Goldstone radar observations of 2000 PH5, July 27-30, 2001

Background

2000 PH5 is a small (H=22.5) asteroid with a semi-major axis extremely close to that of the Earth (0.998 Astronomical Units). It has an interesting dynamical history with repeated close approaches to Venus and Earth. The radar observations were planned to provide information about the object's shape, spin, and surface properties, and to refine the knowledge of its orbital parameters. Apart from contributing to our understanding of asteroid properties, all of these data would be of great importance should we ever consider mitigation measures or exploration activities.

Discovery Announcement

M.P.E.C. 2000-P32                                Issued 2000 Aug. 7, 15:07 UT
 
     The Minor Planet Electronic Circulars contain information on unusual
         minor planets and routine data on comets.  They are published
   on behalf of Commission 20 of the International Astronomical Union by the
          Minor Planet Center, Smithsonian Astrophysical Observatory,
                          Cambridge, MA 02138, U.S.A.

             Prepared using the Tamkin Foundation Computer Network

             BMARSDEN@CFA.HARVARD.EDU or GWILLIAMS@CFA.HARVARD.EDU
          URL http://cfa-www.harvard.edu/iau/mpc.html  ISSN 1523-6714


                                   2000 PH5
 
Observations:
     K00P05H* C2000 08 03.16150 17 38 49.52 -01 16 41.6          17.2        704
     K00P05H  C2000 08 03.17575 17 38 59.56 -01 17 46.2          17.5        704
     K00P05H  C2000 08 03.20449 17 39 19.76 -01 19 56.5          17.8        704
     K00P05H  C2000 08 03.21874 17 39 29.75 -01 21 00.6          17.8        704
     K00P05H  C2000 08 04.14083 17 50 34.82 -02 25 31.0          18.0        704
     K00P05H  C2000 08 04.15472 17 50 43.12 -02 26 24.3          17.7        704
     K00P05H  C2000 08 04.18251 17 50 59.73 -02 28 11.7          18.2        704
     K00P05H  C2000 08 04.19640 17 51 08.00 -02 29 05.1          18.3        704
     K00P05H  C2000 08 04.94225 17 58 50.47 -03 14 48.8                      611
     K00P05H FC2000 08 04.94322 17 58 50.96 -03 14 53.0                      611
     K00P05H  C2000 08 05.18172 18 01 12.29 -03 27 32.6                      711
     K00P05H  C2000 08 05.18632 18 01 14.64 -03 27 47.8                      711
     K00P05H  C2000 08 05.19017 18 01 16.55 -03 28 00.6                      711
     K00P05H  C2000 08 06.87547 18 15 30.78 -04 50 26.4                      118
     K00P05H  C2000 08 06.87953 18 15 32.64 -04 50 36.4                      118
     K00P05H  C2000 08 06.88220 18 15 33.83 -04 50 42.3                      118
 
Observer details:
118 Modra.  Observers A. Galad, J. Toth.  0.6-m f/5.5 reflector + CCD.
611 Starkenburg.  Observers S. Kluegl, M. Busch, R. Stoss.  0.45-m f/4.4 
    reflector + CCD.
704 Lincoln Laboratory ETS, New Mexico.  Observers M. Blythe, F. Shelly,
    M. Bezpalko, M. Elowitz, R. Huber, L. Manguso.  Measurers J. Stuart,
    R. Sayer, J. B. Evans, H. Viggh.  1.0-m f/2.15 reflector + CCD.
711 McDonald Observatory.  Observers P. J. Shelus, J. G. Ries.  0.76-m
    reflector + CCD.
 
Orbital elements:
2000 PH5                                                             PHA 0.008
Epoch 2000 Aug. 4.0 TT = JDT 2451760.5                  Hergenrother
M  88.71800              (2000.0)            P               Q
n   0.98795493     Peri.  271.21711     -0.96191471     +0.27106056
a   0.9984155      Node   284.51109     -0.23405096     -0.88344146
e   0.2319119      Incl.    2.08979     -0.14120989     -0.38217452
P   1.00           H   21.9           G   0.15
From 16 observations 2000 Aug. 3-6.

