On the co-orbital motion in the planar restricted three-body problem: the quasi-satellite motion revisited

In the framework of the planar and circular restricted three-body problem, we consider an asteroid that orbits the Sun in quasi-satellite motion with a planet. A quasi-satellite trajectory is a heliocentric orbit in co-orbital resonance with the planet, characterized by a non zero eccentricity and a resonant angle that librates around zero. Likewise, in the rotating frame with the planet it describes the same trajectory as the one of a retrograde satellite even though the planet acts as a perturbator. In the last few years, the discoveries of asteroids in this type of motion made the term "quasi-satellite" more and more present in the literature. However, some authors rather use the term "retrograde satellite" when referring to this kind of motion in the studies of the restricted problem in the rotating frame. In this paper we intend to clarify the terminology to use, in order to bridge the gap between the perturbative co-orbital point of view and the more general approach in the rotating frame. Through a numerical exploration of the co-orbital phase space, we describe the quasi-satellite domain and highlight that it is not reachable by low eccentricities by averaging process. We will show that the quasi-satellite domain is effectively included in the domain of the retrograde satellites and neatly defined in terms of frequencies. Eventually, we highlight a remarkable high eccentric quasi-satellite orbit corresponding to a frozen ellipse in the heliocentric frame. We extend this result to the eccentric case (planet on an eccentric motion) and show that two families of frozen ellipses originate from this remarkable orbit.Comment: 30 pages, 13 figures, 1 tabl

The family of Quasi-satellite periodic orbits in the circular co-planar RTBP

In the circular case of the coplanar Restricted Three-body Problem, we studied how the family of quasi-satellite (QS) periodic orbits allows to define an associated libration center. Using the averaged problem, we highlighted a validity limit of this one: for QS orbits with low eccentricities, the averaged problem does not correspond to the real problem. We do the same procedure to L 3 , L 4 and L 5 emerging periodic orbits families and remarked that for very high eccentricities F L4 and F L5 merge with F L3 which bifurcates to a stable family

New solution for the geometric distorsion in astronomical images : application to Phoebe observatons

Program available at: http://www.imcce.fr/hosted_sites/naroo/program.htmlInternational audienceA new approach for the correction of the geometric distorsion is proposed. This approach is applied to observations of three open clsuters taken at the Yunnan Observatory. It is shown that the correction depends on the filter used. The technique is then used to correct the positions of Phoebe (ninth satellite of Saturn). The precision on the positions is significantly improved

Titan's rotation: A 3-degree of freedom theory

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A new catalogue of observations of the eight major satellites of Saturn (1874-2007)

The original publication in Astronomy & Astrophysics is available at www.aanda.org.International audienceContext : The lastest catalogue of observations includes about 51 000 observations (over 3500 nights) of Saturn's satellites from 1874 to 1989. Since 1989, many observations have been published, often in different formats, based on the publication. Aims : Our new catalogue of observations of the eight major satellites of Saturn includes the observations of the previous catalogues, newly published data and also old observations left out of the previous catalogue. The observations are tabulated in a consistent format. Methods : We give, for each observation, the corrections applied for reduction such as refraction, aberration or phase effects. Furthermore, when it was possible, the instrument and catalogue are also indicated. Results : The new catalogue presents more than 130 000 observations (over 6000 nights) of the eight major satellites of Saturn from 1874 to 2007

Estimating the accuracy of satellite ephemerides using the bootstrap method

International audienceContext: The accuracy of predicted orbital positions depends on the quality of the theorical model and of the observations used to fit the model. During the period of observations, this accuracy can be estimated through comparison with observations. Outside this period, the estimation remains difficult. Many methods have been developed for asteroid ephemerides in order to evaluate this accuracy. Aims: This paper introduces a new method to estimate the accuracy of predicted positions at any time, in particular outside the observation period. Methods: This new method is based upon a bootstrap resampling and allows this estimation with minimal assumptions. Results: The method was applied to two of the main Saturnian satellites, Mimas and Titan, and compared with other methods used previously for asteroids. The bootstrap resampling is a robust and practical method for estimating the accuracy of predicted positions

CCD Positions of Saturn and its Major Satellites from 2002-2006

International audienceThis paper presents 2154 precise positions of Saturn and its major satellites from 359 CCD exposures taken with the 1 m telescope at the Yunnan Observatory during the years 2002-2006. It also describes the improved image-processing techniques for the pixel positional measurement of Saturn's rings and its major satellites, especially for Mimas and Enceladus. The four bright satellites S3-S6 (i.e., Tethys, Dione, Rhea, and Titan) of Saturn are used to calibrate the CCD field of view by comparing their pixel positions with their theoretical ones from the theory TASS1.7. The observational positions of these major satellites, when measured with respect to Rhea, usually have a good agreement with their theoretical ones except for Mimas, which has the biggest systematic difference of about -0.3 arcsec in R.A. in its 2002 observational data sets. However, these differences of Mimas become much smaller when the recent Jet Propulsion Laboratory ephemeris is replaced. The rms errors in each coordinate are about 40 mas for Saturn and its bright satellites S2-S6, and 90 mas for Mimas. These positional observations are comparable to the best ground-based CCD observations

A Convenient Solution to Geometric Distortion and Its Application to Phoebe's Observations

International audienceA simple but effective approach is proposed for measuring the geometric distortion of a CCD field of view of a ground-based telescope. For three open clusters (M35, M67, and NGC 2324), 425 CCD frames taken by a 1 m telescope at the Yunnan Observatory are used to test this approach. It is found that the geometric distortion pattern depends strongly on the corresponding filter used. The geometric distortion is then used to correct the pixel positions for Phoebe, the ninth satellite of Saturn, and its reference stars imaged in 220 CCD frames taken by the same telescope. The standard deviation of the (O - C; observed minus computed) residuals of Phoebe is significantly improved after correcting the geometric distortions