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Petr Pravec and Lenka Sarounová
Astronomical Institute, Academy of Sciences of the Czech Republic, CZ-25165 Ondrejov, Czech Republic
E-mail: ppravec@asu.cas.cz
Lance A. M. Benner, Steven J. Ostro, Michael D. Hicks
Raymond F. Jurgens, Jon D. Giorgini, Martin A. Slade, and Donald K. Yeomans
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109
David L. Rabinowitz
Yale University Physics Department, P. O. Box 208121, New Haven CT 06520-8121
Yurij N. Krugly
Astronomical Observatory, Kharkiv National University, Sumska Str. 35, Kharkiv 61022, Ukraine
and
Marek Wolf
Astronomical Institute, Charles University Prague, V Holesovickách 2, CZ-18000 Praha, Czech Republic
Pages: 16, Figures: 1, Tables: 2
km
(Dermott et al. 1984, Binzel et al. 1989, Fulchignoni et al. 1995, Pravec and Harris 1999). Asteroid collisional evolution models explain small asteroids as fragments generated in catastrophic disruptions or cratering of larger asteroids and predict their spin-up but not significant numbers of slow rotators (Harris 1979, Farinella et al. 1992). Mechanisms causing spin-down of small asteroids have been suggested (see Discussion below) but none of the hypotheses has been proven to satisfactorily explain the basic observational data.
The largest known slow rotator is C-type main belt asteroid 253 Mathilde, which has a rotation period of 17.41 days and a mean diameter of 53 km (Mottola et al. 1995, Veverka et al. 1997). The best-studied slow rotator is S-type near-Earth asteroid 4179 Toutatis, which radar observations have shown is an elongated body in a non-principal axis (NPA) rotation state characterized by periods of 5.37 days (rotating about the long axis) and 7.42 days (precession of the long axis about the angular momentum vector; Hudson and Ostro 1995, Ostro et al. 1999a). Toutatis' NPA rotation causes its lightcurve to appear non-periodic but it contains characteristic frequencies (corresponding to the observed synodic periods of 7.3 and 3.1 days) that are related to the periods of the NPA rotation (Spencer et al. 1995, Kryszczynska et al. 1999).
Lightcurves of several other asteroids with long periods have shown deviations from simple periodicity that are suggestive of NPA rotation: 1689 Floris-Jan (Harris 1994), 288 Glauke, 3288 Seleucus (Harris et al. 1999), and 3691 (1982 FT) and 1997 BR (Pravec et al. 1998). Thus, although we cannot say that all slowly rotating asteroids are in NPA rotation states, such states appear to be common among them.
The size distribution of very slow rotators extends from Mathilde( km) down to 1997 BR ( 
km, Pravec et al. 1998). Here we present observations of the 
km object 1999 GU3 that reveal very slow rotation that is probably NPA.
Figure 1a plots lightcurve measurements reduced to a phase angle of 60° (assuming a linear phase parameter of 0.031 mag/deg; see below) vs. time. The relatively densely covered part of the lightcurve obtained between April 14-24 shows a long period, large amplitude variation. If we assume that there are two maxima/minima pairs per cycle, then this ten-day interval appears to cover slightly more than one cycle. Realizingthat we needed additional data to determine the rotation period more precisely, we observed the asteroid on six more nights from 1999 May 4 to 19. Due to telescope schedules and the short duration of the observing intervals on each night, we obtained only one point (that is the average of several measurements taken in quick succession) on each of the May nights. The May data show a large variation of the asteroid's brightness that is even larger than the amplitude seen in April.
We obtained the following mean color indices at Table Mountain on 1999 April 14.4 and 15.4: 
, and 
. The distinct spectral absorption longward of 0.7 
m is presumably characteristic of the olivine/pyroxene
composition of ordinary chondrites and of the QRV asteroid types.
