Multiple solutions in preliminary orbit determination from three observations

Charlier’s theory (1910) provides a geometric interpretation of the occurrence of multiple solutions in Laplace’s method of preliminary orbit determination, assuming geocentric observations. We introduce a generalization of this theory allowing to take into account topocentric observations, that is observations made from the surface of the rotating Earth. The generalized theory works for both Laplace’s and Gauss’ methods. We also provide a geometric definition of a curve that generalizes Charlier’s limiting curve, separating regions with a different number of solutions. The results are generically different from Charlier’s: they may change according to the value of a parameter that depends on the observations.     

Galaxy formation and evolution – I. The Padua tree-sph code (pd-sph)

In this paper we report on pd-sph , the new tree-sph code developed in Padua. The main features of the code are described and the results of a new and independent series of 1D and 3D tests are shown. The paper is mainly dedicated to the presentation of the code and to the critical discussion of its performance. In particular, great attention is devoted to the convergency analysis. The code is highly adaptive in space and time by means of individual smoothing lengths and individual time-steps. At present it contains both dark and baryonic matter, this latter in the form of gas and stars, cooling, thermal conduction, star formation, feedback from Type I and II supernovae, stellar winds, and ultraviolet flux from massive stars, and finally chemical enrichment. New cooling rates that depend on the metal abundance of the interstellar medium are employed, and the differences with respect to the standard ones are outlined. Finally, we show the simulation of the dynamical and chemical evolution of a disc-like galaxy with and without feedback. The code is suitably designed to study in a global fashion the problem of formation and evolution of elliptical galaxies, and in particular to feed a spectrophotometric code from which the integrated spectra, magnitudes and colours (together with their spatial gradients) can be derived.     

Logarithmic spiral trajectories generated by Solar sails

Analytic solutions to continuous thrust-propelled trajectories are available in a few cases only. An interesting case is offered by the logarithmic spiral, that is, a trajectory characterized by a constant flight path angle and a fixed thrust vector direction in an orbital reference frame. The logarithmic spiral is important from a practical point of view, because it may be passively maintained by a Solar sail-based spacecraft. The aim of this paper is to provide a systematic study concerning the possibility of inserting a Solar sail-based spacecraft into a heliocentric logarithmic spiral trajectory without using any impulsive maneuver. The required conditions to be met by the sail in terms of attitude angle, propulsive performance, parking orbit characteristics, and initial position are thoroughly investigated. The closed-form variations of the osculating orbital parameters are analyzed, and the obtained analytical results are used for investigating the phasing maneuver of a Solar sail along an elliptic heliocentric orbit. In this mission scenario, the phasing orbit is composed of two symmetric logarithmic spiral trajectories connected with a coasting arc.     

Non-resonant secular dynamics of trans-Neptunian objects perturbed by a distant super-Earth

We use a secular model to describe the non-resonant dynamics of trans-Neptunian objects in the presence of an external ten-Earth-mass perturber. The secular dynamics is analogous to an “eccentric Kozai mechanism” but with both an inner component (the four giant planets) and an outer one (the eccentric distant perturber). By the means of Poincaré sections, the cases of a non-inclined or inclined outer planet are successively studied, making the connection with previous works. In the inclined case, the problem is reduced to two degrees of freedom by assuming a non-precessing argument of perihelion for the perturbing body. The size of the perturbation is typically ruled by the semi-major axis of the small body: we show that the classic integrable picture is still valid below about 70 AU, but it is progressively destroyed when we get closer to the external perturber. In particular, for \(a>150\) AU, large-amplitude orbital flips become possible, and for \(a>200\) AU, the Kozai libration islands at \(\omega =\pi /2\) and \(3\pi /2\) are totally submerged by the chaotic sea. Numerous resonance relations are highlighted. The most large and persistent ones are associated with apsidal alignments or anti-alignments with the orbit of the distant perturber.     

The nature of η carinae

We give an overview of the Car phenomenon on the basis of ground and space observations. We discuss in particular the IRAS images. We conclude that Car, initially with a mass > 100M , is presently an intermediate-type hypergiant withL=5×10⁶ L , in a rapid evolutionary stage. This phase started with a large increase of mass loss in mid-1800 followed by dust condensation and a large visual fading, at constant bolometric luminosity.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.