Observatório Nacional/MCT, Rua General José Cristino 77, 20921-400 Rio de Janeiro, Brazil

Abstract
The astrometric positions of eight irregular Jovian satellites are given for the oppositions of the planet from 1995 to 1999. These positions were measured on 204 CCD frames obtained at the Cassegrain focus of a 1.6 m reflector. They are compared with the theoretically calculated positions from JPL Development Ephemeris. The observed minus-calculated standard deviation for all observations of the eight satellites are $\sigma_\alpha=$ 0 $\hbox{$.\!\!^{\prime\prime}$ }$ 071 and $\sigma_\delta=$ 0 $\hbox{$.\!\!^{\prime\prime}$ }$ 052. The USNO-A2.0 catalog was used for the astrometric calibration.

Around Jupiter, 63 satellites are known nowadays, with 8 regular and 55 irregular. Regular satellites are in nearly circular, near equatorial orbits revolving about Jupiter in the same direction as Jupiter's rotation. The irregular satellites orbit far from the planet in eccentric orbits, but with a significant inclination toward Jupiter's equator.

There are some difficulties in determining the positions of Jupiter's irregular satellites: the satellites are faint bodies with visual magnitudes between 15 and 20. In this paper, the images are immerged in a very rich stellar field, therefore identifying the satellites becomes very difficult and even exhausting. Also, the determination of the center of the images with only a number of very small pixels requires specific algorithms to allow the accomplishment of precise measurement.

This work is a systematic program of astrometric observation of Jupiter's satellite system which was started in 1982 at the Laboratório Nacional de Astrofísica (LNA/MCT), Brazil (Veiga et al. 2005). The observations recorded in this paper were made during 19 nights, with in the period of 1995 to 1999, when 204 CCD frames were obtained. In this work precise positions of the satellites are presented for the four irregular Jovian satellites with direct orbits, Himalia (J VI), Elara (J VII), Lysithea (J X), and Leda (J XIII), and for the four irregular satellites with retrograde orbits, Pasiphae (J VIII), Sinope (J IX), Carme (J XI), and Ananke (J XII) (Aksnes 1978; Jacobson 2000).

2 The observations

The observations were made at the Cassegrain focus of the 1.6 m Ritchey-Chretien reflector (Perkin-Elmer) at the Laboratório Nacional de Astrofísica (LNA/MCT) Itajubá-Brazil, with geographical coordinates of $3^{\rm h}02^{\rm m}19^{\rm s}$ longitude, $-22^{\circ}32\hbox{$^\prime$ }04\hbox{$^\prime$ }\hbox{$^\prime$ }$ latitude, and 1872 m of altitude. The focal distance of the Cassegrain combination is equal to 15.8 m, and the focal plane is 13 $.\!\!^{\prime\prime}$ 0/mm (see Veiga et al. 1995).

Two CCD's type were used to take the 204 images: the first with an array of 770 $\times$ 1152 square pixels corresponding to 22.5 $\mu$ m, 0 $\hbox{$.\!\!^{\prime\prime}$ }$ 294 on the sky. The second had an array of 1024 $\times$ 1024 square pixels corresponding to 24 $\mu$ m, 0 $\hbox{$.\!\!^{\prime\prime}$ }$ 312 on the sky. No filter was used and the exposure time for the observations of the eigth satellites varied from 5 to 300 s depending on the meteorological conditions. More details are shown in Table 1.

3 The measurements and astrometric calibration

The ASTROL routines package (Colas & Serrau 1993) was employed to measure the satellite and stellar image centers. Each center was determined by a two-dimensional Gaussian fitting a circular area around the image, and the background was removed by a second-degree polynomial. This background removal is essential for avoiding systematic errors in the measurements of the satellite centers. The errors of the centering procedure were 0 $\hbox{$.\!\!^{\prime\prime}$ }$ 028 for all satellites and 0 $\hbox{$.\!\!^{\prime\prime}$ }$ 015 for the field stars.

The classical process of astrometric calibration was used to determine the observed coordinates of the satellites in the sky. In this process, the stars' USNO-A2.0 catalog was used as a reference system. The UCAC2 catalog, which has better astrometric precision, was used to correct the local systematic errors of the USNO-A2.0 catalog.

Table 1: The main information about the observations for each night and each irregular satellite. In the sequence we have: the number of the frames (Fr.), the mean exposure time in seconds (Ex.), and the number of reference stars (St.) used in the astrometric calibration of the frames. The CCD type is given in the last column: type I with an array of the 770 $\times$ 1152 square pixels, corresponding to 22.5 $\mu$ m, and type II with an array of the 1024 $\times$ 1024 square pixels, corresponding to 24 $\mu$ m.

$\begin{figure} \par\includegraphics[width=5.75cm,clip]{4644Him.eps}\hspace{1.5c... ...ps}\hspace{1.5cm} \includegraphics[width=5.75cm,clip]{4644Led.eps}\end{figure}$	Figure 1: Residuals, in arcseconds, for each one of the eight satellites as a function of time. $\Delta \alpha$ and $\Delta \delta$ , $(\alpha _{\rm observed}-\alpha _{\rm calculated})$ and $(\delta _{\rm observed}-\delta _{\rm calculated})$ , refer to respectively.
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Table 2: Sample of the list of observations available only in electronic form. Starting from Col. 1 we have: the international code adopted for Jupiter's satellites; the time in year, month, and decimals of the day in Universal Time; and the coordinates' right ascension and declination, given in degree and fraction. These topocentric observed positions of eight satellites refer to a mean equator and equinox J2000 system.