Since the solar phase angle varied over a relatively narrow range between 56-70° during the optical observing window (Table i), we assumed that the asteroid's phase relation is linear with a coefficient of 0.031 mag/deg, corresponding to a phase slope parameter G=0.15. We experimented with phase parameters varied by 
mag/deg about this value (corresponding to G between -0.05 to 0.35, the range that is observed for most asteroids; Bowell et al. 1989) and found that our assumption did not introduce any significant systematic error to the results. The uncertainty of 0.003 mag/deg in the linear phase coefficient propagates as a relative error of 0.04 mag between reduced points of 1999 April 14.4 and 24.1, the epochs corresponding to the minimum and maximum solar phase angles observed. Accounting also for possible calibration errors (see above), we consider 0.05 mag as a likely maximum error of points in the reduced lightcurve during the analysis reported below; the only exception is the May 10.1 point that has a random error of 0.08 mag (see Table i). The mean error of all points in the reduced lightcurve is about 0.03 mag.
We searched for a period in the data using a Fourier series method (Harris et al. 1989). Figure 1b plots 
(for a fit with a fourth-order Fourier series) vs. period. There are two possible periods: 
d and
d. The shorter period corresponds to a lightcurve with a single maximum/minimum pair per cycle. Large-amplitude lightcurves dominated by the first harmonic are virtually unknown among asteroids, so we consider it likely that the shorter period solution corresponds to one-half of the synodic period of 
d, where we have adopted an error a few times larger than the formal statistical error to account for possible systematic effects (e.g., change of the synodic period with time) that are not incorporated in the model. The difference between the synodic and sidereal periods could be significant for this long-period, fast-moving object; from the motion of the phase angle bisector (PAB; Table i), we estimate that the synodic-sidereal difference could be as large as 
day.
Figure 1c plots the composite lightcurve for a period of 9.0 days. The peak-to-trough amplitude is about 1.4 mag and it is consistent with an elongated shape. Most of the lightcurve points are from a single cycle between April 14-21. Points from the other cycles agree well with the same lightcurve except for the points on 1999 May 4.1 and 8.1 (plus symbols at phases 0.23 and 0.67, respectively, in Fig. 1c). The May 8.1 point is fainter by 0.36 mag than the average of points taken on April 20.0 and May 17.1 that occur around the same phase (0.67) in the composite lightcurve. Since the difference is much greater than the uncertainty, it is likely real and it indicates that the asteroid's brightness was significantly lower on May 8.1 than at the same phase two cycles earlier and one cycle later. The point on May 4.1 (at phase 0.23 in Fig. 1c) is fainter than expected relative to adjacent points. Although incomplete coverage of the cycle that includes the points on May 4.1 and 8.1 does not allow us to draw firm conclusions, it seems possible that both maxima (near phases 0.2 and 0.7 in Fig. 1c) had significantly lower levels during that cycle than during the cycles 18 days before and (in the case of the maximum at the phase 0.7) 9 days later. Change of lightcurve shape due to a change of aspect (the PAB changed by 19° from April 20.0 to May 8.1) does not explain the deviation well because the point on May 17.1 agrees with the April 20.0 points. The discrepancy of the May 4.1 and 8.1 points with the rest of the lightcurve hints that the asteroid's rotation may be complex.
We derived a mean absolute magnitude 
from the zeroth order of the best fit Fourier series extrapolated to zero solar phase angle and by assuming 
.
Hz to our initial Doppler prediction ephemeris, which was based on JPL orbit solution 10; this correction was comparable to the estimated 1- 
uncertainty. We promptly used that measurement to generate a new ephemeris (solution 12). Subsequent analysis revealed that the echo was drifting in Doppler frequency relative to solution 10 by Hz/h, which could have corrupted estimation of the echo bandwidth and interpretation of the echoes had the drift gone unnoticed. Therefore, except for the initial astrometry, where we assigned an appropriately large uncertainty, we did not use the cw echoes obtained with solution 10 in our analyses. We completed ten more cw runs using solution 12, measured a Doppler correction of 
Hz at the epoch 1999 April 17 14:00:00 UTC, and concluded the experiment by attempting (unsuccessfully) to measure the asteroid's range. The Doppler astrometry is available at the JPL Solar System Dynamics website at http://ssd.jpl.nasa.gov/radar_data.html (Chamberlin et al. 1997).
