A&A 378, L14-L16 (2001)
DOI: 10.1051/0004-6361:20011206

CCD photometry of the binary asteroid 90 Antiope

T. Michaowski ¹ - F. Colas ² - T. Kwiatkowski ¹ - A. Kryszczynska ¹ - R. Hirsch ¹ - J. Michaowski ³

1 - Astronomical Observatory, A. Mickiewicz University, Soneczna 36, 60-286 Poznan, Poland
2 - Institut de Mécanique Céleste, 77 av. Denfert Rochereau, 75014 Paris, France
3 - Poznan University of Technology, Poznan, Poland

Received 23 July 2001 / Accepted 28 August 2001

Abstract
Lightcurves of the binary asteroid 90 Antiope were obtained at two observatories (Borowiec and Pic du Midi) on 14 nights in September through November 2000. The synodical period was found to be $16.496 \pm 0.001$ hours and the observed amplitude of brightness variation was 0.08 mag. This amplitude was due to the noncircular shapes of the components of the binary system rather than to mutual occultations. Some predictions of a possibility of observations of the eclipsing events during future oppositions have also been made.

Key words: techniques: photometric - minor planets: asteroids

1 Introduction

The first photometric observations of 90 Antiope, covering full rotational cycle, were performed on four nights in December 1996 (Hansen et al. 1997). The composite lightcurve with two minima and an amplitude of 0.70 mag yielded a period of 16.509 hours. This lightcurve was not quasi-sinusoidal as shown by most asteroids but similar to a typical lightcurve of an eclipsing binary star.

The binarity of this asteroid was confirmed by Merline and his collaborators in August 2000 (http://www.boulder.swri.edu/~merline/press/). Using the Keck Adaptive Optics system, they found that 90 Antiope was a double asteroid with similar-sized components, separated by 170 km. The orbital period was about 16.5 hours, consistent with the period derived from the 1996 photometric observations.

If we accept Antiope's diameter of 120 km as determined by IRAS satellite (http://pdssbn.astro.umd.edu/) and assume that it is a binary system of two spherical objects, we can found the diameter of each component to be 85 km.

2 CCD photometry in 2000

We observed 90 Antiope on 14 nights in September - November 2000 at two observatories - Borowiec (near Poznan, Poland) and Pic du Midi (France) where 0.40 m and 1.05 m telescopes, respectively, were used. Both of them were equipped with CCD cameras, and all details concerning the instruments and the reduction procedure were described by Michaowski et al. (2000).

The aspect data of the asteroid are listed in Table 1. The columns give the date of the observation referring to the mid-time of the observed lightcurve, asteroid-Sun (r) and asteroid-Earth ($\Delta$) distances (in AU), solar phase angle, ecliptic longitude ($\lambda$) and latitude ($\beta$) for the J2000 epoch, and the name of the observatory. The last four columns provide times (corrected for light-time) of observed brightness maxima (M1, M2) and minima (m1, m2).

Our observations are presented as composite lightcurve (Fig. 1) which has been constructed according to a procedure described in Magnusson & Lagerkvist (1990). A vertical position of each lightcurve was obtained by minimizing the dispersion of data points relative to their neighbours. The abscissa is the rotational phase with zero point corrected for light-time. The observed maxima (M1, M2) and minima (m1, m2) are indicated in the graph.

The brightness of the asteroid varied with an amplitude of about 0.08 mag within the period of $16.496~\pm~0.001$ hours, which was consistent with the earlier reported values as mentioned above. This small amplitude was due to the non-circular shapes of the components rather than to mutual occultation.

   

Table 1: Aspect data and times of observed extremes of 90 Antiope.

Date	r	$\Delta$	Phase	$\lambda$	$\beta$	Obs.		M1	M2	m1	m2
(UT)			angle	(J2000)			Julian Days
	(AU)	(AU)	$(\hbox{$^\circ$ })$	$(\hbox{$^\circ$ })$	$(\hbox{$^\circ$ })$		$+ 2\,451\,800$
2000
Sep. 29.9	2.815	1.820	3.0	359.3	-3.2	Bor				17.384
Sep. 30.9	2.816	1.823	3.4	359.1	-3.2	Bor			18.321
Oct. 21.9	2.842	1.956	11.0	355.8	-2.9	Bor				39.379
Oct. 22.9	2.843	1.965	11.4	355.7	-2.9	Bor			40.320		40.471
Oct. 23.8	2.845	1.974	11.7	355.6	-2.9	Bor		41.297		41.441
Nov. 01.9	2.856	2.066	14.2	354.9	-2.7	Bor				50.378
Nov. 02.8	2.858	2.077	14.4	354.9	-2.7	Bor			51.321
Nov. 03.8	2.859	2.088	14.7	354.9	-2.7	Bor		52.295
Nov. 10.9	2.868	2.173	16.2	354.8	-2.6	Pic				59.312
Nov. 11.9	2.870	2.185	16.4	354.8	-2.5	Pic			60.253		60.400
Nov. 14.9	2.874	2.224	17.0	354.8	-2.5	Pic		63.294		63.436
Nov. 15.9	2.875	2.238	17.1	354.9	-2.5	Pic			64.354		64.533
Nov. 16.8	2.876	2.250	17.3	355.0	-2.4	Bor		65.354
Nov. 19.8	2.880	2.289	17.7	355.1	-2.4	Bor				68.246

Observatory code: Bor - Borowiec; Pic - Pic du Midi.

