Introduction State of knowledge Predictions Conclusion References Contacts

Updated Jan. 18, 2007


In 2007, the asteroid Kalliope will reach one of its annual equinoxes. As a consequence, its small satellite Linus orbiting in the equatorial plane will undergo a season of mutual eclipses and occultations very similar to the one that the Galilean satellites undergo every 6 years.

OA Kalliope image

Fig. 1: Comparison of Kalliope observed with ESO-NACO (DDT time) and its theoretical shape model based on Kaasalainen et al., 2002 and a Minnaert law profile. (Click on the figure to enlarge it)

This page is aimed at organizing a campaign of observations of these mutual events occurring from February to May 2007. This opportunity occurs only under favorable geometric conditions when the Sun and/or the Earth are close to the orbital plane of the system. This is the first international campaign devoted to the observation of photometric events within an asteroidal binary system. We took advantage of a reliable orbit solution of Linus to predict a series of 24 mutual eclipses and 12 mutual occultations observable in the spring of 2007. Thanks to its (the system Kalliope-Linus) brightness (visual magnitude of 11), these observations are easy to perform even with a small telescope. Anomalous attenuation events could be observed lasting for about 1 – 3 hrs with amplitude up to 0.09 mag. The attenuations are of two distinct types that can clearly be identified as primary and secondary eclipses similar to those that have been previously observed in other minor planet binary systems (Pravec et al., 2006). With those these favorable circumstances, such photometric observations will provide us tight constraints regarding physical properties of Linus such as the size, shape and sidereal spin period.

Among all large binary systems known so far, the secondary-to-primary size ratio of the Kalliope system is the highest with a value estimated to 0.2 which is considered as the lower photometric detection limit of a binary system (Pravec et al., 2006).

Photometric observation of mutual events is a powerful technique to detect and study small asynchronous binaries (Pravec et al. 1998, Ryan et al., 2004, Pravec et al., 2006). But this technique has not been applied to a large size binary asteroids so far. A similar campaign dedicated to the doubly synchronous asteroid (90) Antiope took place last year which allowed full characterization of the system (Descamps et al., 2007).

22 Kalliope: State of knowledge

The preliminary orbit solution of Linus is a simple circular keplerian orbit with a semi-major axis of 1095±10km and an orbital period of 3.5955±0.0008 days. Linus itself was always below the resolving power of the largest Earth-based telescopes. Accordingly, we ignore almost all of its physical properties.

The only roughly estimated parameter at the present time is its size derived by measuring the secondary to primary flux ratio which bounds its size between 20 and 40 km. Recently, on Nov. 7, 2006, the first successful observation of a stellar occultation by the Kalliope’s moonlet was made using a prediction we made less than one day before (Berthier et al., 2004, Soma et al., 2006). The observed position of Linus was shifted with respect to the prediction by about 70 mas or 100 km in the occultation plane. This observation not only confirmed the reliability of our orbit solution but also provided a direct measurement of a 40 km-wide shadow of Linus. This observation was added to our data set to improve the orbit solution and refine the events predictions.

The shape and pole solution are crucial parameters to predict and interpret lightcurves. Kaasalainen et al. (2002) derived a polyhedral shape solution from lightcurves inversion. The spin axis was derived from our orbit solution of Linus. After collecting observations spanning nearly 5 years (2001-2006) no change in the orbit pole has been detected, implying the absence of precession. Consequently, we can identify both the orbit and spin poles. This leads to an adopted pole olution, expressed in J2000 ecliptic coordinates, of λ = 197 ± 2° and β = -3 ± 2°.

Kalliope lightcurve

Fig. 2: Rotational lightcurve of Kalliope taken with the 0.4m telescope at Appalachian State University's Rankin Science Observatory located in western North Carolina. Images were taken in the R band using an SBIG ST-9e CCD camera and the data were reduced by aperture photometry using MIRA. (Click on the figure to enlarge it)

To check the validity of the shape and the pole solution we compared observations of different nature with predictions based on our global model. The computed Kalliope aspect shown in Figure 1 compares very well with a high resolution adaptive optics image of Kalliope taken on 2004 June , 28 with the 8 m VLT telescope.

More recently, in December 2006, long duration photometric observations of Kalliope were performed with the 0.4 m telescope at Appalachian State University’s Rankin Science Observatory located in western North Carolina. Images were taken in the R band using an SBIG ST-9e CCD camera and the data were reduced by aperture photometry using MIRA. A synthetic lightcurve was then generated and superimposed on the observations as seen in figure 2. The agreement is satisfactory apart from some local discrepancies in the neighbourhood of the minima.

Prediction of events

As a consequence of the distance of (22) Kalliope from the Earth (>2AU) and its axial tilt to the ecliptic plane of nearly 90°, a series of mutual eclipses will begin in February 2007 and last until the beginning of April to be followed by a series of occultations beginning later in May. Owing to the fast-evolving aspect of the system as seen by an Earth observer, the season of mutual events lasts for only three months. The low elongation of the Sun to 22 Kalliope in May will make the mutual occultations more difficult to observe.

Synthetic lightcurves of 22 Kalliope during an event

Fig. 3: Synthetic lightcurves showing anomalous attenuation events. They have been calculated from our spin pole and orbit solution with the shape model of Kaasalainen et al., 2002. (Click on the figure to enlarge it)

The table of predictions (PDF format) summarizes the characteristics of the observable events presented in table 1 as well as the geometric circumstances. For each event, the duration and the predicted amplitudes of the primary and secondary mutual eclipses are given.