Figure 1d shows an echo power spectrum of 1999 GU3. A weighted sum of ten cw runs gives an OC radar cross section 
km2; uncertainties are dominated by systematic pointing and calibration errors and we assign standard errors of 50% to the estimates. The asteroid's circular polarization ratio SC/OC 
(the uncertainty is due to receiver noise) is larger than 
% of the NEA ratios reported in the peer-reviewed literature (Benner et al. 1999b) and it indicates that the near-surface of 1999 GU3 at decimeter scales is morphologically rougher than those of most radar-detected NEAs.
The spectrum resolves the asteroid into four 0.076-Hz Doppler cells exceeding five standard deviations and establishes a bandwidth of 0.3 Hz. Narrow bandwidth requires either that 1999 GU3 is a very slow rotator, that the apparent spin vector was near the line of sight, and/or that the effective diameter is smaller than the a priori estimate of several hundred meters.
1999 GU3 was not resolved in range, but the echo bandwidth (given by 
, where D is the breadth of the object, 
is the subradar latitude, 
is the radar wavelength, and P is the rotation period) and rotation period of 9 days place a lower bound on the maximum pole-on breadth 
km. If we assume that the effective diameter (the diameter of a sphere with the same projected area as the target) 
and we adopt the 1- upper limit on 
and the formal lower limit on H,
then we obtain upper bounds on the radar albedo (equal to projected area) and visual geometric albedo (computed from 
) of 0.07 and 0.08 that are among the lowest for any near-Earth asteroid. The radar observations occurred at the phase 0.40 in Fig. 1c near a minimum of the asteroid's lightcurve. This suggests that asteroid's long axis may have been oriented within a few tens of degrees of Earth during the radar observations, implying that the effective diameter may be larger than 0.64 km and that the radar and visual albedos may be even lower.
The upper bound on the radar albedo is consistent with those observed among BFGP- and C-type (Magri et al. 1999). Among NEAs for which shape reconstructions have been published (4769 Castalia [Hudson and Ostro 1994], 4179 Toutatis [Hudson and Ostro 1995], 2063 Bacchus [Benner et al. 1999a], and 1620 Geographos [Hudson and Ostro 1999]), the upper bound on the radar albedo of 1999 GU3 is comparable only to that of 1998 KY26 (Ostro et al. 1999b). The upper bound on the visual geometric albedo suggests the same taxonomic classes as the upper bound on the radar albedo (see Tholen and Barucci 1989). Although systematic errors due to uncertainties in extrapolation of high phase angle observations to zero phase could allow visual albedos greater than 0.10 that are marginally consistent with Q type suggested by the color indices, we conclude that no taxonomic class is consistent with all of the constraints. It is also possible, although unlikely, that the period is one-half of the estimate of 9 days. If so, then 
km and the upper bounds on the radar and visual geometric albedos (assuming ) are 0.28 and 0.32, values that are consistent with the color indices.
The 9-day rotation period exceeds more than 99% of all reported asteroid rotation periods (Pravec and Harris 1999). How did the slow rotation state of 1999 GU3 originate? Among possible explanations are that the slow rotation resulted from the disruption of a larger progenitor, of which 1999 GU3 is a fragment; from tidal interactions during one or more very close terrestrial planetary flybys (Richardson et al. 1998, Scheeres et al. 1999); from secular drag due to Yarkovsky thermal forces (Rubincam 1999); or due to a combination of these mechanisms.
Another possibility is that the slow rotation is the result of tidal despinning between components of a direct binary system (Weidenschilling et al. 1989), possibly followed by removal of the secondary during a close encounter with a terrestrial planet, a scenario that could leave both components with rotation periods of up to several days (Farinella and Chauvineau 1993, Chauvineau et al. 1995). Recent studies suggested that binary asteroids are common among near-Earth asteroids (Pravec et al. 2000), thus there may be a source for slow rotators created by this mechanism. However, we find no evidence for a satellite in the radar data nor is there evidence for eclipses/occultations in the photometry.
