblateness up to the zonal harmonic J 4 of the smaller primary and gravitational potential from a belt (circular cluster of material points) on the linear stability of the triangular libration points. It is found that the positions of triangular libration points and their linear stability are affected by axis-symmetric of the bigger primary, oblateness up to J 4 of the smaller primary and the potential created by the belt. The axis-symmetric of the bigger primary and the coefficient J 2 of the smaller primary have destabilizing tendency, while the coefficient J 4 of the smaller primary and the potential from the belt have stabilizing tendency. The overall effect of these perturbations has destabilizing tendency. This study can be useful in the investigation of motion of a particle near axis-symmetric—oblate bodies surrounded by a belt.  相似文献   

15.
Subdwarf B stars (sdBs) can significantly change the ultraviolet spectra of populations at age t～1 Gyr, and have been even included in the evolutionary population synthesis (EPS) models by Han et al. (Mon. Not. R. Astron. Soc. 380:1098, 2007). In this study we present the spectral energy distributions (SEDs) of binary stellar populations (BSPs) by combining the EPS models of Han et al. (Mon. Not. R. Astron. Soc. 380:1098, 2007) and those of the Yunnan group (Zhang et al. in Astron. Astrophys. 415:117, 2004; Mon. Not. R. Astron. Soc. 357:1088, 2005), which have included various binary interactions (except sdBs) in EPS models. This set of SEDs is available upon request from the authors. Using this set of SEDs of BSPs we build the spectra of Burst, E, S0–Sd and Irr types of galaxies by using the package of Bruzual and Charlot (Mon. Not. R. Astron. Soc. 344:1000, 2003). Combined with the photometric data (filters and magnitudes), we obtain the photometric redshifts and morphologies of 1502 galaxies by using the Hyperz code of Bolzonella et al. (Astron. Astrophys. 363:476, 2000). This sample of galaxies is obtained by removing those objects, mismatched with the SDSS/DR7 and GALEX/DR4, from the catalogue of Fukugita et al. (Astron. J. 134:579, 2007). By comparison the results with the SDSS spectroscopic redshifts and the morphological index of Fukugita et al. (Astron. J. 134:579, 2007), we find that the photo-z fluctuate with the SDSS spectroscopic redshifts, while the Sa–Sc galaxies in the catalogue of Fukugita et al. (Astron. J. 134:579, 2007) are classified earlier as Burst-E galaxies.  相似文献   

16.
The dynamics of the two Jupiter triangular libration points perturbed by Saturn is studied in this paper. Unlike some previous works that studied the same problem via the pure numerical approach, this study is done in a semianalytic way. Using a literal solution, we are able to explain the asymmetry of two orbits around the two libration points with symmetric initial conditions. The literal solution consists of many frequencies. The amplitudes of each frequency are the same for both libration points, but the initial phase angles are different. This difference causes a temporary spatial asymmetry in the motions around the two points, but this asymmetry gradually disappears when the time goes to infinity. The results show that the two Jupiter triangular libration points should have symmetric spatial stable regions in the present status of Jupiter and Saturn. As a test of the literal solution, we study the resonances that have been extensively studied in Robutel and Gabern (Mon Not R Astron Soc 372:1463–1482, 2006). The resonance structures predicted by our analytic theory agree well with those found in Robutel and Gabern (Mon Not R Astron Soc 372:1463–1482, 2006) via a numerical approach. Two kinds of chaotic orbits are discussed. They have different behaviors in the frequency map. The first kind of chaotic orbits (inner chaotic orbits) is of small to moderate amplitudes, while the second kind of chaotic orbits (outer chaotic orbits) is of relatively larger amplitudes. Using analytical theory, we qualitatively explain the transition process from the inner chaotic orbits to the outer chaotic orbits with increasing amplitudes. A critical value of the diffusion rate is given to separate them in the frequency map. In a forthcoming paper, we will study the same problem but keep the planets in migration. The time asymmetry, which is unimportant in this paper, may cause an observable difference in the two Jupiter Trojan groups during a very fast planet migration process.  相似文献   

