Introduction
16 Psyche is a well studied main belt asteroid listed as M-class with a rotational period of 4.196 hours. Lightcurve amplitude varies from 0.03 to 0.42 (Lagerkvist et al.). Previously published pole position for spin vector have varied in ecliptic longitudes 215û to 225û, and ecliptic latitudes 4û to 55û (Magnusson, P. ÒPole Determinations of AsteroidsÓ). Orbital velocity of 16 Psyche has made observations at opposition possible only at four heliocentric longitudes (near 70û, 160û, 220û & 310û). This fact has increased uncertainty on pole position.calculations. A more accurate pole latitude designation for 16 Psyche is likely from the ten nights of favorable data taken at N/F Observatory.
Observations
C.C.D. exposures were made through a Johnson V filter on a CRAF-Cassini 1024x1024 CCD. The pixel size is 1.2 arc seconds. The chip and amplifier floor noise is 27 electrons. Full well is 100,000 electrons. The telescope is a 0.45-m Newtonian. Control of the observatory was done by radio link and has been described elsewhere (Neely, 1989).
Differential photometry was used between the asteroid and comparison star within the same field. Exposures were made for 80 seconds. Data reduction and analysis was accomplished using PCVISTA (written by Michael Richmond at Berkeley). After the centroids of the asteroid and comparison stars were found, an aperture of 8 arc seconds was integrated, and an annulus was used for computing and subtracting the sky background. The V magnitudes were all transformed to the standard system.
Nine nights of observations in April ,May, June, 1993:
16 Psyche was imaged with differential comparison stars on U.D dates 4/27, 5/1, 5/2, 5/3, 5/11, 6/4, 6/5, 6/6 & 6/7. During this apparition, a heliocentric longitude of Å228û presents the lowest photometric amplitude variation. Star 4383-0434 (Guide Star Catalogue) was imaged on May 3, 1993 and used for calibration of the comparison stars. Time variable extinction was calculated by plotting a curve of the calibration star and comparison stars . Star 4383-0434 had been extensibly studied for calibration in photometry of S.N. 1993j (Vaucouleurs, 1994) and has a good color match with 16 Psyche. Additional photometry of comparison stars in all fields were used to callibrate instrumental V magnitude to the standard magnitude system.
One night of observations, U.D. August 14, 1994:
On this date, 16 Psyche was imaged at heliocentric longitude 314û and presented a high photometric amplitude. Calibration frames were made using Landholdt 112-275. Airmass between comparison and calibration stars were negligible .
Results
The observational circumstances for two apparitions are shown in table #1 and include Vmax reduced to standard distance to determine V(1,0). It should be noted that on U.D. 5/11/93, 16 Psyche was at heliocentric longitude of 228û 14Õ and yielded an absolute magnitude of 5.80 which is brighter than previous measurements. It is possible that data contained within this paper represents the most favorable observational circumstances to determine aspect angle.
Using data from observations cited and previously published sources (Taylor et al., Tedesco et al. 1982, Tedesco et al. 1984, Lupishko et al., Pfleiderer et al., Zhou et al. and Weidenschilling et al..), pole position was calculated by amplitude-magnitude method . A north pole longitude of Å222û is in general agreement with past research. However, north pole latitude are much harder to determine.
Previously published pole positions vary as much as 51û in latitude. Latitude designations widely vary for a number of reasons. First, the ecliptic plane and pole latitude are in apparent proximity. Due to this proximity, small errors in the variation of V max amplitude produces wide results using the amplitude-magnitude method. For instance, a latitude of 37û could be explained by an amplitude variation of .07. Additional latitudes have been derived using the epoch method. Although the epoch method has the advantage of not being phase angle dependent, two varying solutions for pole position are inherently produced.
