# P. Bretagnon's research while affiliated with French National Centre for Scientific Research and other places

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## Publications (58)

Based on the current IAU hierarchy of the relativistic reference systems, practical formulae for the transformation between barycentric (BCRS) and geocentric (GCRS) celestial reference systems are derived. BCRS is used to refer to ICRS, International Celestial Reference System. This transformation is given in four versions, dependent on the time ar...

Based on the current IAU hierarchy of the relativistic reference systems, practical formulae for the transformation between barycentric (BCRS) and geocentric (GCRS) celestial reference systems are derived. BCRS is used to refer to ICRS, International Celestial Reference System. This transformation is given in four versions, dependent on the time ar...

Expressions for the torques exerted by components of the tidal potential
of any degree and order (n, m) are given and used to obtain the high
frequency rotations excited, and the corresponding polar motions, as
functions of frequency. Special features relating to different types of
excitations are discussed, and a few examples of numerical results...

The accuracy of the rigid-Earth solution SMART97 is 2 microarcseconds over the time interval 1968-2023. To obtain a nonrigid-Earth solution, the authors use the transfer function of Mathews (1999). The perturbations of the third component of the angular velocity vector are taken into account.

SMART97 solution for a rigid Earth; transfer functions of Wahr, Mathews
(1991), Dehant-Defraigne; transfer functions of Mathews (1999). The
geophysical model includes the effects of electromagnetic coupling, the
ocean effects, mantle inelasticity effects, atmospheric effects and
changes in the global Earth dynamical flattening and in the core
flatt...

Report of the IAU WGAS (Working Group on Astronomical Standards) sub - working group on relativity in celestial mechanics and astrometry (RCMA SWG).

The study of the rotation of the Earth consists of two parts: the calculation of the precession-nutation of the Earth in the rigid case, then the determination of complements due to the geophysical components of the Earth. The SMART97 solution (Bretagnon et al., 1998) for the rigid Earth ensures an accuracy at the level of 2 microarcseconds for the...

The Earth rotation solution SMART97 (Solution du Mouvement de l'Axe de Rotation de la Terre) is an analytical solution of the Earth rotation in the rigid case. It gives the expressions of precession-nutation and rotation of the Earth for the 3 Euler angles psi, omega, phi as well as for the quantities p, ε, chi, and the sidereal time. For the axis...

RCMA SWG was appointed by the IAU WGAS (Working Group on Astronomical Standards) in accordance with IAU Resolution C6 (1994) with the aim ‘to provide definitions of the astronomical units, of the quantities linking these astronomical units to the units of the International System (SI), and of other astronomical quantities, compatible with the theor...

The solution SMART97 (Solution du Mouvement de l'Axe de Rotation de la
Terre) is an analytical solution of the motion of the axis of rotation
of the Earth, resulting from an improvement of the theory presented in
Bretagnon et al. (1997). This solution is built with the analytical
theories of the motion of the Moon, the Sun and the planets of the
Bu...

We present the computation of the precession and nutation expressions
built with the analytical theories of the motion of the Moon, the Sun
and the planets of the Bureau des longitudes. We take into account the
influence of the Moon, the Sun and all the planets on the potential of
the Earth limited to C_j,0_ for j from 2 to 5, C_2,2_, S_2,2_, C_3,k...

We present the results of a solution of the Earth’s rotation built with analytical solutions of the planets and of the Moon’s motion. We take into account the influence of the Moon, the Sun and all the planets on the potential of the Earth for the zonal harmonics C
j,0 for j from 2 to 5, and also for the tesseral harmonics C2,2, S2,2C3,k
, S3,k
for...

We present the use of the analytical solutions of the planets and of the Moon's motion in the determination of the quantities which relate the barycentric and the geocentric coordinate systems and of the expressions of precession-nutation. The computation of the precession and nutation quantities are built with the analytical theories of the motion...

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...

