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Bruno Morando est né en 1931 à Courbevoie, près de Paris. Après des études à la Faculté des Sciences de Paris, il est nommé assistant à la Faculté en 1960 et, en 1963, il entre au Bureau des longitudes, oò il effectuera sa carrière d'astronome. Il soutient sa thèse en 1966 sur le thème: “Théorie planétaire semi-numérique sans introduction de termes séculaires; application à Vesta”. Grâce à André Danjon, Jean Kovalevsky et Bruno Morando vont transformer le Service des calculs du Bureau des longitudes en un laboratoire de recherche en mécanique céleste mondialement réputé. Il en sera le directeur de 1971 à 1984.
Lagrange and Laplace were two of the first members of Bureau des longitudes which, among other tasks, were responsible for the improvement of astronomical tables and the progress of celestial mechanics. Between 1795 and 1850, many improved tables were published under the auspices of Bureau des longitudes: tables of the Sun by Delambre (1806), of the Moon by Burg (1806), Burckhardt (1812) and Damoiseau (1828), of Jupiter, Saturn and Uranus by Bouvard (1808, 1821), of Mercury by Le Verrier (1844), of the satellites of Jupiter by Delambre (1817) and Damoiseau (1836). In his tables, Bouvard showed there was a problem for Uranus. This led to the calculations of the elements of an unknown planet by Le Verrier and Adams and the discovery of Neptune in 1846. Le Verrier's calculations were published in Connaissance des Temps for 1849. In the second half of the XIXth century, two prominent members of Bureau des longitudes, Le Verrier and Delaunay, made major contributions to celestial mechanics by building elaborate theories for the motions of the Sun, the planets and the Moon. Other theories, which improved the above, appeared elsewhere at the end of the century, especially those of Newcomb, Hill and Brown. During the first half of the XXth century, there was a decline of the studies in celestial mechanics which seemed to have reached its limits owing to the difficulties of the computations involved. Yet Sampson's theory of the motion of the satellites of Jupiter and Chazy's first attempts to introduce general relativity into classical celestial mechanics should be quoted. In 1961, thanks to A. Danjon, Bureau des longitudes was reorganized so that its computation service became a research laboratory where, since then, important work in the theories of the planets, the Moon and the satellites has been made.
Part II - Planets and Moon: Theory and Ephemerides
The results of a planetary theory built by an iterative method are given here in order to show the relation with the secular variation theories and the meaning of the mean elements in these latter theories. The general theories have a validity span of several millions years but a weak precision; on the contrary, the secular variation theories reach a great precision over several thousand years. Two applications of the analytical planetary theories are presented: the relation between the barycentric coordinates and the geocentric ones; the determination of the terms of precession and nutation for the rigid Earth.
DE403/LE403 is the latest JPL Planetary and Lunar Ephemeris. It represents a number of changes and improvements to previous JPL ephemerides: the reference frame is now that of the IERS, newer and more accurate observations are used in the adjustment process, some of the data reduction techniques have been refined, and improved dynamical modeling has been incorporated into the equations of motion. As a result, the internal accuracy of the inner four planets has been improved. Further, various measurements accurately tie Jupiter onto the IERS Reference Frame. In the future, use of CCD measurements and the Hipparcos Catalogue should improve the ephemerides of the outermost four planets.
DE403/LE403 has been integrated over 6000 years, from 3000 BC to 3000 AD. A more condensed representation has been made from this, named DE404/LE404. It replaces DE102 as the new JPL “Long Ephemeris”.
The Jet Propulsion Laboratory (JPL) has recently produced a new integrated planetary and lunar ephemeris DE403/LE403. This ephemeris spans the interval JED 624912.5 (December 2, −3002, Julian) – JED 2817104.5 (November 14, 3000, Gregorian) and is an improvement on DE102 (Newhall et al., 1983) and DE200 (Standish, 1990). This integration carries the Cartesian states of the Sun, Moon, and planets, along with the three Euler angles describing the lunar physical librations.
