We observed 2000 PH5 with the Goldstone radar in 2001 and determined that it was a fast rotator with an equivalent diameter of about 150 m. Four observing sessions at Arecibo on 2003 Jul 28-31 will allow us to obtain images at ~10 m resolution with good rotational coverage. We will apply asteroid radar astronomy techniques [Ostro, Reviews of Modern Physics, 65, 1993] and shape modeling techniques [Hudson, Remote Sensing Reviews, 8, 1993] to obtain the best possible characterization of this minor planet. Our objectives are 1) to measure reflection properties to help constrain a possible source region, 2) to obtain precise radar astrometry to refine the orbital history of this object, 3) to determine the orientation of the spin vector to allow lightcurve data obtained at several apparitions to be linked, 4) to obtain a detailed shape model for morphological studies and modeling of the YORP effect.
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| Figure 1: Evolution of the position of 2000 PH5 in a frame co-rotating with Earth over a period of 200 years (the 2003 orbit is shown in red). The Sun is at the origin and Earth is at +1 on the X axis. Close Earth approaches occur only because of the significant eccentricity and corresponding epicycle motion superposed on the mean longitude evolution. |
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Figure 2: Evolution of the ecliptic longitude of 2000 PH5 compared to that of Earth over a 200 year period. The plot clearly shows the horseshoe orbit behavior, with the object slowly catching up to Earth at a rate of 3 degrees/year, interacting with Earth, and then receding at a rate of -3 degrees/year. The July 2003 close approach to Earth is near MJD 52850. |
2000 PH5 is a near-Earth object with an orbital period extremely similar to that of Earth. Over the past ~100 years it has been trailing Earth while slowly catching up at a rate of about 3 degrees per year in mean longitude. The asteroid is presently at one end of its horseshoe orbit, at a mean longitude that is lagging Earth by about 30 degrees, and it is undergoing an abrupt change in orbital parameters. Earth's gravity is increasing the asteroid's orbital energy, such that the semi-major axis is changing from its former value of ~0.994 AU to a value of ~1.006 AU. The asteroid will now recede at a rate of about 3 degrees per year in mean longitude, until it reaches the other end of the horseshoe, 30 degrees ahead of Earth, almost 100 years from now.
The pattern of close Earth approaches by this object is dictated by a combination of its horseshoe orbit and a moderate eccentricity of 0.2. The figures above show the longitude evolution which is the superposition of the slow (100 year) libration in mean longitude and a fast (1 year) epicycle-like motion due to the eccentricity. 2000 PH5 approaches Earth within a few lunar distances because of its significant eccentricity and the resulting departure in longitude from the mean value. Figure 1 shows the motion in the Earth co-rotating frame typically used in the restricted circular three-body problem. The fact that this object happens to have just the right eccentricity to bring it so close to Earth suggests that it may have been barely ejected from the Earth-Moon system into an heliocentric orbit.
Petr Pravec and Lenka Sarounova of Ondrejov posted some lightcurve results showing the rotation period of 2000 PH5 derived from the 2001 observations. Pravec and collaborators are planning a campaign of observations during the 2003 apparition in an attempt to link the lightcurve data over the 2001, 2002, and 2003 apparitions. The idea is to obtain a rotational period with the required accuracy to detect YORP.
An estimate of the pole location is required in order to link lightcurve data from multiple apparitions. What is measured by the lightcurve observations is a synodic period affected by the motion of the asteroid and the spin vector orientation. With good radar data, we should be able to determine the orientation of the pole. A radar-derived shape model will also help in interpreting the lightcurve (amplitude variations) and in modeling the shape-dependent YORP torques. Therefore, the lightcurve and radar data will be highly complementary.
On 2001 July 24, just two days before the radar observations, the LONEOS astronomers/gastronomes recovered the asteroid (MPEC 2001-O37) and earned Belgian fermented beverages in the process.
With the 2001 radar astrometry, pointing uncertainties are now much smaller than the Arecibo radar beam.
Date UT Window DEC RTT (s) SNR/run 2003-07-29 02:02-04:30 +28 16.9 185 2003-07-30 01:55-04:42 +21 20.0 106 2003-07-31 01:58-04:40 +15 23.4 63 2003-08-01 02:03-04:34 +10 27.1 38
The 2001 time on the Deep Space Network 70 m antenna was graciously made available to us by Tom Kuiper, Albert Haldemann, and Mike Klein, respectively (UT times):
DOY SOA BOT EOT EOA Antenna 207 2300 0030 0945 1015 DSS-14 GSSR AST 2000PH5 X-TX 209 0300 0430 0710 0740 DSS-14 GSSR MARS/2000PH5 XTX 210 2030 2200 0330 0400 DSS-14 GSSR AST 2000PH5 X-TX
/share/olda/Ephm/2000PH5.PRDX.OUT.s53
The object should be detectable in a single run, but we will accumulate CW runs until we have a clear detection. According to Jon Giorgini, 3-sigma Doppler uncertainties should be less than 0.2 Hz thanks to the radar astrometry that we obtained in 2001. Range uncertainties will be less than one mile. Therefore we will immediately switch from the CW setup to a 0.1 us baud, 65535 length code, high resolution imaging setup. I will reduce the first few runs of imaging data while we continue accumulating, and I will generate a new ephemeris solution that should reduce run-to-run range smear.
Jon Giorgini's uncertainty analysis:
With 297 usable optical observations spanning 2000-Aug-3 to
2002-Aug-19, 2 delay and 1 Doppler, 3-sigma S-band uncertainties
are as follows:
DATE Pointing S-band Dop Delay
(") Hz (sec)
----------------- --------- ---------- ----------
28-JUL-2003 00:00 2.392 0.277 0.000010
29-JUL-2003 00:00 1.999 0.278 0.000012
30-JUL-2003 00:00 1.671 0.275 0.000021
31-JUL-2003 00:00 1.417 0.272 0.000031
1-AUG-2003 00:00 1.222 0.269 0.000040
jlm@astro.cornell.edu
