Electronic Telegram No. 212
Central Bureau for Astronomical Telegrams
INTERNATIONAL ASTRONOMICAL UNION
M.S. 18, Smithsonian Astrophysical Observatory, Cambridge, MA 02138, U.S.A.
IAUSUBS@CFA.HARVARD.EDU or FAX 617-495-7231 (subscriptions)
CBAT@CFA.HARVARD.EDU (science)
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(99942) APOPHIS
     J. D. Giorgini, L. A. M. Benner, S. J. Ostro, Jet Propulsion
Laboratory; M. C. Nolan, Arecibo Observatory; and M. W. Busch,
California Institute of Technology, report:  "Arecibo (2380-MHz,
12.6-cm) radar observations of (99942) Apophis = 2004 MN_4 made
during Aug. 7.655-7.769 UTC produced a CW detection and a Doppler
measurement of 8186.8 Hz at Aug. 7.713, a correction of +0.3 +/-
0.2 Hz (+18.9 +/- 12.6 mm/s) relative to nominal prediction.
Including this Doppler correction in a new orbit estimate and
n-body gravitational propagation increases the 2029 April 13.9
Earth-center miss-distance from 5.77 +/- 0.39 to 5.86 +/- 0.12
Earth radii, reducing the along-track position uncertainty at
closest approach from +/- 1957 to +/- 757 km; the volume of the
spatial uncertainty region decreases from 173000 to 39800 km**3.
The new Doppler measurement increases the predicted nominal Earth
close approach in 2036 from 0.005 to 0.14 AU.  However, we have
found that computational noise intrinsic to 64-bit representations
of real numbers used in arithmetical operations, exacerbated by the
close Earth encounter in 2029, can accumulate trajectory-prediction
error exceeding the radius of the Earth by 2036.  Using more precise
128-bit representations, the specified local error tolerance was
reduced from 10**-14 to 10**-19 and the maximum predictor/corrector
order (used for step-size and error-control decisions) increased from
14/15 to 21/22.  This approach reduces error growth in the integration
due to the finite representation of real numbers and permits
examination of those specific orbit variations in 2036 for which
trajectory offsets comparable to the size of the earth are significant."


NOTE: These 'Central Bureau Electronic Telegrams' are sometimes
      superseded by text appearing later in the formal IAU Circulars.

                         (C) Copyright 2005 CBAT
2005 September 2                 (CBET 212)               Daniel W. E. Green