ettore perozzi CV
THE LUNAR SAROS CYCLE

The 1999 solar eclipse as seen from Europe

A peculiar feature of the Earth-Moon-Sun system is the existence of the Saros, a cycle of 6585.321 days (18 years and 10 or 11 days depending on the number of leap years within) widely used for eclipse prediction since the time of the ancient chaldeans. After one Saros the type of eclipse repeats itself implying that the geometry of the Earth-Moon-Sun system also repeats. In collaboration with the Department of Physics and Astronomy of the University of Glasgow a research project has been started in 1988 in order to to give a modern interpretation to this historically known lunar cycle.
The existence of the saros depends upon high-number commensurabilities between the mean motions of the Sun and the Moon, and the lunar nodical and anomalistic months. Using eclipse records, the JPL ephemeris and results from three-body numerical integration it is shown that the Earth-Moon-Sun system moves in a nearly periodic orbit of period equivalent to the Saros and that the Saros is the natural period of time for averaging solar perturbations in any study on the long-term evolution of the lunar


THE POINCARE' PROJECT
 
A set of eight periodic orbits whose time evolution closely resemble that of the Moon is found in the restricted circular three-body problem; a survey of "saros-like" periodic orbits is therefore performed and it is shown that they are very abundant in Earth-Moon-Sun system, exhibiting a rather peculiar arrangement.
The existence of so many periodic orbits associated with the Saros cycle can be viewed in the light of Poincare's conjecture, stated by the French mathematician at the end of the previous century: according to it there should be infinitely many, of longer and longer period.


LUNAR TIDES
 
The implication on the frequency of occurrence of saros-like configurations is also investigated, as the Moon slowly recedes from the Earth due to tidal friction, and one example of a saros of different length than the present one is found relative to the probable lunar orbit of the late Precambrian, almost 700.000 years ago.


references

Significant High-Number Commensurabilities in the Main Lunar Problem I: The Saros as a Near-Periodicity of the Moon's Orbit.
E. Perozzi, A.E. Roy, B.A. Steves, G.B. Valsecchi. Celestial Mechanics and Dynamical Astronomy 52, 241-261, 1991.
Significant High-Number Commensurabilities in the Main Lunar Problem II: The  Occurrence of Saros-like Periodicities.
B.A. Steves,  G.B. Valsecchi, E. Perozzi, A.E. Roy. Celestial Mechanics and Dynamical Astronomy 57, 341-368, 1993.
Significant High-Number Commensurabilities in the Main Lunar Problem: a Postscript to a Discovery of the Ancient Chaldeans. A.E. Roy, B.A. Steves, G.B. Valsecchi, E. Perozzi. In proc 'Predictability, Stability and Chaos in N-Body Dynamical Systems', A.E.Roy ed, Plenum Press, New York, 273-282, 1991
Periodic Orbits Close to that of the Moon.
G.B. Valsecchi, E. Perozzi, A.E. Roy, B.A. Steves. Astronomy & Astrophysics 271, 308-314, 1993.
The Arrangement in Mean Elements' Space of the Periodic Orbits Close to that of the Moon
.
G.B. Valsecchi, E. Perozzi, A.E. Roy, B.A. Steves. Celestial Mechanics and Dynamical Astronomy 56, 373-380, 1993.
Hunting for  Periodic Orbits Close to that of the Moon in the Restricted Circular Three-Body Problem
.
G.B. Valsecchi, E. Perozzi, A.E. Roy, B.A. Steves. In proc. 'From Newton to Chaos', A.E.Roy and B.A.Steves eds, Plenum Press, New York and London, 231-234, 1995.
La Luna e il Saros.
E. Perozzi & G.B. Valsecchi. L'Astronomia 182, 1997.


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