Is 1999 GU3 a non-principal axis (NPA) rotator? NPA rotation is suggested by the lightcurve (Fig. 1c) which, as discussed above, may not be strictly periodic. Most small asteroids probably formed during catastrophic disruption of larger parent bodies. Impact simulations by Asphaug and Scheeres (1999) suggest that excitation of NPA rotation may be common among fragments of catastrophic disruptions; if so, then the question is whether enough time has elapsed for damping into a principal axis rotation state. A simple expression for estimating the damping timescale is 
(Harris 1994), where P is the sidereal rotation period in hours, 
is the effective diameter in km, and C is a parameter that depends on the material properties of the asteroid. Using 
km, P = 216 h, and 
, we obtain 
y, a timescale so long that it strongly suggests that unless 1999 GU3 originated in uniform rotation, it probably is a NPA rotator. Several other asteroids, notably 288 Glauke, 1689 Floris-Jan, 3288 Seleucus, 3691 (1982 FT), and 1997 BR are suspected of being NPA rotators (Harris 1994, Harris et al. 1999, Pravec et al. 1998), but their damping timescales are at least an order of magnitude less than that of 1999 GU3. The only confirmed NPA
rotator among the NEA population, 4179 Toutatis (Hudson and Ostro 1995), has an estimated damping time of 
y.
1999 GU3 is currently near a temporary mean-motion resonance that brings the asteroid close to Earth every three years. The next opportunity for optical and radar observations of 1999 GU3 occurs in April 2002, when the asteroid will approach within 0.081 AU of Earth and reach 
. Estimated SNRs at Arecibo are on the order of several thousand per day and should be strong enough to reconstruct the asteroid's detailed three-dimensional shape and to define the spin state.
References
Asphaug, E., and D. J. Scheeres 1999. Deconstructing Castalia: Evaluating a postimpact state. Icarus 139, 383-386.
Benner, L. A. M., R. S. Hudson, S. J. Ostro, K. D. Rosema, J. D. Giorgini, D. K. Yeomans, R. F. Jurgens, D. L. Mitchell, R. Winkler, R. Rose, M. A. Slade, M. L. Thomas, and P. Pravec 1999a. Radar observations of asteroid 2063 Bacchus. Icarus 139, 309-327.
Benner, L. A. M., S. J. Ostro, K. D. Rosema, J. D. Giorgini, D. Choate, R. F. Jurgens, R. Rose, M. A. Slade, M. L. Thomas, R. Winkler, and D. K. Yeomans 1999b. Radar observations of asteroid 7822 (1991 CS). Icarus 137, 247-259.
Binzel, R. P., P. Farinella, V. Zappalà, and A. Cellino 1989. Asteroid rotation rates: Distributions and statistics. In Asteroids II, eds. R. P. Binzel, T. Gehrels, and M. S. Matthews. Univ. of Arizona Press, Tucson, pp. 416-441.
Bowell, E., B. Hapke, D. Domingue, K. Muinonen, J. Peltoniemi, and A. W. Harris 1989. Application of photometric models to asteroids. In Asteroids II, eds. R. P. Binzel, T. Gehrels, and M. S. Matthews. Univ. of Arizona Press, Tucson, pp. 524-556.
Chamberlin, A. B., D. K. Yeomans, P. W. Chodas, J. D. Giorgini, R. A. Jacobson, M. S. Keesey, J. H. Lieske, S. J. Ostro, E. M. Standish, and R. N. Wimberly 1997. JPL solar system dynamics WWW site. Bull. Am. Astron. Soc. 29, 1014. [Abstract]
Chauvineau, B., P. Farinella, and A. W. Harris 1995. The evolution of Earth-approaching binary asteroids: A Monte Carlo dynamical model. Icarus 115, 36-46.
Dermott, S. F., A. W. Harris, and C. D. Murray 1984. Asteroid rotation rates. Icarus 57, 14-34.
Farinella, P., and B. Chauvineau 1993. On the evolution of binary Earth-approaching asteroids. Astron. Astrophys. 279, 251-259.
Farinella, P., D. R. Davis, P. Paolicchi, A. Cellino, and V. Zappalà 1992. Asteroid collisional evolution: An integrated model for the evolution of asteroid rotation states. Astron. Astrophys. 253, 604-614.
Fulchignoni, M., M. A. Barucci, M. Di Martino, and E. Dotto 1995. On the evolution of the asteroid spin. Astron. Astrophys. 299, 929-932.
Harris, A. W. 1979. Asteroid rotation rates II. A theory for the collisional evolution of rotation rates. Icarus, 40, 145-153.