Opportunities to gather data for pole position of 16 Psyche have been limited due to an orbital period of 4.99 years and synodic period of Å1.25 years. Using the amplitude-magnitude method demands a phase angle of <15û(Magnusson et al.), yet the orbital period offers only four heliocentric longitudes to gather data. A synodic orbital period of Å1.25 years,coupled with a pole latitude proximate to the ecliptic offers an observed amplitude at true minimum in five year increments. Using the epoch method, Tedesco et al. indicates a pole longitude, latitude of 223û and 37û respectively, but chose not to use data taken by Lupishko et al. (1980) on May 5, 1978 due to incongruities in the reported lightcurve (Tedesco et al.). However, a minimum variation in amplitude of 0.03 ±0.005 reported by this paper is in agreement with Lupishko et al.(1980). A designation of 8.7û±5û in pole latitude is further strengthened by the superimposed lightcurves of three nights of data shown in figure #1.
Finally on 8/14/94, 16 Psyche offered opposition at heliocentric longitude 314û 19Õ. A Vmag of 0.32 ±0.05 was observed on this date. Shape of 16 Psyche was derived from this Vmag and the minimum amplitude variation of 0.03 ±0.005 mentioned above. The result are as follows: a/b=1.35, b/c=1.29, a/c=1.76.
Table 1
Observational Circumstances
U.D. Long. Earth-Ast. (A.U) Sun- Ast. (A.U.) Phase Vmax V(1,0)
4/27/94 226û 01Õ 2.26 3.25 3.4û 10.56 . . .
5/01/93 226û 39Õ 2.25 3.25 2.8û 10.54 . . .
5/02/93 226û 49Õ 2.25 3.25 2.6û 10.38 . . .
5/03/93 226û 58Õ 2.25 3.25 2.4û 10.32 . . .
5/11/93 * 228û 14Õ 2.25 3.24 2.0û 10.27 5.80
6/04/93 232û 04Õ 2.32 3.23 9.8 10.80 . . .
6/05/93 232û 14Õ 2.33 3.23 10.1 10.78 . . .
6/06/93 232û 24Õ 2.34 3.23 10.5 10.79 . . .
6/07/93 232û 33Õ 2.34 3.23 10.9û 10.85 . . .
8/14/94 314û 19Õ 1.71 2.71 2.0û 9.62 6.13
*U.D. 5/11/94 used for extrapolation of V(1,0)
References
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Lupishko, D. F. (1982). ÒPhotometry of the M-Type Asteroids 16 Psyche and 22 KalliopeÓ. Solar System Research Vol. 16, No. 2, pp 101-108
Magnusson, P. (1989). ÒDetermination of Pole Orientations and Shapes of AsteroidsÓ. In Asteroids II (Binzel R.P., Ed.), pp 66-97. Univ. Arizona Press, Tucson.
Magnusson, P. (1989). ÒPole Determinations of AsteroidsÓ. In Asteroids II (Binzel, R. P., Ed.), pp 1183. Univ. Arizona Press, Tucson.
Magnusson, P. (1989). ÒSpin Vectors of 22 Large AsteroidsÓ. Icarus (1990) 85, pp 229-240
Pfleider, J. (1986). ÒPhotoelectric Five-Colour Photometry of the Asteroids 16 Psyche, 201 Penelope and 702 AlaudaÓ. Astronomy & Astrophysics. Supplement Series. Ser. 69, pp 117-122, (1987).
Taylor, R. C. (1976). ÒMinor Planets and Related Objects. XXI. Photometry of Eight AsteroidsÓ. The Astronomical Journal, Vol. 81, No. 9, September 1976.
Tedesco, Edward F. (1982). ÒWorldwide Photometry and Lightcurve Observations of 16 Psyche During the 1975-1976 ApparitionÓ. Icarus (1983) 54, pp 30-37
Tedesco, Edward F., and Taylor, Ronald C., (1985). ÒPole Orientation of 16 Psyche by Two Independent MethodsÓ. Icarus (1985) 61, 241-251.
Weidenschilling, S. J. (1987). ÒPhotometric Geodesy of Main Belt Asteroids: I. Lightcurves of 26 Large, Rapid RotatorsÓ. Icarus (1987) 70, pp 191-245.
Zhou, Xing-hai (1982). ÒLight Curves of Asteroids, paper 5Ó. Chinese Astronomy and Astrophysics , June 1983, 7, pp 129-131.