Ephemeris:
2000 PH5                 a,e,i = 1.00, 0.23, 2                   q = 0.7669
Date    TT    R. A. (2000) Decl.     Delta      r     Elong.  Phase     V
2000 08 04    17 48.96   -02 14.4    0.046    1.045   131.4    46.8    17.1
2000 08 09    18 29.64   -06 07.8    0.066    1.064   138.0    39.7    17.7
2000 08 14    18 52.70   -08 11.8    0.088    1.081   139.7    37.3    18.3
2000 08 19    19 08.24   -09 28.6    0.111    1.098   139.2    37.0    18.8
2000 08 24    19 20.15   -10 21.1    0.135    1.114   137.6    37.7    19.3
2000 08 29    19 30.23   -10 58.8    0.159    1.129   135.5    38.8    19.7
2000 09 03    19 39.44   -11 26.4    0.185    1.143   133.1    40.1    20.1
2000 09 08    19 48.26   -11 46.0    0.212    1.156   130.5    41.5    20.5
2000 09 13    19 56.94   -11 58.9    0.239    1.168   127.9    42.8    20.8
2000 09 18    20 05.61   -12 06.1    0.268    1.180   125.2    44.1    21.1
2000 09 23    20 14.37   -12 08.1    0.297    1.190   122.5    45.4    21.4
2000 09 28    20 23.31   -12 05.2    0.327    1.198   119.8    46.5    21.6
2000 10 03    20 32.47   -11 57.6    0.357    1.206   117.2    47.6    21.9
2000 10 08    20 41.86   -11 45.3    0.388    1.213   114.6    48.5    22.1
2000 10 13    20 51.46   -11 28.6    0.420    1.219   112.0    49.4    22.3

Carl W. Hergenrother         (C) Copyright 2000 MPC           M.P.E.C. 2000-P32

Observations

On DOY 207, we had to reconfigure for single klystron operation. We obtained 57 cycles of CW and at least 54+56+56+20 cycles of 1/8 usec data. On DOY 209, we obtained 8 cycles of 10 us ranging, 5 cycles of 11 us ranging, 105 cycles of 1/4 usec imaging, and 61 cycles of CW. On DOY 211, we did not obtain data due to antenna tracking problems. Our first echoes, from a continuous wave transmission, were Fourier transformed to generate power spectra at about 1 Hz resolution. Shown here is a sum of such spectra accumulated over 25 minutes.

From these data we can evaluate the cross-section of the target and, given some estimate of the object size, place upper limits on the rotation rate. In addition, if we obtain such echoes over a range of sky positions and/or rotational coverage, we can place constraints on the pole direction and/or convex hull of the object. With a bandwidth of about 28 Hz and a diameter of 150 meters, 2000 PH5 must have a spin period less than 32 minutes. The fast rotation was confirmed by Lenka Sarounova and Petr Pravec of Ondrejov who posted some lightcurve results.

A very preliminary reduction of a small subset of the imaging data is shown below. These images were obtained with a range resolution of 19 meters (increasing to the bottom) and a frequency resolution of about 1.9 Hz (increasing to the right). Each look represents about 10 seconds worth of integration, and the mosaic covers a time span of 25 minutes. Further analysis will include summing to improve the noise statistics and to reduce speckle. Because we obtained good rotational coverage of this object, it should be possible to derive a shape model from these data.

A search for satellites in summed images does not reveal anything striking:

Astrometry

On the first night of observations, we obtained range and line of sight velocity measurements for 2000 PH5. These data were used to generate a new ephemeris solution for the second night of observations.

On the second night of observations, we found that the radar astrometry from the first night had resulted in significant improvements to the ephemeris. The range predicted for the asteroid was within 300 meters of its actual value. Another range measurement with an uncertainty equivalent to the size of the object was reported on the basis of the second night's data.