Harris, A. W. 1994. Tumbling Asteroids. Icarus 107, 209-211.
Harris, A. W., J. W. Young, E. Bowell, L. J. Martin, R. L. Millis, M. Poutanen, F. Scaltriti, V. Zappalà, H. J. Schober, H. Debehogne, and K. W. Zeigler 1989. Photoelectric observations of asteroids 3, 24, 60, 261, and 863. Icarus 77, 171-186.
Harris, A. W., J. W. Young, E. L. G. Bowell, and D. J. Tholen 1999. Asteroid lightcurve observations from 1981-1983. Icarus 142, 173-201.
Hudson, R. S., and S. J. Ostro 1994. Shape of asteroid 4769 Castalia (1989 PB) from inversion of radar images. Science 263, 940-943.
Hudson, R. S., and S. J. Ostro 1995. Shape and non-principal axis spin state of asteroid 4179 Toutatis. Science 270, 84-86.
Hudson, R. S., and S. J. Ostro 1998. Photometric properties of asteroid 4179 Toutatis from lightcurves and a radar-derived physical model. Icarus 135, 451-457.
Hudson, R. S., and S. J. Ostro 1999. Physical model of asteroid 1620 Geographos from radar and optical data. Icarus 140, 369-378.
Kryszczynska, A., Kwiatkowski, T., S. Breiter, and T. Michalowski 1999. Relation between rotation and lightcurve of 4179 Toutatis. Astron. Astrophys. 345, 643-645.
Landolt, A. U. 1992. UBVRI photometric standard stars in the magnitude range 11.5;SPMlt;V;SPMlt;16.0 around the celestial equator. Astron. J. 104, 340-371.
Magri, C., S. J. Ostro, K. D. Rosema, M. L. Thomas, D. L. Mitchell, D. B. Campbell, J. F. Chandler, I. I. Shapiro, J. D. Giorgini, and D. K. Yeomans 1999. Mainbelt asteroids: Results of Arecibo and Goldstone radar observations of 37 objects during 1980-1995. Icarus 140, 379-407.
Mottola, S., W. D. Sears, A. Erikson, A. W. Harris, J. W. Young, G. Hahn, M. Dahlgren, B. E. A. Mueller, B. Owen, R. Gil-Hutton, J. Licandro, M. A. Barucci, C. Angeli, G. Neukum, C.-I. Lagerkvist, and J. F. Lahulla 1995. The slow rotation of 253 Mathilde. Planet. Space Sci. 43, 1609-1613.
Ostro, S. J., D. B. Campbell, R. A. Simpson, R. S. Hudson, J. F. Chandler, K. D. Rosema, I. I. Shapiro, E. M. Standish, R. Winkler, D. K. Yeomans, R. Velez, and R. M. Goldstein 1992. Europa, Ganymede, and Callisto: New radar results from Arecibo and Goldstone. J. Geophys. Res. 97, 18,227-18,244.
Ostro, S. J., R. S. Hudson, K. D. Rosema, J. D. Giorgini, R. F. Jurgens, D. K. Yeomans, P. W. Chodas, R. Winkler, R. Rose, D. Choate, R. A. Cormier, D. Kelley, R. Littlefair, L. A. M. Benner, M. L. Thomas, and M. A. Slade 1999a. Asteroid 4179 Toutatis: 1996 radar observations. Icarus 137, 122-139.
Ostro, S. J., P. Pravec, L. A. M. Benner, R. S. Hudson, L. Sarounová, M. D. Hicks, D. L. Rabinowitz, J. V. Scotti, D. J. Tholen, M. Wolf, R. F. Jurgens, M. L. Thomas, J. D. Giorgini, P. W. Chodas, D. K. Yeomans, R. Rose, R. Frye, K. D. Rosema, R. Winkler, and M. A. Slade 1999b. Radar and optical observations of asteroid 1998 KY26 . Science, 285, 557-559.
Pravec, P., and A. W. Harris 1999. Fast and slowly rotating asteroids. Icarus, submitted.
Pravec, P., L. Sarounová, and M. Wolf 1996. Lightcurves of 7 near-Earth asteroids. Icarus 124, 471-482.
