Aims. Spectroscopic and photometric properties of low and high-z supernovae Ia (SNe Ia) have been analyzed in order to achieve a better understanding of their diversity and to identify possible SN Ia sub-types. Methods. We use wavelet transformed spectra in which one can easily measure spectral features. We investigate the Si II 4000 equivalent width (EW w {Si II}). The ability and, especially, the ease in extending the method to SNe at high-z is demonstrated.Results. We applied the method to 110 SNe Ia and found correlations between EW w {Si II} and parameters related to the light-curve shape for 88 supernovae with available photometry. No evidence for evolution of EW w {Si II} with redshift is seen. Three sub-classes of SNe Ia were confirmed using an independent cluster analysis with only light-curve shape, colour, and EW w {Si II}. Conclusions. SNe from high-z samples seem to follow a similar grouping to nearby objects. The EW w {Si II} value measured on a single spectrum may point towards SN Ia sub-classification, avoiding the need for expansion velocity gradient calculations.
A geometric view of the possible outcomes of elastic collisions of two massive bodies is developed that integrates laboratory, center of mass, and relative body frames in a single diagram. From these diagrams all the scattering properties of binary collisions can be obtained. The particular case of gravitational scattering by a moving massive object corresponds to the slingshot maneuver, and its maximum velocity is obtained.Comment: 7 pages, 5 figure
We derive the equations for the gravity assist manoeuvre in the general 2D case without the constraints of circular planetary orbits or widely different masses as assumed by Broucke (AIAA/AAS 1988) and obtain the slingshot conditions and maximum energy gain for arbitrary mass ratios of two colliding rigid bodies. Using the geometric view developed in an earlier paper by the authors (Rica da Silva, A., Lemos, J.P.S.: Am. J. Phys. 74, [584][585][586][587][588][589][590] 2006) the possible trajectories are computed for both attractive or repulsive interactions yielding a further insight on the slingshot mechanics and its parametrization. http:// centra.ist.utl.pt/amaro/Collisions/Collisions.html. The general slingshot manoeuvre for arbitrary masses is explained as a particular case of the possible outcomes of attractive or repulsive binary collisions, and the correlation between asymptotic information and orbital parameters is obtained in general.
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