On The Concept Of Periapsis In Hill’s Problem     

B.F. Villac  D.J. Scheeres 《Celestial Mechanics and Dynamical Astronomy》2004,90(1-2):165-178

The concept of closest approach is analyzed in Hill’s problem, resulting in a partitioning of the position space. The different behavior between the direct and retrograde motion is explained analytically, resulting in a simple estimate of the variation of Hill’s periodic and quasi-circular orbits as a function of the Jacobi constant. The local behavior of the orbits on the zero velocity surfaces and an analytical definition of local escape and capture in Hill’s problem are also given.  相似文献   

Structures in the phase space of a four dimensional symplectic map     

Ch. Skokos  G. Contopoulos  C. Polymilis 《Celestial Mechanics and Dynamical Astronomy》1996,65(3):223-251

We numerically investigate the projections of non periodic orbits in a 4-dimensional (4-D) symplectic map composed of two coupled 2-dimensional (2-D) maps. We describe in detail the structures that are produced in different planes of projection and we find how the morphology of the 4-D orbits is influenced by the features of the 2-D maps as the coupling parameter increases. We give an empirical law that describes this influence.  相似文献   

Spectroscopic binaries near the North Galactic Pole paper 18: HD 118670     

R. F. Griffin 《Journal of Astrophysics and Astronomy》1990,11(4):533-540

Photoelectric radial-velocity measurements show that HD 118670 is a double-lined spectroscopic binary in an orbit which is not quite circular and whose period is about 48 days. Spectral types of K0 V and K7 V would satisfy the photometry and the mass ratio; the mass function would then suggest the possibility of eclipses. However, actual spectral classification indicates a luminosity somewhat above the main sequence  相似文献   

The Homoclinic Tangle of A 1:2 Resonance in a 2-D Hamiltonian System     

C. Polymilis  G. Contopoulos  A. Dokoumetzidis 《Celestial Mechanics and Dynamical Astronomy》2003,85(2):105-144

We study in great detail the geometry of the homoclinic tangle, with respect to the energy, corresponding to an unstable periodic orbit of type 1:2, on a surface of section representing a 2-D Hamiltonian system. The tangle consists of two resonance areas, in contrast with the tangles of type-l or -{l, m, k, x = 0} considered in previous studies, that consist of only one resonance area. We study the intersections of the inner and outer lobes of the same resonance area and of the two resonance areas. The intersections of the lobes follow certain rules. The detailed study of these rules allows us to derive quantitative relations about the number of intersections and to understand the complex behavior of the higher order lobes by studying the lower order lobes. We find 1st, 2nd, 3rd, etc. order intersections formed by lobes making 1, 2, 3, etc. turns around an island. After a sufficiently high order of iterations a lobe may intersect its image and thus produce a Poincaré recurrence. Numerical results for a wide interval of energies are presented. The number of intersections changes through tangencies. In any finite interval of the energy between two tangencies of 1st order, an infinite number of higher order tangencies occur and thus, according to the Newhouse theorem, there exist nearby islands of stability.  相似文献   

Geometric Derivation of the Delaunay Variables and Geometric Phases     

Dong Eui Chang  Jerrold E. Marsden 《Celestial Mechanics and Dynamical Astronomy》2003,86(2):185-208

We derive the classical Delaunay variables by finding a suitable symmetry action of the three torus T³ on the phase space of the Kepler problem, computing its associated momentum map and using the geometry associated with this structure. A central feature in this derivation is the identification of the mean anomaly as the angle variable for a symplectic S ¹ action on the union of the non-degenerate elliptic Kepler orbits. This approach is geometrically more natural than traditional ones such as directly solving Hamilton–Jacobi equations, or employing the Lagrange bracket. As an application of the new derivation, we give a singularity free treatment of the averaged J ₂-dynamics (the effect of the bulge of the Earth) in the Cartesian coordinates by making use of the fact that the averaged J ₂-Hamiltonian is a collective Hamiltonian of the T³ momentum map. We also use this geometric structure to identify the drifts in satellite orbits due to the J ₂ effect as geometric phases.  相似文献   

Resonant Periodic Orbits of Trans-Neptunian Objects     

Kotoulas  Thomas A.  Hadjidemetriou  John D. 《Earth, Moon, and Planets》2002,91(2):63-93

We study two and three-dimensional resonant periodic orbits, usingthe model of the restricted three-body problem with the Sun andNeptune as primaries. The position and the stability character ofthe periodic orbits determine the structure of the phase space andthis will provide useful information on the stability and longterm evolution of trans-Neptunian objects. The circular planarmodel is used as the starting point. Families of periodic orbitsare computed at the exterior resonances 1/2, 2/3 and 3/4 withNeptune and these are used as a guide to select the energy levelsfor the computation of the Poincaré maps, so that all basicresonances are included in the study. Using the circular planarmodel as the basic model, we extend our study to more realisticmodels by considering an elliptic orbit of Neptune and introducingthe inclination of the orbit. Families of symmetric periodicorbits of the planar elliptic restricted three-body problem andthe three-dimensional problem are found. All these orbitsbifurcate from the families of periodic orbits of the planarcircular problem. The stability of all orbits is studied. Althoughthe resonant structure in the circular problem is similar for allresonances, the situation changes if the eccentricity of Neptuneor the inclination of the orbit is taken into account. All theseresults are combined to explain why in some resonances there aremany bodies and other resonances are empty.  相似文献   

