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Phase Angle, Degrees R Educed V M a Gn Itu Lunar and Planetary Science XXX 1595.pdf MAGNITUDE PHASE DEPENDENCE OF ASTEROID 433 EROS. Yu. N. Krugly and V. G. Shevchenko, Astronomical Observatory of Kharkiv State University, 35 Sumska str., 310022 Kharkiv, Ukraine, e-mail address: [email protected]. Introduction: 10.2 The NEAR spacecraft is coming to the near-Earth asteroid 433 Eros and it will provide us an important information about this body. The data obtained from 10.7 the space experiments will require disk-integral obser- vations of the asteroids at various aspects and solar phase angles. In that connection the ground-based ob- servations of 433 Eros can be very useful. We present 11.2 the results of long-term observations of 433 Eros in- cluding measurements of the magnitude phase depend- ence. V Magnitude Reduced 11.7 Observations: 0 10203040 433 Eros was observed photometrically during three Phase Angle, degrees apparitions in 1993, 1995 and 1997 using the 70-cm reflector at Kharkiv Observatory and 1-m reflector at Figure 1. Phase curve of Eros obtained from the Simeis Observatory (Ukraine). The observations were observations during the 1993 opposition. Solid line is carried out in standard V band. Table gives aspect data an approximation by function proposed in [3]. Dashed (ecliptic coordinates and phase angle) of the asteroid at line is a best fit approximation of a linear part of the the midtimes of the observations. The last column pre- phase curve. sents magnitudes of the asteroid reduced to the primary maximum of the lightcurve. Parameters of HG-function [1] were determinated Date λ2000 β2000 P.A. V (1,α) UT o to be H = 10.40, G = 0.20. The linear part of phase 1993 dependence is approximated with the phase coefficient m 07/22.0 308°.0 -0°.6 5°.0 10 .86 0.031 mag/deg and Vo(1,0) = 10.71 mag. The phase 07/23.0 307.6 -0.5 4.2 10.79 coefficient value is typical for the S-type asteroids and 07/26.8 305.9 0.1 1.1 10.53 different from that obtained in opposition of 1974 - 75 07/27.9 305.4 0.3 0.3 10.40 [2]. For more precise approximation of the phase curve 08/06.9 301.3 1.9 7.5 10.91 especially at small phase angles and estimation of the 08/18.8 297.1 3.5 16.1 11.21 asteroid absolute magnitude we used the function pro- 08/18.9 297.0 3.6 16.2 11.21 08/19.9 296.7 3.7 16.8 11.25 posed in [3]. The computed function parameters of the 08/21.9 296.2 3.9 18.0 11.27 phase curve are V(1,0) = 10.76, a = 0.51, b = 0.030. 08/22.9 296.0 4.0 18.6 11.30 The values of a and b parameters correspond to aver- 09/21.8 294.1 6.5 31.4 11.65 age values of the S-type asteroids [4]. 1995 According to our estimate the absolute magnitude 07/31.0 11.8 10.6 33.0 of Eros in 1993 apparition (close to the equatorial 08/22.9 14.4 16.1 26.9 ± 10/15.9 357.6 27.7 23.3 aspect) was equal to V = 10.35 0.03 mag. 1997 11/07.1 145.7 8.9 56.2 Lightcurves: Phase Curve: The Eros composite lightcurve for 1993 opposition Our observations in July - September 1993 cov- is shown in Fig. 2. The amplitude of brightness varia- ered the phase angle range from 31.4 to 0.3 deg. Dur- tions close to opposition was 0.73 mag. The lightcurves ing this time interval the Eros position on the sky of two other apparitions are presented in Fig. 3 and 4. changed a little so that aspect did not affect the Eros They have different amplitudes and represent near brightness considerably. For obtaining phase curve we pole-on (1995) and equatorial (1997) aspects. The cor- used the magnitudes reduced to primary maximum of responding amplitudes are 0.05 and 1.50 mag which the lightcurve (see last column in Table). The phase represent minimum and maximum amplitudes ever curve is shown in Fig. 1. observed for Eros. Lunar and Planetary Science XXX 1595.pdf PHASE DEPENDENCE OF EROS: Yu. N. Krugly and V. G. Shevchenko 10.0 Conclusions: The phase dependence of Eros obtained from obser- vations up to 0.3 deg shows a well-defined opposition effect that is typical for the S-type asteroids and allows 10.5 to estimate the absolute magnitude of the asteroid with high precision. The presented phase curve and lightcurves can be used for modeling shape and axis orientation of Eros as 11.0 a test of different methods for inversion of integral photometry of asteroids with large changing viewing and illumination. Reduced VReduced M agnitude 11.5 Acknowledgment: The work is partly supported by the Grant #97-02- 0.00 0.25 0.50 0.75 1.00 18221 of Russian Foundation of Fundamental Re- Rotational Phase search. Figure 2. The composite lightcurve obtained during the 1993 opposition. Solid line is a best fit by the 6th-order Fou- References: rier series. [1] Bowell E. et al. (1989) in Asteroids II, eds. Bin- zel R., Gehrels T., and Matthews. [2] Millis R.L. et al. (1976) Icarus, 28, 53 - 67. [3] Shevchenko V.G. 11.3 (1996) LPS XXVII, 1193-1194. [4] Shevchenko V.G. (1997) Astron. Vest., 31, 246-251. 11.4 11.5 19 21 23 25 Reduced VReduced Magnitude UT (c), hours Figure 3. The lightcurve obtained on Oct 15, 1995. Solid line is a best fit by the 4th-order Fourier series. 12.0 12.5 13.0 Reduced V Magnitude 13.5 23.5 25.5 27.5 UT (c), hours Figure 4. The lightcurve obtained on Nov 6, 1997. Solid line is a best fit by the 6th-order Fourier series..
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