Table 3: Observed minus calculated statistics for all observations of each satellite. The units are arcseconds and $\overline {\alpha }$ , $\sigma _{\overline {\alpha }}$ , $\overline {\delta }$ , $\sigma _{\overline {\delta }}$ are the means and the standard deviations for the residuals in right ascension and declination. ${N}_{\rm obs}$ is the final number of observations for each satellite. $\sigma _{\alpha ^*}$ and $\sigma _{\delta ^*}$ is the standard deviation of the stars' reference residuals. Those two columns give the means of the standard deviations, in arcseconds, over all observed nights for the each satellite. In the last column, $\overline {N}_{\rm stars}$ , we have the mean number of reference stars used in the astrometric calibration.

Using the mean coordinate for all the observations on each night, the same stars in the UCAC2 catalog and USNO-A2.0 were identified, in a field of 2 degrees by 2 degrees. A least-square procedure was used with those positions based on a Householder transformation (Lawson & Hanson 1974) to fit the transformation parameters. A second-degree polynomial was used to determine the stars of the USNO-A2.0 catalog corrected coordinates. The characteristic standard deviation of the residuals for the stars from all the stellar fields was at 0 $\hbox{$.\!\!^{\prime\prime}$ }$ 18.

Finally, using the star positions in the field of each CCD frame observation (measured and from the corrected catalog), a new least-square procedure was used to determine the parameters of the scale and orientation. The first-degree polynomial was then used to determine the equatorial coordinates of the satellites. The standard deviation of the mean residuals and the mean of the star number, used for the astrometric calibration of the observations of each satellite, are shown in the last three columns of Table 3.

In the list, available only in electronic form, the topocentric observed positions of eight satellites are referred to a mean equator and equinox J2000 system. The time is given in year, month, and decimals of the day in Universal Time. The coordinates' right ascension and declination are given in degree and fraction, with seven significant digits.

Based on the international code, adopted for Jupiter's satellites, starting from Col. 1 of the list, we have: the number of satellite, the date of the observation, topocentric observed right ascension and declination. Table 2 gives a sample of the electronic list.

4 Results

In this section the observed positions of the eight irregular Jovian satellites are compared with their theoretical positions. The ephemerides used in this work are available electronically from the JPL Horizons on-line solar system data and ephemeris computation service (Giorgini et al. 1996). The model for the orbits of these satellites is a numerical integration of their motion equations (Peters 1981) that includes the effects of an oblate Jupiter, pertubations from the Galilean satellites, and pertubations from the Sun, Saturn, Uranus, and Neptune (Jacobson 1991, 2000).

Table 3 gives the $\Delta \alpha$ and $\Delta \delta$ residual means and the standard deviation of each satellite. From Table 3 we can see the mean of the observed residuals minus the calculated ones for all satellites: $\Delta\overline{\alpha}=$ -0 $\hbox{$.\!\!^{\prime\prime}$ }$ 005 and $\Delta\overline{\delta}=$ 0 $\hbox{$.\!\!^{\prime\prime}$ }$ 019 and the standard deviations, $\sigma_{\overline{\alpha}}=$ 0 $\hbox{$.\!\!^{\prime\prime}$ }$ 071 and $\sigma _{\overline {\delta }}$ = 0 $\hbox{$.\!\!^{\prime\prime}$ }$ 052.

In Fig. 1 we have the distribution of residual $\Delta \alpha$ and $\Delta \delta$ in function of time for the eight satellites.

5 Concluding remarks

In this work were presented 204 CCD observations of the eight irregular satellites of Jupiter, made with the same telescope and distributed over 19 nights between 1995 and 1999. Their error $(\sqrt{(\sigma_{\overline{\alpha}})^2 + (\sigma_{\overline{\delta}})^2})$ is about 0 $\hbox{$.\!\!^{\prime\prime}$ }$ 09. This result shows that the CCD observations and the measure and astrometric calibration system together allowed us to determine precise positions. We can see that in the distribution of residuals (Fig. 1) no tendency is verified for the 5 years, showing a good agreement with the Jacobson ephemeris. The result of $\sqrt{\sum{\overline{\alpha}^2} + \sum{\overline{\delta}^2}}$ is smaller than 0 $\hbox{$.\!\!^{\prime\prime}$ }$ 02.

If we compare the residuals with those presented by Jacobson (2000), we conclude that they are very small. Unfortunately, the number of observations is relatively small for each satellite; however, putting these observations together with all the other ones published, the results can contribute to improved accuracy of the ephemerides.

CCD positions for eight Jovian irregular satellites^,

1 Introduction

2 The observations

3 The measurements and astrometric calibration

4 Results

5 Concluding remarks

References

CCD positions for eight Jovian irregular satellites,

1 Introduction

2 The observations

3 The measurements and astrometric calibration

4 Results

5 Concluding remarks

References

CCD positions for eight Jovian irregular satellites^,