LUNAR SAROS CYCLE
The 1999 solar eclipse as seen from Europe
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
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..
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.
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
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