Orbital perturbations using geopotential coefficients up to high degree and order: Highly eccentric orbits

Several methods have been proposed for calculations of the eccentricity function for a high value of the eccentricity, however they cannot be used when the high degree and order coefficients of gravity fields are taken into account. The method proposed by Wnuk(1) is numerically stable in this case, but when is used. a large number of terms occurs in formulas for geopotential perturbations. In this paper we propose an application of expansions of some functions of the eccentric anomaly E as well as Hansen coefficients in power series of (e - e*), where e* is a fixed value of the eccentricity derived by da Silva Fernandes(2,3,4). These series are convergent for all e < 1.

ORBITAL PERTURBATIONS OF THE GALILEAN SATELLITES DURING PLANETARY ENCOUNTERS

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Some orbital characteristics of lunar artificial satellites

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Manobra orbital terra-lua-terra

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Pertubação orbital devida a um terceiro corpo com distribuição não uniforme de massa e em órbita elíptica

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A long marine history of carbon cycle modulation by orbital-climatic changes

Pacing of the marine carbon cycle by orbital forcing during the Pliocene and Pleistocene Ice Ages [past 2.5 million years (Myr)] is well known. As older deep-sea sediment records are being studied at greater temporal resolution, it is becoming clear that similar fluctuations in the marine carbon system have occurred throughout the late Mesozoic and Tertiary, despite the absence of large continental ice sheets over much of this time. Variations in both the organic and the calcium carbonate components of the marine carbon system seem to have varied cyclically in response to climate forcing, and carbon and carbonate time series appear to accurately characterize the frequency spectrum of ancient climatic change. For the past 35 Myr, much of the variance in carbonate content carries the “polar” signal of obliquity [41,000 years (41 kyr)] forcing. Over the past 125 Myr, there is evidence from marine sediments of the continued role of precessional (≈21 kyr) climatic cycles. Repeat patterns of sedimentation at about 100, 400, and 2,400 kyr, the modulation periods of precession, persistently enter into marine carbon cycle records as well. These patterns suggest a nonlinear response of climate and/or the sedimentation of organic carbon and carbonates to precessional orbital perturbations. Nonlinear responses of the carbon system may help to amplify relatively weak orbital insolation anomalies into more significant climatic perturbations through positive feedback effects. Nonlinearities in the carbon cycle may have transformed orbital-climatic cycles into long-wavelength features on time scales comparable to the residence times of carbon and nutrient elements in the ocean.

On the rotation of co-orbital bodies in eccentric orbits

We investigate the resonant rotation of co-orbital bodies in eccentric and planar orbits. We develop a simple analytical model to study the impact of the eccentricity and orbital perturbations on the spin dynamics. This model is relevant in the entire domain of horseshoe and tadpole orbit, for moderate eccentricities. We show that there are three different families of spin-orbit resonances, one depending on the eccentricity, one depending on the orbital libration frequency, and another depending on the pericenter's dynamics. We can estimate the width and the location of the different resonant islands in the phase space, predicting which are the more likely to capture the spin of the rotating body. In some regions of the phase space the resonant islands may overlap, giving rise to chaotic rotation.

FROZEN ORBITS AROUND EUROPA

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Comparação de modelos para o cálculo de pertubações orbitais devidas à maré terrestre

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Estudo de manobras evasivas com perturbações orbitais

Pós-graduação em Física - FEG

(Table 1) Ooze/chalk cycles: frequency of occurrence at DSDP Leg 74 Sites

Shallow- to deep-water environments are represented by the sediments and rocks recovered from the Walvis Ridge- Angola Basin transect. These calcareous oozes, chalks, limestones, and volcaniclastic sedimentary rocks are used to define and correlate four lithostratigraphic units. The sediments were deposited in cycles which represent recurring tectonic or Oceanographic events and may be related to climatic fluctuations and orbital perturbations. Turbidites are the most common and easily identified sedimentary cycle. They are Late Cretaceous to Paleocene in age and are repeated in intervals ranging from thousands to tens of thousands of years. They are also found interbedded between basalt layers. Turbidites are easily distinguished from the other cycles present by their sedimentary structures, mineral composition, alteration products, and physical properties (GRAPE) data. Large-scale turbidites, debris, or slump breccias are found at or just above the Cretaceous/Tertiary boundary and indicate an event of considerable energy possibly related to intense tectonic activity. Diagenetic cycles, interpreted as small-scale dissolution cycles or sequences produced by biogenic activity, occur in early Paleocene chalks. The recurrence intervals average -20,000 y. but have a wide range of values. Variations in CaCO3 content, color, gradational boundaries, and trace fossil content characterize these sediments. These cycles reflect bottom-water conditions. Ooze-chalk cycles occur in upper Oligocene to upper Paleocene sediments and represent conditions that once existed at the sediment/water interface where they obtained their diagenetic potential. These oscillations are repeated over tens of thousands of years and may have no modern analogs. Color variations in sediments at the Cretaceous/Tertiary boundary indicate local fluctuations in oxygen content within the sediments or the water column. This situation lasted for several hundred thousand years and is not repeated elsewhere in the sequence. Large dissolution cycles are recorded in the sediments at Site 527 that are of middle Miocene and early Oligocene to middle Eocene age. During this time the seafloor at this site appears to have been located at or subsided to a depth occupied by a fluctuating CCD and lysocline.

Analytical direct planetary perturbations on the orbital motion of satellites

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. © 2012 Springer Science+Business Media Dordrecht.

Resonant and Secular Orbital Interations

In stable solar systems, planets remain in nearly elliptical orbits around their stars. Over longer timescales, however, their orbital shapes and sizes change due to mutual gravitational perturbations. Orbits of satellites around a planet vary for the same reason. Because of their interactions, the orbits of planets and satellites today are different from what they were earlier. In order to determine their original orbits, which are critical constraints on formation theories, it is crucial to understand how orbits evolve over the age of the Solar System. Depending on their timescale, we classify orbital interactions as either short-term (orbital resonances) or long-term (secular evolution). My work involves examples of both interaction types. Resonant history of the small Neptunian satellites In satellite systems, tidal migration brings satellite orbits in and out of resonances. During a resonance passage, satellite orbits change dramatically in a very short period of time. We investigate the resonant history of the six small Neptunian moons. In this unique system, the exotic orbit of the large captured Triton (with a circular, retrograde, and highly tilted orbit) influences the resonances among the small satellites very strongly. We derive an analytical framework which can be applied to Neptune's satellites and to similar systems. Our numerical simulations explain the current orbital tilts of the small satellites as well as constrain key physical parameters of both Neptune and its moons. Secular orbital interactions during eccentricity damping Long-term periodic changes of orbital shape and orientation occur when two or more planets orbit the same star. The variations of orbital elements are superpositions of the same number of fundamental modes as the number of planets in the system. We investigate how this effect interacts with other perturbations imposed by external disturbances, such as the tides and relativistic effects. Through analytical studies of a system consisting of two planets, we find that an external perturbation exerted on one planet affects the other indirectly. We formulate a general theory for how both orbits evolve in response to an arbitrary externally-imposed slow change in eccentricity.

Orbital evolution of the mu and nu dust ring particles of Uranus

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)