The drop in flux during the events will be small, and quite dependent on the primary shape and the orbit solution. Nevertheless, thanks to the brightness of 22 Kalliope (mv = 11), it should be possible to detect this variation and get valuable information about the size ratio and the shape of the secondary. Our calculations show that the brightness variation for the integrated flux will reach at most 0.09 mag (assuming a 40-km spherical moonlet). Very precise photometric capabilities and data-processing are necessary to get magnitude accuracy better than 0.005.

The figure 3 shows two synthetic lightcurves of Kalliope during an event. In both cases a global attenuation can be seen, indicative of the additional dimming of the sunlight reflected by the asteroid. The shape and the intensity of the attenuation will depend on the shapes and size ratio of the components as well as on the illumination and viewing geometries of the system at the time of the event. The terms “primary event” and “secondary event” refer to which body is being eclipsed (Pravec et al., 2006). Due to a small secondary-to-primary size ratio (~0.2), no steeper dips in the slope are visible in the lightcurves.

The following table lists all events to be observed from February to May 2007. The columns display the following predicted parameters:

  • Date: the date of the event
  • Event: the type of event: 'O' = occultation, 'E' = eclipse, '1' = Kalliope, '2' = Linus
  • Begin: the hour of the beginning of the event
  • End: the hour of the ending of the event
  • Δt: the duration of the event
  • Δmag: the drop in flux
  • View: the icons allow one to download a screenshot (PNG format), an MPEG animation and the predicted lightcurve of the event (Postscript format)
The timing accuracy of the events is of the order of a few minutes. For the period of the events, the geocentric distance of Kalliope varies from 2.21 AU (in February) to 3.44 AU (in June) and its visual magnitude varies from 11.25 (in February) to 12.07 (in June).

2012-02-04 1E2 08h11m 10h04m 01:53 0.0057 16.54
2012-02-06 2E1 03h05m 05h15m 02:10 0.0175 16.96
2012-02-07 1E2 22h23m 00h06m 01:43 0.0217 17.37
2012-02-09 2E1 17h26m 19h20m 01:54 0.0172 17.76
2012-02-11 1E2 12h10m 14h47m 02:37 0.0446 18.12
2012-02-13 2E1 07h16m 09h57m 02:41 0.0281 18.47
2012-02-15 1E2 02h31m 05h25m 01:54 0.0440 18.80
2012-02-16 2E1 21h44m 00h38m 02:54 0.0547 19.10
2012-02-18 1E2 16h36m 19h14m 02:38 0.0491 19.39
2012-02-20 2E1 11h40m 14h29m 02:49 0.0447 19.65
2012-02-22 1E2 06h55m 09h43m 02:48 0.0511 19.90
2012-02-24 2E1 02h12m 04h57m 02:45 0.0567 20.13
2012-02-25 1E2 21h26m 23h48m 02:22 0.0453 20.34
2012-02-27 2E1 16h06m 18h52m 02:46 0.0462 20.53
2012-02-29 1E2 11h22m 13h58m 02:36 0.0441 20.70
2012-03-02 2E1 06h50m 09h11m 02:21 0.0639 20.86
2012-03-04 1E2 02h07m 04h01m 01:54 0.0307 20.99


These upcoming mutual events within the Kalliope system represent an unprecedented opportunity to conduct very precise astrometry of the two components with modest aperture telescopes equipped with CCD cameras while also providing access to the physical properties of Linus.

The number of observed events will depend greatly on the number and geographical distribution of available observers. This is the reason why an international campaign of observations of these events is being set up by IMCCE which will coordinates the efforts to gather observations of as many of the events as possible.


  • Berthier, J., Marchis, F., Descamps, P., Hestroffer, D., 2004. Prediction of stellar occultations by satellite of asteroids. BAAS, 36, 1142.
  • Descamps, P., Marchis, F., Michalowski, T., et al., 2007. Figure of the double asteroid 90 Antiope from AO and lightcurves observations. Icarus, In press.
  • Kaasalainen, M., Torppa, J. and J. Piironen, 2002. Models of twenty asteroids from photometric data. Icarus, 159, 369-395.
  • Marchis, F., Descamps, P., Hestroffer, D., Berthier, J., Vachier, F., Boccaletti, A., de Pater, I., Gavel, D., 2003 A three-dimensional solution for the orbit of the asteroidal satellite of 22 Kalliope. Icarus, 165, 112-120.
  • Margot, J.L., and M.E. Brown 2003. A low density M-type asteroid in the main belt. Science 20, 300, 1939-1942.
  • Pravec, P., and G. Hahn, 1997. Two-period lightcure of 1994 AW1: Indication of a binary asteroid ? Icarus, 127, 431-440.
  • Pravec, P., Scheirich, P., et al. 2006 Photometric survey of binary near-Earth asteroids. Icarus, 181, 63-93.
  • Ryan, W. H., Ryan, E. V. and C. T. Martinez, 2004. 3782 Celle: Discovery of a Binary System within the Vesta Family of Asteroids. Planetary and Space Science, 52, 1093-1101.
  • Soma, M., Hayamizu, T., Berthier, J., Lecacheux, J., 2006. Kalliope and (22) Kalliope I. CBET 732. Edt. By Green, D.W.E.


Attention : Ce serveur a été mis en place avec l'aide du Ministère de l'Education Nationale, du CNRS et du CNES. Tout usage des données diffusées par ce serveur nécessite l'accord de l'IMCCE.