Andrea Milani

The passage of 2011 MD on 27 June 2011 was such a close approach that
the orbit was significantly affected by the shape of the Earth; the
effect was also amplified by the very low velocity (the asymptotic
approach velocity to the Earth's sphere of influence was about 1.5
km/s). These subtle effects do not change very much the orbit before
the closests approach, but have dramatic effects on the post-encounter
orbit. Moreover, this object has been very extensively observed
immediately before the closest approach (more than 1000 observations)
and also after reappearing on the other side of the Earth, 34 times in
the first night and 35 times later.

Our NEODyS system, which tries to automatically improve the NEA orbits
by using all the new observations, has not been able to cope, in
particular it has discarded all the post encounter observations, with
residuals in some cases exceeding 20 arcsec. A simple order of
magnitude computation shows that the perturbation due to the
oblateness of the Earth (the C_20 term in the gravity potential
expansion) was enough to generate the residuals of the post-encounter
observations. The effects of lesser deviations of the shape of the
Earth from a sphere, such as the ellipticity of the equator (C_22 and
S_22 terms), are on the contrary negligible with respect to the
observational accuracy.

Thus we have implemented a model of the Earth gravity field including
oblateness, which kicks in only when the distance from the geocenter
is less than 0.001 AU, and recomputed the fit to the observations. Now
the residuals of most of the observations after the encounter are
compatible with the observational error. There is a signifcant number
of observations still discarded, but about half of them should be due
to timing errors of the order of 1 second, which give large residuals
when the object is moving at 2.5 arcsec/s in RA and 4 arcsec/s in DEC,
as it was the case for the last pre-encounter observations. These
residuals are available, as usual, from the NEODyS service, at


We have also performed our usual impact monitoring, checking for
possible collisions of 2011 MD with Earth after the encounter but
before 2090, and found nothing.

The NEODyS team

Andrea Milani, Fabrizio Bernardi, Davide Farnocchia and Giovanni B. Valsecchi

Andrea Milani Comparetti
Dipartimento di Matematica
Piazzale B. Pontecorvo 5

tel. +39-050-2213254 fax +39-050-2213224
cellular phone +39-349-4482751
E-mail: milani@...
WWW: http://adams.dm.unipi.it/~milani/

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