Preliminary Study on the Translunar Halo Orbits of the Real Earth–Moon System     

Miquel A. Andreu 《Celestial Mechanics and Dynamical Astronomy》2003,86(2):107-130

The computation of translunar Halo orbits of the real Earth–Moon system (REMS) has been an open problem for a long time, but now, it is possible to compute Halo orbits of the REMS in a systematic way. In this paper, we describe the method used for the numerical computation of Halo orbits for a time span longer than 41 years. Halo orbits of the REMS are computed from quasi-periodic Halo orbits of the quasi-bicircular problem (QBCP). The QBCP is a model for the dynamics of a spacecraft in the Earth–Moon–Sun system. It is a Hamiltonian system with three degrees of freedom and depending periodically on time. In this model, Earth, Moon and Sun are moving in a self-consistent motion close to bicircular. The computed Halo orbits of the REMS are compared with the family of Halo orbits of the QBCP. The results show that the QBCP is a good model to understand the main features of the Halo family of the REMS.  相似文献   

Pervasive wetland flooding in the glacial drift prairie of North Dakota (USA)     

Paul E. Todhunter  Bradley C. Rundquist 《Natural Hazards》2008,46(1):73-88

This article describes a unique flood hazard, produced by the dramatic expansion of wetlands in Nelson County, located within the North American Prairie Pothole Region of North Dakota, USA. There has been an unprecedented increase in the number, average size, and permanence of prairie wetlands, and a significant increase in the size of a closed lake (Stump Lake) due to a decade-long wet spell that began in 1993 following a prolonged drying trend. Base-line land cover information from the 1992 USGS National Land Cover Characterization dataset, and a Landsat TM scene acquired 9 July 2001 are used to assess the growth of the closed lake and wetland pond surface areas, and to analyze the type and area of various land cover classes inundated between 1992 and 2001. The open water profile in Nelson County changed from one marked by relatively comparable coverage of closed lake and wetland pond areas in 1992, to one in which wetland open water accounted for the vast majority of total open water in 2001. The bulk of the wetland pond area expansion occurred by displacing existing wetland vegetation and agricultural cropland. Producers responded to the flood hazard by filing Federal Crop Insurance Corporation (FCIC) claims and enrolling cropland in the Conservation Reserve Program (CRP), a federal land retirement program. Land taken out of agricultural production has had an enormous impact upon the agricultural sector that forms the economic base of the rural economy. In 2001 the land taken out of production due to CRP enrollment and preventive planting claims represented nearly 42% of Nelson County’s 205.2 K ha base agricultural land. The patterns obtained from this detailed study of Nelson County are likely to be the representative of the more publicized flood disaster occurring within the Devils Lake Basin of North Dakota.  相似文献   

封闭体系有机质与有机碳氢氮恢复动力学研究   总被引：3，自引：0，他引：3  

彭平安  秦艳  张辉  刘大永  张善文  隋风贵  李钜源  李政 《海相油气地质》2008,13(2):27-36

在封闭体系的条件下,对典型的Ⅰ、Ⅱ、Ⅲ型干酪根在热演化过程中的损失进行生烃动力学研究,获得了Ⅰ、Ⅱ、Ⅲ型干酪根的总量、有机碳、氢以及氮质量损失动力学参数。用Kinetics软件计算了封闭体系干酪根有机碳丰度、氢碳原子比和氮碳原子比的恢复系数。认为在对高成熟—过成熟干酪根进行生烃评价时,Ⅰ、Ⅲ型干酪根残余有机碳丰度需要进行恢复,而Ⅱ型干酪根残余有机碳丰度不需要恢复。三种类型干酪根的氢碳原子比均需要进行恢复。  相似文献   

On solving Kepler's equation for nearly parabolic orbits     

Richard A. Serafin 《Celestial Mechanics and Dynamical Astronomy》1996,65(4):389-398

We deal here with the efficient starting points for Kepler's equation in the special case of nearly parabolic orbits. Our approach provides with very simple formulas that allow calculating these points on a scientific vest-pocket calculator. Moreover, srtarting with these points in the Newton's method we can calculate a root of Kepler's equation with an accuracy greater than 0.001 in 0–2 iterations. This accuracy holds for the true anomaly || 135° and |e – 1| 0.01. We explain the reason for this effect also.Dedicated to the memory of Professor G.N. Duboshin (1903–1986).  相似文献