The Planetary solutions VSOP87 (Variations Seculaires des Orbites Planetaires) are analytical solutions of the motion of the planets in different versions. The main version VSOP87 consists of the series in elliptic elements as in the case of VSOP82 solution and the other versions VSOP87 (A-B-C-D-E) are built in in rectangular and spherical variable...

In 1976, the IAU recommended for the value of the precession constant 50".290 966 per Julian year and, since 1984, most of the ephemerides have used the formulas of Lieske
et al.
(1977). In this paper, the motion of the ecliptic was based on Newcomb’s theory. The ecliptic was defined with an accuracy of 0".3 over 1000 years and of 6 mas over one ce...

The files given here refer to the paper A&A 282, 663 (1994) which concerns the following topics: - numerical expressions for the precession quantities, - mean elements for Moon and planets, from Mercury to Neptune, - formulae for computing approximate ephemerides for Moon and planets. The files concern only precession and approximate ephemerides of...

We present, in this paper, a coherent set of formula giving numerical expressions for precession quantities and mean elements of the Moon and the planets. First, using the notations of Lieske et al. (1977), we construct expressions for the precession quantities based upon the use of the secular variations of the ecliptic pole from the planetary the...

Extending the results of our preceding paper (Brumberg et al. 1992) we
evaluate here the solar, lunar and planetary terms in the relativistic
transformations between the references systems and their associated time
scales. The results presented in Tables 1-3 may be also considered as
some extension of the currently used expansions in the theory of...

A planetary theory of the system: the sun-Jupiter-Saturn-Uranus-Neptune
is constructed. The method described in Simon & Joutel (1988) is
used to compute the perturbations in the form of Poisson series of only
one angular variable. As an illustration, a solution of the motion of
Jupiter represented with heliocentric sherical variables reckoned to th...

An iterative method for the construction of planetary theories has been developed in order to determine the high order perturbations with respect to the masses. These perturbations are indeed needed to enlarge the validity span of analytical theories up to some million years. The application to the simplified Sun-Jupiter-Saturn problem gives a solu...

Using the analytical planetary theories VSOP87 (Bretagnon and Francou,
1988) and the relativistic theory of astronomical reference systems of
Brumberg and Kopejkin (1989) the authors have derived the analytical
expressions of the relativistic quantities enabling one to set the
relationships between (1) TCB and TCG, (2) barycentric spatial
coordinat...

A general theory of the simplified sun-Jupiter-Saturn system is
developed using an iterative method. Convergence difficulties
encountered for the long-period terms of the semimajor axes of the two
planets were resolved. The solution is compared to a numerical
integration of the same system over 600,000 yr, and good agreement is
found.

An iterative method is developed in the construction of general
planetary theories. Due to the speed of computers, the study of
long-period variations of planetary orbits can now be done by numerical
integration over multimillion-year time spans. The iterative method
enables the development of higher-order perturbations with respect to
the planetar...

An analytical formula for the time transformation TB-TT valid over a few
thousand years around J2000 has been computed with an accuracy at the 1
ns level. The 127 coefficients presented in this paper provide a formula
accurate at the 100 ns level. The numerical and analytical procedures to
compute this transformation are discussed and compared. It...

An analytical formula for the time transformation TB-TT valid over a few
thousand years around J2000.0 has been computed with an accuracy at the
1 ns level. The numerical and analytical procedures to compute this
transformation are discussed and compared.

Up to this time, the VSOP (Variations Séculaires des Orbites
Planètaires) analytical solutions of the motion of the planets
were only represented in elliptic variables, but the cartesian or
spherical variables are much more convenient in many problems:
determination of the planetary perturbations of the Moon, analytical
expressions for the computat...

An analytical formula for the time transformation TDB–TDT valid over a few thousand years around J2000 has been computed with an accuracy at the 1 ns level. The coefficients for a formula accurate at the 100 ns level are provided here. The numerical and analytical procedures to compute this transformation are discussed. We note that these procedure...