The extremely precise Viking (1972–1982) and Mariner data (1971–1972) were processed simultaneously with the radar-ranging observations of Mars made in Goldstone, Haystack and Arecibo in 1971–1973 for the improvement of the orbital elements of Mars and Earth and parameters of Mars rotation. Reduction of measurements included relativistic corrections, effects of propagation of electromagnetic signals in the Earth troposphere and in the solar corona, corrections for topography of the Mars surface. The precision of the least squares estimates is rather high, for example formal standard deviations of semi-major axis of Mars and Earth and the Astronomical Unit were 1–2 m.
A planetary theory of the planets Jupiter, Saturn, Uranus and Neptune is presented here. It is a classical planetary theory where the perturbations are computed in the form of Poisson series of only one angular variable. It is built with modern values of the planetary masses and fitted to the numerical integration DE245 of the Jet Propulsion Laboratory (Standish, 1994). Its validity time span is of several thousand of years.
Kuiper(1973) suggested that the stability of the Solar System may be meaningfully investigated by studying the stability of the Sun-Jupiter-Saturn system. Numerical investigations by Nacozy(1976) showed that mass enhancement of the two planets beyond a factor of 29.25 led to instabilities in the system. In this new investigation similar mass enhancements were studied in detail numerically and compared with the analytical values derived from the c2H method. In addition, the eccentricities of the two planets were varied as well as their masses. It was found that the system soon showed signs of instability for the increased eccentricities when the masses of the planets were enhanced by fairly small factors.
The motion of the Jovian planets is investigated using Hamiltonian perturbation theory and numerical integrations. Experiments varying the mass of Neptune exhibit 1:1 secular resonance between the perihelion motions of Jupiter and Uranus.
Pluto's motion is chaotic in the sense that the maximum Lyapunov exponent is positive and the Lyapunov time (the inverse of the Lyapunov exponent) is about 20 million years (Myr). We have carried out the numerical integration of Pluto over the age of the solar system (5.7 billion years towards the past and 5.5 billion years towards the future), which is about 280 times of the Lyapunov time. Our integration does not show any indication of gross instability in the motion of Pluto. The time evolution of Keplerian elements of a nearby trajectory of Pluto at first grow linearly with the time and then start to increase exponentially. These exponential divergences stop at about 420 Myr and saturate. The exponential divergences are suppressed by the following three resonances that Pluto has:
(1) Pluto is in the 3:2 mean motion resonance with Neptune and the libration period of the critical argument is about 20000 years.
(2) The argument of perihelion librates around 90 degrees and its period is 3.8 Myr.
(3) The motion of the Pluto's orbital plane referred to the Neptune's orbital plane is synchronized with the libration of the argument of perihelion (a secondary resonance). The libration period associated with the second resonance is 34.5 Myr.
We briefly discuss the motions of Kuiper belt objects in a 3:2 mean motion resonance with Neptune and several possible scenarios how Pluto evolves to the present stable state.
We present the results of numerical integrations of Pluto and some fictitious Plutos in three different models (the circular and the elliptic restricted three body problem and the outer solar system). We determined the “extension” of the stable region in these models by means of the Lyapunov Characteristic Numbers and by an analysis of the orbital elements.
The motion of the planets is one of the best modelized problems in physics, and its study can be practically reduced to the study of the behavior of the solutions of the well known gravitational equations, neglecting all dissipation, and treating the planets as mass points. In fact, the mathematical complexity of this problem, despites its apparent simplicity is daunting and has been a challenge for mathematicians and astronomers since its formulation three centuries ago.
Introduction of Jacobi elliptic functions in planetary, satellite and cometary problems of celestial mechanics is a transformation of variables to present the analytical theories of motion in the more compact form as compared with the traditional series in multiples of mean longitudes or mean anomalies.