The data in the MPC format look like this: 

     K00P05H  R2001 07 27.079167               -    1522346    8560 253      253
     K00P05H  r2001 07 27.079167C                        5          253      253
     K00P05H  R2001 07 27.334028   135070545                   8560 253      253
     K00P05H  r2001 07 27.334028C        10                         253      253
     K00P05H  R2001 07 28.208333   154907263                   8560 253      253
     K00P05H  r2001 07 28.208333C         1                         253      253

Close approach table

On the basis of 137 optical observations (Aug 3, 2000 - Jul 27, 2001), 1 Doppler and 2 range measurements, Jon Giorgini computed the following close approach table, where the horseshoe orbit first became apparent: 
  Column meanings:
    CA-Dist ... Nominal trajectory close-approach distance at nominal time, in AU.
    MinDist ... Minimum (3-standard-deviation) distance at nominal CA time, in AU.
    MaxDist ... Maximum (3-standard deviation) distance at nominal CA time, in AU.
    Vrel ...... Velocity relative to Body at nominal CA time, in km/s
    TCA3Sg .... Uncertainty in time of close-approach, +/- 3-standard-deviation, in minutes.
    Nsigs ..... Number of 1-sigma error ellipses require to intersect Body.
    P_i/p ..... Probability of impacting body

   Date (TDB)      Body   CA Dist  MinDist  MaxDist   Vrel  TCA3Sg  Nsigs  P_i/p
-----------------  ----- -------- -------- -------- ------- ------ ------ -------

