Di↵erent reference systems where we get observed coordinates and general change to ICRS

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Di↵erent reference systems where we get observed coordinates and general change to ICRS

When we want to compare the observed positions of the satellite with the computed posi-tions which at first are the vectors solved from the dynamical equations, we should trans-form these vectors from planetocentric equator or ecliptic system to the reference systems of the observations. We need to find out the reference system for every observation and for simplifying the process of the vectors transformation, we try to reduce the observations in the same reference system. The following reference systems were used in observations of Phoebe and the number that indicate the reference system will be present in the figure 4-4. For each reference system we introduce the general method to change the coordinates in this reference system to the coordinates in the ICRS reference system. We will introduce a new reduction in Chapter 4 with which we do not need to change the reference system as usual for some old observations. The main idea of this new reduction was published in Desmars et al. [2013] at the beginning of our thesis work and only some of earliest old observations had been reduced in that article.

Catalogs used for reductions

We are looking for old observations which had been reduced with di↵erent reference star catalogues. We need to identify which catalogs were used to be able to identify which stars were used to the reduction and then to make corrections to the astrometric positions. The following information for catalogs are from ViZieR database ( Ochsenbein [2000]) from CDS (Centre de Données astronomiques de Strasbourg), and the mark I/number is the catalog identification code in ViZieR.

Catalogs used for old reductions

The Bonner Durchmusterung (BD, Argelander [1859-62], Kuestner [1903], Becker [1951], Schmidt [1968]) is a visual survey of stars in the declination zones +89 to 01 degrees. Ac-tual magnitude estimates were made and reported to 0.1 mag for all stars down to 9.5 mag, with fainter stars being assigned to 9.5. Positions are given to the nearest 0.1 sec in right ascension and 0.1 arcminute in declination. Positions are for Equator 1855 and no proper motion is provided. It has not been used to identify the stars around Phoebe because of the declination zones but it is a well known catalogue used before 1910. The catalogs published before 1920 usually have the BD number in the catalog.

Catalog comparison and the statistics on the used catalogues

The number of reference stars of the old catalogues on photographic plates is small and their positions are inaccurate. As an illustration, figure 2-2 represents the statistics of the di↵erence in angular separation of the stars in old catalogue and modern catalogues used p in current reduction (Here angular separation is given by s = Δ↵2 cos2 + Δ 2 where Δ↵ and Δ are the right ascension and declination di↵erence between older and modern cata-logues.). For many stars, the di↵erence in position between the older and recent catalogues is more than 5 arcsec. The positions of the reference stars in the old catalogues represent a source of systematic errors on Phoebe’s positions.
Phoebe is far away from its planet, most of the observations are in absolute coordinates. The catalogues used in astrometric reduction cause the systematic error. This error depends on the catalogue used and on the zone on the celestial sphere. We will introduce the correc-tion of the catalog bias in chapter 4. Table 2.3 provides statistics on the catalogues used to reduce the astrometric positions of Phoebe for the observations mentioned in section 5.2.3. The number codes indicate the catalogs used to reduce the photographic observations and the alphabet code are similar to MPC flag that used to reduce the CCD observations.

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Table of contents :

1 Introduction 
1.1 History of Phoebe
1.2 Chapter introduction
2 Astrometric reductions: Analysis of the catalogues used for the astrometric reduction 
2.1 Introduction
2.2 Reference Systems and Frames, Fundamental Astronomy Coordinates
2.2.1 ICRS, ICRF
2.2.2 Type of the coordinates
2.2.3 Di↵erent reference systems where we get observed coordinates and general change to ICRS
2.3 Time scales
2.4 Catalogs used for reductions
2.4.1 Catalogs used for old reductions
2.4.2 Modern catalogs
2.4.3 Catalog comparison and the statistics on the used catalogues
2.5 Other corrections for astrometric reduction
3 Search and selection of published observations 
3.1 Introduction
3.2 Old photographic observations
3.2.1 Observatory and telescopes
3.2.2 Di↵erent sets of observations
3.3 New observations
4 The re-reduction of old observations 
4.1 Introduction
4.2 Introduction to the used method
4.3 Identifying the old reference stars in new catalogs
4.4 Choosing new catalogs and the case of no information on reference stars .
4.5 Catalog bias
4.6 Result
5 A new ephemeris of Phoebe 
5.1 Introduction
5.2 The numerical model
5.2.1 Perturbations
5.2.2 Equations of motion
5.2.3 Observations used to fit the dynamical model
5.2.4 Numerical integration
5.3 The frequency analysis
5.3.1 Definition of the elements
5.3.2 Developpement of quasi-periodic series
5.3.3 The principle of the fine analysis
5.3.4 Data windowing
5.3.5 The procedure of the frequencies analysis
5.3.6 Identification and synthetic representation
5.3.7 Conclusion
6 Comparisons and validation of the new ephemeris of Phoebe 
6.1 Observations Comparison
6.1.1 CCD observations calibrated with di↵erent catalogs
6.1.2 Old published photographic observations and the reduced observations
6.2 Ephemeris Comparison
7 Conclusion and future work 

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