We compare numerical efficiency of the two kinds of series for the first-order intermediate orbit for general planetary theory: (1) the classical expansion involving mean longitudes of the planets; (2) an expansion resulting from the theory of elliptic functions. We conclude that mutual perturbations of close couples of planets (the ratio of major semi-axes ∼ 1) can be represented in more compact form with the aid of the second kind of series.
The analysis of pulsar time-of-arrival data is intimately bound up with planetary ephemerides. Highly accurate ephemerides are required for Earth and Moon and, to a lesser degree, for the other planets, in order to make full use of the timing data for millisecond-class pulsars. These data, in turn, present an opportunity for improving planetary ephemerides in a variety of ways. Fitting the Earth and Moon orbital parameters to the timing data is the obvious first step, though it is less valuable in the short term for many applications than using the current accumulation of spacecraft-tracking and lunar laser ranging data. By themselves, the pulsar timing data convey no information on the orientation of Earth's orbit, since each pulsar's position on the sky must be determined from those same data. However, independent pulsar position measurements by VLBI, in combination with the timing-derived positions, can serve to fix the orientation of Earth's orbit with respect to the radio reference frame and thereby link the planetary and radio frames. In the long run, the acquisition of timing data over increasing time spans and with improving precision should prove to be an important factor in determining the shape, as well as the orientation, of Earth's orbit. In addition, pulsar timing over a sufficiently long span can directly measure a planet mass through the reaction of the rest of the solar system. The effect must be observed for a major fraction of the orbital period of the planet in question so that the signature can be separated from that of the ordinary spin-down of each pulsar. Finally, pulsar timing can be used to probe gravitational physics, a field with far-reaching consequences and a basic part of the framework for constructing the ephemerides.
Long planetary and lunar ephemerides like the JPL DE102 and LE51 (Newhall et al., 1983) and the Bureau des Longitudes VSOP (Bretagnon, 1982) and ELP (Chapront-Touze and Chapront, 1983) have enabled more positive ancient eclipse, planetary and cometary identifications, which have in turn refined ephemerides, e.g., the reconstruction of the orbit of comets Halley and Swift-Tuttle (Yeomans and Kiang, 1981; and Yau et al., 1994). The data used to initialize DE102 are pre-1977. Much more observational data have been collected since. The lunar ephemeris has also been improved. The secular lunar acceleration, , from laser ranging, is −25.9±0.5″/cen2 (Williams et al., 1992). We can now uniquely solve for ΔT, the clock error, from ancient eclipse records. The lack of ΔT values before 700 B.C. has left the early timescale of the ephemerides unconstrained (Morrison, 1992). Our solution of this problem is outlined here.
The state of knowledge of the motions of all Saturn's satellites is presented (excluding however the rings and their relating shepherding satellites). In particular, it appears that the theory of motion of the major satellites is now more precise than the available Earth-based observations, allowing to expect new progress with the next observations from mutual events and then with those from the Cassini mission.
The principles are set out for the construction of a theory of the motion of the orbit plane of Hyperion, using the mixed set of angle parameters, using different reference planes for different angles, which it has proved convenient to use. It is found that this leads to additional terms, which have not been shown in previous published theories. The theory is developed in general principles exactly, and in detail as far as is needed to enable comparison to be made with the observational data at present available, and, from parameters which have been derived from opposition means from the period 1875 to 1922, the co-efficients of some of the larger long-period terms are computed.
93 observations of the seventh satellite of Saturn, Hyperion, with 473 observations of Titan—Saturn's sixth and the most massive satellite and the one nearest to Hyperion—are considered. The observations were made in 1967–1981 at several observatories. The values of (O–C) across and along the orbits are obtained. The normality of the distributions of (O–C) is studied.
This paper gives a test of the reliability of TASS from Vienne & Duriez via the comparison of the theory of Iapetus given by Harper & Taylor. From fitting it to photographic observations, we derived a redetermination of the orbit of Iapetus.