	Figure 1: Composite lightcurve of 90 Antiope in September-November 2000.
Open with DEXTER

3 Discussion and future work

In a binary system of two equal components a decrease in brightness, during central occultation, is 0.75 mag at each minimum. In December 1996 the observed amplitude of the lightcurve of Antiope was 0.70 mag, which suggests that the Earth was nearly exactly in the orbital plane of the Antiope system (the inclination i of the orbit was almost $90\hbox{$^\circ$ }$). If we assume the diameter of each component to be 85 km, and their seperation equal to 170 km, then for speherically shaped bodies a partial occultation occurs for $i > 60\hbox{$^\circ$ }$.

The photometric observations obtained so far do not allow us to determine the orientation of the orbital plane of the Antiope's system. However, we can put some limits on the expected inclination i during the future oppositions.

Let $\vec{r}_{ \mathrm{n}}$ is a unit vector normal to the orbital plane of the binary system and $\vec{r}_{\mathrm{e}}$ is a unit vector pointing from the centre of mass towards the Earth. These vectors have the following components:

$$\vec{r}_{\rm n} = \Big[ \cos(\lambda_{\mathrm{n}}) \cos(\be... ...}) \cos(\beta_{\mathrm{n}}), \sin(\beta_{\mathrm{n}}) \Big],$$

$$\vec{r}_{\rm e} = \Big[ -\cos(\lambda) \cos(\beta), -\sin(\lambda) \cos(\beta), -\sin(\beta) \Big],$$

where $(\lambda_{\rm n},~\beta_{\rm n})$ are the ecliptic coordinates of the pole of the orbital system, and $(\lambda, \beta)$ - geocentric ecliptic coordinates of the asteroid. Thus, the inclination i (an angle between the normal to the orbital system and direction to the Earth) can be calculated from:

$$\cos(i) = - \sin(\beta) \sin(\beta_{\mathrm{n}}) - \cos(\... ...os(\beta_{\mathrm{n}}) \cos(\lambda - \lambda_{\mathrm{n}}),$$

or, after putting $\beta \approx 0\hbox{$^\circ$ }$ (which is evident from Table 2):

$$\cos(i) = - \cos(\beta_{\mathrm{n}}) \cos(\lambda - \lambda_{\mathrm{n}}).$$ (1)

This equation can be used to bracket $\lambda_{\mathrm{n}}$ and $\beta_{\mathrm{n}}$. For the 1996 opposition we have $\lambda = 120\hbox{$^\circ$ }$ and $i \approx 90\hbox{$^\circ$ }$, which gives us $\lambda_{\mathrm{n}}= 30\hbox{$^\circ$ }$ (or $210\hbox{$^\circ$ }$) for any value of $\beta_{\mathrm{n}}$.

Additional constraints can be inferred from the 2000 observations. As they showed no visible eclipsing event, from our simplified assumptions (see above) we can get $0\hbox{$^\circ$ }< i < 60\hbox{$^\circ$ }$. Using Eq. (1), the ecliptic longitude $\lambda=355\hbox{$^\circ$ }$ and the previously estimated value for $\lambda_{\mathrm{n}}$ we can bracket $\beta_{\mathrm{n}}$ in the interval $0\hbox{$^\circ$ }< \beta_{\rm n} < 52\hbox{$^\circ$ }$. This allows us to determine the expected inclinations i during the future oppositions.

Table 2 gives the dates of the oppositions, the asteroid ecliptic coordinates ($\lambda$, $\beta$) as well as the expected inclinations i of the orbital plane and brightness drops due to eclipsing events.

We predict it should be possible to observe partial occultations in the Antiope system in the years 2003, 2005, and 2008. The oppositions in 2001, 2004, and 2006 will probably not reveal any eclipsing events. However, due to changes in the observing geometry, photometric observations even in the absence of occultations will be very useful for studying brightness variations of the components caused by their rotation and orbital movement.

It should be mentioned that the predictions presented in Table 2 depend on all approximations assumed for Antiope's system. It is interesting to notice that no future opposition up to 2008 will show a full occultation event as it was in 1996.

 

 

Table 2: Oppositions of 90 Antiope.

	$\lambda$	$\beta$	Expected	Expected
Opposition			inclination	amplitude
	$[\hbox{$^\circ$ }]$	$[\hbox{$^\circ$ }]$	$[\hbox{$^\circ$ }]$	[mag]
1996 Dec.	120	2	90	0.75
2000 Nov.	355	-3	35-60	0
2001 Dec.	80	1	50-66	0	-	0.05
2003 Feb.	137	3	73-80	0.18	-	0.36
2004 Apr.	197	3	13-54	0
2005 Jul.	287	-2	77-82	0.27	-	0.43
2006 Oct.	35	-2	5-53	0
2008 Jan.	103	2	73-80	0.18	-	0.36

Acknowledgements

This work was partially supported by the Polish KBN Grant 2 P03D 007 18. The Borowiec observations were reduced with the CCLRS STARLINK package.

References

 
• Hansen, A. T., Arentoft T., & Lang, K. 1997, Minor Planet Bull., 24, 17 In the text  
• Magnusson P., & Lagerkvist C.-I. 1990, A&AS, 86, 45 In the text NASA ADS  
• Michaowski T., Pych W., Berthier J., et al. 2000, A&AS, 146, 471 In the text NASA ADS