Pravec, P., M. Wolf, and L. Sarounová 1998. Lightcurves of 26 near-Earth asteroids. Icarus 136, 124-153.
Pravec, P., L. Sarounová, D. L. Rabinowitz, M. D. Hicks, M. Wolf, Yu. N. Krugly, F. P. Velichko, V. G. Shevchenko, V. G. Chiorny, N. M. Gaftonyuk, and G. Genevier 2000. Two-period lightcurves of 1996 FG3 , 1998 PG and (5407) 1992 AX: One probable and two possible binary asteroids. Icarus, in press.
Rabinowitz, D. L. 1998. Size and orbit dependent trends in the reflectance colors of Earth-approaching asteroids. Icarus 134, 342-346.
Richardson, D. C., W. F. Bottke, and S. G. Love 1998. Tidal distortion and disruption of Earth-crossing asteroids. Icarus 134, 47-76.
Rubincam, D. P. 1999. Radiative spin-up and spin-down of asteroids. Icarus, submitted.
Scheeres, D. J., S. J. Ostro, R. A. Werner, E. Asphaug, and R. S. Hudson 1999. Effects of gravitational interactions on asteroid spin states. Icarus, submitted.
Spencer, J. R., L. A. Akimov, C. Angeli, P. Angelini, M. A. Barucci, P. Birch, C. Blanco, M. Buie, A. Caruso, V. G. Chiornij, F. Colas, P. Dentchev, M. C. De Sanctis, E. Dotto, M. Fulchignoni, S. Green, A. Harris, T. Hudecek, A. V. Kalashnikov, V. V. Kobelev, V. P. Kozhevnikov, Y. Krugly, D. Lazzaro, J. Lecacheux, J. MacConnell, T. Michalowski, R. A. Mohamed, B. Mueller, T. Nakamura, C. Neese, K. Noll, W. Osborn, P. Pravec, D. Riccioli, V. Shevchenko, D. Tholen, F. Velichko, C. Venditti, R. Venditti, W. Wisniewski, J. Young, and B. Zellner 1995. The lightcurve of 4179 Toutatis: Evidence for complex rotation. Icarus 117, 71-89.
Tholen, D. J., and M. A. Barucci 1989. Asteroid taxonomy. In Asteroids II (R. P. Binzel, T.Gehrels, and M. S. Matthews, Eds.), pp. 1139-1150. Univ. of Arizona Press, Tucson.
Veverka, J., P. Thomas, A. Harch, B. Clark, J. F. Bell III, B. Carcich, J. Joseph, C. Chapman, W. Merline, M. Robinson, M. Malin, L. A. McFadden, S. Murchie, S. E. Hawkins III, R. Farquhar, N. Izenberg, and A. Cheng 1997. NEAR's flyby of 253 Matilde: Images of a C asteroid. Science 278, 2109-2114.
Weidenschilling, S. J., P. Paolicchi, and V. Zappalà 1989. Do asteroids have satellites? In Asteroids II (R. P. Binzel, T.Gehrels, and M. S. Matthews, Eds.), pp. 643-658. Univ. of Arizona Press, Tucson.
Figure 1: Lightcurve of 1999 GU3 (a) vs. time and (c) phased with a period of 9.0 days. Each point is an average of several measurements taken in quick succession. (b) Sum of square residuals of the lightcurve points to the best fit fourth-order Fourier series vs. period. (d) Goldstone echo power spectrum of 1999 GU3 at 0.076 Hz resolution. Echo power is plotted in standard deviations versus Doppler frequency relative to the estimated frequency of echoes from the asteroid's center of mass, which was estimated by eye using the middle of the Doppler cells exceeding five standard deviations. Solid and dashed lines denote echo power in the OC and SC polarizations.