1647 Jul 19.08299  Earth  .091597  .048027  .130955   9.661 1995.0 4135.4 .000000
1648 Jul 16.23245  Earth  .034904  .011069  .056613   8.006 990.31 3801.8 .000000
1649 Jul 15.15659  Earth  .008659  .003764  .013952   6.801 228.66 3559.0 .000000
1650 Jul 19.29817  Earth  .098327  .093155  .103916   4.396 1382.1 147.04 .000000
1657 Dec 13.52800  Earth  .081311  .075969  .087077   4.672 350.27 5391.8 .000000
1658 Dec 12.98913  Earth  .024645  .022337  .027683   7.446 334.65 6434.1 .000000
1700 Jun 10.58647  Venus  .088827  .087679  .089970   4.925 156.48 3950.8 .000000
1705 May 11.32821  Venus  .081234  .081226  .081252   3.880  14.29 72559. .000000
1705 Jul 19.96950  Earth  .096391  .095797  .096984   9.830  13.85 16127. .000000
1706 Jul 17.03219  Earth  .005098  .004378  .005896   7.212  22.02 44094. .000000
1707 Jul 16.64324  Earth  .016122  .014581  .017687   6.575  73.54 48498. .000000
1708 Jul 15.56538  Earth  .060011  .058287  .061768   5.308  21.75 66826. .000000
1722 Dec 17.48205  Earth  .056865  .056578  .057152   5.382   1.11 1.48E5 .000000
1723 Mar 12.76026  Venus  .081561  .081484  .081638   3.593  35.12 8.57E5 .000000
1723 Dec 16.91910  Earth  .018181  .017935  .018436   6.755  20.45 1.25E5 .000000
1724 Dec 14.96114  Earth  .029599  .028756  .030449   7.782  49.48 1.15E5 .000000
1725 Dec 13.30258  Earth  .076871  .075707  .078032   9.274  61.69 1.09E5 .000000
1740 Dec 31.53745  Venus  .098334  .097555  .099117   3.894 184.83 5.84E5 .000000
1763 Oct 20.09349  Venus  .080946  .080884  .081010   3.618  69.71 9.97E5 .000000
1808 Jul 19.55227  Earth  .059714  .059711  .059716   8.732   0.09 1.38E5 .000000
1809 Jul 17.96428  Earth  .009117  .009098  .009137   7.274   1.12 72886. .000000
1810 Jul 17.98681  Earth  .005758  .005757  .005758   7.131   0.15 67757. .000000
1811 Jul 19.33959  Earth  .034944  .034941  .034948   8.018   0.24 69926. .000000
1812 Jul 20.39693  Earth  .080478  .080474  .080481   9.359   0.24 87550. .000000
1899 Feb 23.47619  Venus  .084082  .084081  .084083   2.842   0.18 1.20E6 .000000
1903 Dec 22.30906  Earth  .097175  .097173  .097177   9.927   0.22 2.32E5 .000000
1904 Dec 23.45436  Earth  .049395  .049392  .049397   8.481   0.22 2.53E5 .000000
1905 Dec 25.06890  Earth  .013285  .013283  .013286   7.365   0.18 7.72E5 .000000
1906 Dec 25.38248  Earth  .010659  .010658  .010660   7.255   0.10 66975. .000000
1907 Dec 24.46477  Earth  .041706  .041705  .041708   8.252   0.07 1.02E5 .000000
1908 Dec 22.03780  Earth  .086246  .086244  .086247   9.606   0.06 1.53E5 .000000
1915 Feb 25.70119  Venus  .084514  .084513  .084514   3.002   0.50 8.16E5 .000000
1991 Jun 13.37718  Venus  .090777  .090777  .090778   5.455   0.40 3.19E5 .000000
1999 Jul 28.33601  Earth  .058880  .058880  .058881   8.694   0.02 9.04E5 .000000
2000 Jul 26.23030  Earth  .024137  .024137  .024138   7.624   0.02 8.20E5 .000000
2001 Jul 25.79978  Earth  .012017  .012017  .012018   7.135   0.02 9.06E5 .000000
2002 Jul 25.85751  Earth  .011574  .011574  .011574   7.018   0.02 9.09E5 .000000
2003 Jul 26.08561  Earth  .011573  .011573  .011573   7.028   0.05 9.05E5 .000000
2004 Jul 25.42778  Earth  .012820  .012817  .012822   7.210   0.29 8.54E5 .000000
2005 Jul 26.69471  Earth  .035899  .035880  .035917   8.003   1.12 6.53E5 .000000
2006 Jul 28.58244  Earth  .076836  .076809  .076863   9.248   1.56 4.98E5 .000000
2029 Aug  1.27653  Venus  .081907  .081880  .081934   4.192   2.58 2.58E5 .000000
2054 Oct 21.75850  Venus  .076332  .076311  .076353   3.203   2.39 4.40E5 .000000
2080 Jan 12.84480  Venus  .099326  .099112  .099540   2.981  45.80 2.22E5 .000000
2101 Dec 30.20135  Earth  .076851  .076689  .077013   9.329   8.53 7485.9 .000000
2103 Jan  1.07827  Earth  .033424  .033304  .033544   8.041   5.94 8206.9 .000000
2104 Jan  2.21162  Earth  .005252  .005235  .005269   7.230   0.55 8349.0 .000000
2104 Dec 30.23347  Earth  .071897  .071530  .072264   9.190  17.13 9129.3 .000000
2115 Feb  5.76048  Venus  .081166  .078833  .083480   3.293 547.25 1.26E5 .000000
2120 Jan 13.61263  Venus  .071323  .068928  .073953   4.826 491.25 1.66E5 .000000
2152 Aug 17.46540  Venus  .076389  .066668  .086605   3.261 2654.6 2.86E5 .000000
2157 Jul 25.07343  Venus  .077217  .066388  .090746   5.297 1729.3 1.54E5 .000000
2170 Aug  5.29240  Earth  .038694  .018873  .059998   8.045 1155.0 1.66E5 .000000
2171 Aug  3.81496  Earth  .026486  .016858  .041329   6.400 535.82 1.68E5 .000000
2172 Aug  4.29589  Earth  .090062  .084580  .096035   4.509 555.14 1.82E5 .000000
2183 Jan  2.72483  Earth  .051119  .002568  .591168   5.489 1555.1 22024. .000000
2184 Jan  2.03853  Earth  .014426  .002453  .084658   7.471 4096.5 19285. .000000