Corrections to the numerical integration of the planetary constants
developed by Oesterwinter and Cohen (1972) from 40,000 observations of
the sun, moon, and other planets are presented. The constants of
integration include the average planetary longitude, the orbital
eccentricity, the longitude of the perihelion, the inclination, the
longitude of...

La construction de théories planétaires a été entreprise au Bureau des Longitudes pour l'ensemble du système solaire. Il s'agit de théories semi-analytiques à variations séculaires ce qui signifie que les termes à longues périodes (périodes des périhélies et des noeuds comprises entre 50 000 ans et 2 000 000 d'années) ont été développés par rapport...

New theories for the motions of the Moon and the planets, which were developed at the Bureau des Longitudes, are compared with observations and with numerical methods. These new theories will be introduced in ‘Connaissance des Temps’ from 1984 on.

The relativistic perturbations in the osculating elements of all the
planets, due to the theory of General Relativity, are presented where
only the gravitational field of the sun is taken into account and the
effects are calculated in the post-Newtonian approximation. The
relativistic effects are calculated with the requirement that an
accuracy of...

The precession quantities are completely determined by the two motions
of the equatorial pole and the ecliptic pole. The precessional
formulae derived by (Lieske et al., 1977) are based upon the use of
the secular variations of the ecliptic pole from Newcomb's theory of
the Sun. Taking advantage of the analytic formular given by Lieske et
al., the...

Together with a solution working order after order with respect to the
masses, we have undertaken, at the Bureau des Longitudes, the
construction of a theory for the outer planets Jupiter, Saturn, Uranus,
and Neptune through an iterative method.
This method makes it possible to reach a high order with respect to the
masses, particularly for Jupite...

The paper sketches some work being done on the construction of planetary
theories with secular variations. The long period arguments (perihelion
and node motion) are developed in time power series. Calculation methods
employed are of two types: (1) iterative method, and (2) incremental
method. Secular terms in the semimajor axes were found as early...

At the Bureau of Longitudes the construction of planetary theories have been developed in three directions: A general theory of the motion of the four largest planets in the solar system is in the course of development at the Faculty of Sciences at Lille by L. Duriez (1977) following the methods of V. A. Brumberg and J. Chapront (1973). Theories of...

La construction de théories planétaires précises est un travail long et, pour ce qui nous concerne, n’est pas encore achevée. Aussi, les résultats dont nous parlerons ici ne sont que des résultats provisoires. Nous développerons quelques aspects des difficultés que nous avons rencontrées et les conséquences de ces difficultés sur l’orientation des...

We give here results dealing with the perturbations at the first order
of masses for the four large planets as well as their derivatives with
respect to the integration constants. Five tables show the integration
constants used, the secular variations of the first order, the
periodical perturbations of the first order for the four large planets,
th...

The first-order perturbations of Jupiter, Saturn, Uranus, and Neptune
are obtained from Lagrange's equations by two different methods:
integration order by order with respect to masses and a method of
successive approximations. The first order perturbations are presented
in the form of Fourier series with numerical coefficients for the
periodic com...

Les auteurs présentent un formulaire sous une forme compacte pour la construction des perturbations planétaires d'ordres élevés par rapport aux masses perturbatrices. Elles ont été construites par un processus itératif et donnent les variations des éléments osculateurs. Il n'y a pas de singularités pour les excentricités et inclinaisons nulles dans...

The authors present formulas in compact form for constructing high order
planetary perturbations with respect to the disturbing masses. They have
been built by an iterative process and give the variations of osculating
elements. Singularities due to vanishing eccentricities and inclinations
are not present in the differential equations. All element...