| Date UT | RA | DEC | LPAB | BPAB |  |
r |  |
Error | Observatory |
| h m | ° ' | [deg] | [deg] | [AU] | [AU] | [deg] | [mag] | ||
| 1999 Apr. 14.4 | 15 57.8 | 36 58 | 211.6 | 29.1 | 0.0427 | 1.0263 | 55.9 | 0.01 | Table Mountain |
| 14.9 | 16 09.8 | 37 27 | 213.1 | 30.0 | 0.0448 | 1.0263 | 57.7 | 0.01 | Ondrejov |
| 15.4 | 16 20.9 | 37 50 | 214.6 | 30.7 | 0.0470 | 1.0264 | 59.3 | 0.01 | Table Mountain |
| 16.9 | 16 48.8 | 38 28 | 218.5 | 32.4 | 0.0538 | 1.0268 | 63.1 | 0.02 | Kharkiv |
| 17.9 | 17 03.8 | 38 37 | 220.9 | 33.2 | 0.0585 | 1.0273 | 65.0 | 0.02 | Ondrejov |
| 18.0 | 17 05.2 | 38 37 | 221.1 | 33.3 | 0.0590 | 1.0273 | 65.1 | 0.01 | Kharkiv |
| 18.9 | 17 16.5 | 38 38 | 223.1 | 33.8 | 0.0634 | 1.0279 | 66.4 | 0.01 | Kharkiv |
| 19.0 | 17 17.6 | 38 38 | 223.3 | 33.9 | 0.0639 | 1.0279 | 66.5 | 0.01 | Ondrejov |
| 20.0 | 17 28.2 | 38 34 | 225.3 | 34.4 | 0.0688 | 1.0287 | 67.6 | 0.01 | Ondrejov, Kharkiv |
| 21.0 | 17 37.4 | 38 27 | 227.2 | 34.8 | 0.0739 | 1.0296 | 68.4 | 0.01 | Kharkiv |
| 21.1 | 17 38.2 | 38 27 | 227.4 | 34.8 | 0.0744 | 1.0297 | 68.5 | 0.01 | Ondrejov |
| 23.1 | 17 52.6 | 38 09 | 230.8 | 35.3 | 0.0846 | 1.0320 | 69.4 | 0.02 | Ondrejov |
| 24.1 | 17 58.4 | 37 59 | 232.3 | 35.5 | 0.0897 | 1.0333 | 69.6 | 0.01 | Ondrejov |
| May 4.1 | 18 30.5 | 36 20 | 244.7 | 35.9 | 0.1412 | 1.0541 | 67.4 | 0.04 | Ondrejov |
| 6.1 | 18 33.6 | 36 02 | 246.7 | 35.8 | 0.1513 | 1.0598 | 66.4 | 0.04 | Ondrejov |
| 8.1 | 18 36.1 | 35 44 | 248.6 | 35.7 | 0.1613 | 1.0659 | 65.3 | 0.05 | Ondrejov |
| 10.1 | 18 38.0 | 35 26 | 250.5 | 35.6 | 0.1712 | 1.0726 | 64.1 | 0.08 | Ondrejov |
| 17.1 | 18 41.6 | 34 21 | 256.2 | 35.1 | 0.2052 | 1.0993 | 59.6 | 0.04 | Ondrejov |
| 19.0 | 18 41.9 | 34 02 | 257.5 | 34.9 | 0.2143 | 1.1075 | 58.3 | 0.03 | Ondrejov |
| Date UT | RA | DEC | |
Ptx | Band | OSOD | Runs |  |
 |
TXoff |
| h m | ° ' | [AU] | [kW] | [Hz] | soln | [UTC h] | [Hz] | [Hz] | ||
| 1999 Apr. 17.6 | 16 59.6 | 38 35 | 0.0571 | 438 | 20000 | 10 | 8 | 09.06-09.30 | 9.8 | 0 |
| 20000 | 10 | 28 | 09.34-10.21 | 9.8 | -1171.875 | |||||
| 5000 | 12 | 10 | 13.87-14.18 | 4.9 | 0 |
Note to Tables I and II:
Times are the mid-epochs of the observations, given to the nearest one-tenth of a day. The geocentric right ascension, declination, phase-angle bisector are all given for equinox J2000. and r are the geocentric and heliocentric distances and is the solar phase angle. Errors of the points are formal and were derived from the average of several consecutive R measurements. Ptx is the average transmitter power and Band is the sampling rate. The orbital solution number is given in column seven. The number of transmit-receive cycles (runs) is listed in the eighth column. is the interval spanned by each type of observation, is the raw frequency resolution in the real-time display, and TXoff is the transmitter frequency offset.