17.
A formulation of the perturbed two-body problem that relies on a new set of orbital elements is presented. The proposed method represents a generalization of the special perturbation method published by Peláez et al. (Celest Mech Dyn Astron 97(2):131–150, 2007) for the case of a perturbing force that is partially or totally derivable from a potential. We accomplish this result by employing a generalized Sundman time transformation in the framework of the projective decomposition, which is a known approach for transforming the two-body problem into a set of linear and regular differential equations of motion. Numerical tests, carried out with examples extensively used in the literature, show the remarkable improvement of the performance of the new method for different kinds of perturbations and eccentricities. In particular, one notable result is that the quadratic dependence of the position error on the time-like argument exhibited by Peláez’s method for near-circular motion under the $J_{2}$ perturbation is transformed into linear. Moreover, the method reveals to be competitive with two very popular element methods derived from the Kustaanheimo-Stiefel and Sperling-Burdet regularizations.  相似文献   

18.
The Helioseismic and Magnetic Imager (HMI) instrument onboard the Solar Dynamics Observatory (SDO) satellite is designed to produce high-resolution Doppler-velocity maps of oscillations at the solar surface with high temporal cadence. To take advantage of these high-quality oscillation data, a?time?–?distance helioseismology pipeline (Zhao et al., Solar Phys. submitted, 2010) has been implemented at the Joint Science Operations Center (JSOC) at Stanford University. The aim of this pipeline is to generate maps of acoustic travel times from oscillations on the solar surface, and to infer subsurface 3D flow velocities and sound-speed perturbations. The wave travel times are measured from cross-covariances of the observed solar oscillation signals. For implementation into the pipeline we have investigated three different travel-time definitions developed in time?–?distance helioseismology: a Gabor-wavelet fitting (Kosovichev and Duvall, SCORE’96: Solar Convection and Oscillations and Their Relationship, ASSL, Dordrecht, 241, 1997), a?minimization relative to a reference cross-covariance function (Gizon and Birch, Astrophys. J. 571, 966, 2002), and a linearized version of the minimization method (Gizon and Birch, Astrophys. J. 614, 472, 2004). Using Doppler-velocity data from the Michelson Doppler Imager (MDI) instrument onboard SOHO, we tested and compared these definitions for the mean and difference travel-time perturbations measured from reciprocal signals. Although all three procedures return similar travel times in a quiet-Sun region, the method of Gizon and Birch (Astrophys. J. 614, 472, 2004) gives travel times that are significantly different from the others in a magnetic (active) region. Thus, for the pipeline implementation we chose the procedures of Kosovichev and Duvall (SCORE’96: Solar Convection and Oscillations and Their Relationship, ASSL, Dordrecht, 241, 1997) and Gizon and Birch (Astrophys. J. 571, 966, 2002). We investigated the relationships among these three travel-time definitions, their sensitivities to fitting parameters, and estimated the random errors that they produce.  相似文献   

19.
We give a constructive proof of the existence of elliptic lower dimensional tori in nearly integrable Hamiltonian systems. In particular we adapt the classical Kolmogorov normalization algorithm to the case of planetary systems, for which elliptic tori may be used as replacements of elliptic Keplerian orbits in Lagrange-Laplace theory. With this paper we support with rigorous convergence estimates the semi-analytic work in our previous article (Sansottera et al., Celest Mech Dyn Astron 111:337–361, 2011), where an explicit calculation of an invariant torus for a planar model of the Sun-Jupiter-Saturn-Uranus system has been made. With respect to previous works on the same subject we exploit the characteristic of Lie series giving a precise control of all terms generated by our algorithm. This allows us to slightly relax the non-resonance conditions on the frequencies.  相似文献   

20.
This paper deals with the existence of triangular points and their linear stability when the primaries are oblate spheroid and sources of radiation considering the effect of oblateness up to 10?6 of main terms in the restricted three-body problem; we see that the locations of the triangular points are affected by the oblateness of the primaries and solar radiation pressure. It is further seen that these points are stable for 0 ≤ μ ≤μ c ; and unstable for μ c  ≤ μ ≤1/2; where μ c is the critical mass value depending on terms which involve parameters that characterize the oblateness and radiation repulsive forces such that $ \mu_{c} \in (0,1/2) $ ; in addition to this an algorithm has been constructed to calculate the critical mass value.  相似文献   

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