## Citations

... where the spatial gradient operator is given by ∂ i ≡ ∂/∂ x i , the Newtonian gravitational potential is given by U and the subscripts j, k denote the j-th gravitational and k-th nongravitational perturbation, respectively. Owing to the increased accuracy requirements in fields such as astrometry (Soffel and Han 2019), geodesy (Müller et al. 2008;Soffel and Langhans 2012), the rapid improvements in time and frequency stability (Exertier et al. 2019), and further, the development and utilisation of advanced telecommunication systems for radio tracking of interplanetary probes, we require that Einstein's general theory of relativity (d'Inverno 1992;Weinberg 1972) be taken into account for any mission requiring highly accurate orbit information and practically all astronomical and geodynamical observations (Brumberg et al. 1998). Within the Solar System, the so-called effects of general relativity are accounted for using the first post-Newtonian (PN) approximation (Soffel and Han 2019) and we refer the reader to the seminal papers Damour et al. (1991Damour et al. ( , 1992bDamour et al. ( , 1993Damour et al. ( , 1994 for extensive technical details. ...

... To construct a planetary theory two major ways can be considered: the use of a numerical integrator [8], [6] or the use of analytical methods to integrate the problem [2], [22], [23], [26]. ...

... In the present case, the same effect should eventually be observed by performing a much longer integration. It might be interesting to remark that a similar calculation, namely approximating the dynamics of the SJS system with a quasi–periodic motion, has been performed by Bretagnon and Simon ([3]). Their method was based on the technique introduced by Krylov and Bogoliubov (which is reminiscent of the Lindstedt's series method). ...

... The mean orbital elements of the inner planets are given in the form of segments of the power series to the second power of time (23). Bretagnon (1982c) complemented the theory of motion of the inner planets by the third approximation that includes the relativistic perturbations from the Sun (Lestrade and Bretagnon, 1982). As a result, the ephemerides were computed with an accuracy of 0.0005′′ for Mercury, 0.0030′′ for Venus and the Earth, and 0.0047′′ for Mars. ...

... The Lagrange equations were presented in compact form (Chapront et al., 1975), which makes it possible to obtain the perturbations using an iterative process. The mutual perturbations of all pairs of outer planets are given in Simon and Bretagnon (1975b). ...

... Expressions for the non-rigid Earth nutations in the longitude and the obliquity, presented in (2), in the paper of Bretagnon et al. (1999) contain only the real parts of the complex values. The exact expressions for the non-rigid Earth nutations in the longitude and the obliquity, in the complex values, are obtained in this investigation: ...

... The angular arguments, ζ ( j) (t), are linear combinations of the Delaunay arguments, whose linear change rates then specify the respective frequencies (Simon et al. 1994;Petit and Luzum 2010). The real constants C 2m( j) , S 2m( j) measure the frequency-dependent contribution of the potential raised by Earth and Sun with respect to the lunar reference sphere of radius R, more specifically, through ...

... Comparison of the frequencies obtained analytically and numerically by Applegate et al. (1986), Bretagnon and Francou (1992), Laskar (1990), andNobili et al. (1989) showed good agreement between the results (Table 3). Bretagnon (1996) considered the relationship between the general planetary theory constructed by an iterative method and the classical theory containing secular terms in the inclinations and eccentricities. The interval of applicability of the general planetary theory reaches several million years at a low ephemeris accuracy. ...

... This equation can be solved only by numerical integration and the results are given in polynomial form. To date, the best approximation is given by Williams (1994) and Simon et al. (1994); however, these solutions are applied only in the best professional computer codes, while the large majority of commercial programs use the older Lieske et al. (1977) solution (the so called "IAU formula", since it is based upon the International Astronomical Union IAU/1976/ system of astronomical constants) or its �rst order approximation or even a simple proportional correction with the average value of -0.024 arcsec per century. ...

... In order to get the time transformation between t TX and t TB , the differential (54) must be integrated for the whole time span we consider for the radio-science experiment (nominally, the duration of the space mission). In literature, there are also some approximate analytical solutions of (54) (see [22]), which can be used to perform the time transformations. ...