Biotic response to the latest Cenomanian drowning and OAE2: A case study from the Eastern Desert of Egypt

The changes in macrofauna and microfauna, before, during and after the latest Cenomanian global Oceanic Anoxic Event (OAE2), from the Eastern Desert of Egypt are documented, along with an inferred paleoenvironment. The age of the studied OAE2 interval is constrained by the last occurrence of the marker calcareous nannofossils species Axopodorhabdus albianus along with the previously identified positive δ¹³C excursion from the coeval ammonite Vascoceras cauvini Zone (= Neocardioceras juddii Zone), enabling correlation with the peak ‘b’ of the OAE2. Based on the studied microfaunal assemblages, a warm shallow restricted lagoonal environment with mesotrophic conditions and strong seasonality is inferred. The presence of a rare ammonite (and ostracods) attest to the intermittent introduction of marine waters within this inner ramp setting. In terms of sequence stratigraphy, two 3rd order depositional sequences are recorded. The top surface of the first depositional sequence, at the sequence boundary, SB Ce 5 (the start of the OAE2), is marked by an abrupt faunal change with reduced abundances of the macrofaunal elements. This is in tune with other Egyptian records of relatively smaller loss (10 %) at the Cenomanian-Turonian boundary, as compared to much higher numbers (53–79% of species), globally. This faunal (biotic bottleneck) and lithological change (from siliciclastic-dominated deposits to a largely carbonate-dominated one) at the SB Ce 5 is attributed as a response to the latest Cenomanian drowning (the highest sea-level during the Phanerozoic), that also resulted in the formation of carbonate platform.     

Station-keeping for a translunar communication station

A translunar communication station is to be kept close to a nominal unstable periodic ‘Halo’ orbit, visible at all times from Earth. The analytically computed nominal orbit is not perfect, requiring an average control acceleration of about 10^?6 g's for tight control. An adjustable quadratic combination of position deviation and control acceleration is minimized to provide an (adjustable) control law with period feedback gains and a periodic bias. The average control acceleration can be reduced to less than 10^?8 g's with an error settling time of less than 21/2 months. The resulting limiting motion provides, in turn, an improved nominal, permitting the same low control cost with much tighter control, corresponding to settling times of the order of one day.     

Expansion of the first order planetary disturbing function by Smart's method

In this part we expand the indirect part of the planetary perturbing function by Smart's method, via Taylor's theorem. We neglect, in our expansion, terms of degree higher than the fourth with regard to the eccentricities and tangents of the inclinations.     

Quasi-periodic orbits about the translunar libration point

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.     

Third-order Uranus-Neptune planetary theory

In this part we calculate the secular and critical terms arising from the indirect part of the classical planetary Hamiltonian for Uranus and Neptune. We neglect in our expansions powers higher than the second in the eccentricity-inclination. Our required results, are expressed in terms of Poincaré variables.     

Third order uranus-neptune planetary theory

We calculate in this paper the secular and critical terms arising from the principal part of the classical planetary Hamiltonian. This is the first step to establish a third order canonical planetary theory of Uranus-Neptune through the Hori-Lie technique. We truncate our expansions at the second degree of eccentricity-inclination. Our planetary theory is expressed in terms of the canonical variables of H. Poincaré.     

Third-order Jupiter — Saturn planetary theory

The construction of a third order J-S theory is presented. The Hori theory of planetary perturbations is employed. No Critical J-S terms due to the 2:5 commensurabilities and its multiples exist, when we take into account the periodic terms of order 0, 1, 2 with respect to the eccentricity- inclination. In this case the Lie series transformation degenerates and is meaningless. The J-S equations of motion for secular perturbations are solved when we neglect in our treatment, the Poisson terms of degree > 2 in the Poincaré canonical variables H _u , K _u , P _u Q _u (u = 1, 2). The Jacobi-Radau referential is adopted, and the theory is expressed in terms of the canonical variables of H. Poincaré.Now at the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, U.S.A.     

A second order Jupiter-Saturn planetary theory

We present a second order secular Jupiter-Saturn planetary theory through Poincaré canonical variables, von Zeipel's method and Jacobi-Radau referential. We neglect in our expansions terms of power higher than the fourth with respect to eccentricities and sines of inclinations. We assume that the disturbing function is composed of secular and critical terms only. We shall deriveF _2si and writeF _2s in terms of Poincaré canonical variables in Part II of this problem.     

Lie transforms and the Hamiltonization of non-Hamiltonian systems

To develop the perturbation solution of the non-Hamiltonian system of differential equationsy=g(y, t; ), it is sufficient to obtain the perturbation solution of a Hamiltonian system represented by the HamiltonianK=Y·g(y, t; ) which is linear in the adjoint vectorY. This Hamiltonization allows the direct use of the perturbation methods already established for Hamiltonian systems. To demonstrate this fact, a Hamiltonian algorithm developed by this author and based on the Lie-Deprit transform is applied to the Hamiltonized system and is shown to be equivalent to the application of the non-Hamiltonian form of this same algorithm to the original non-Hamiltonian system.