Statistics – Computation
Scientific paper
Sep 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999aca....49..421s&link_type=abstract
Acta Astronomica, v.49, pp.421-431, (1999).
Statistics
Computation
2
Minor Planets: Asteroids
Scientific paper
The Earth-crossing asteroids can approach the Earth at dangerously small distances. If the observation arc of a single apparition orbit is short the determined orbital elements and hence a prediction of the future encounter with the Earth are uncertain. We presented the method of finding an impact orbit by the least squares correction with the "forced" equality constraints. As a solution we obtain: (i) initial values of rectangular coordinates and velocity components (and hence the orbital elements) allowing the asteroid to collide with the Earth, and (ii) the minimum value of the rms residual resulting from the impact orbit. The latter value is very important since it may serve as a kind of measure of probability of the collision, and in any case it allows us to exclude a possibility of the expected catastrophe. We performed computations of the impact orbits for two asteroids: 1997 XF11 and 1999 AN10. We found two impact orbits for hypothetical collisions of 1997 XF11 with the Earth in 2028 and 2033, and four orbits for 1999 AN10 colliding with the Earth in 2027, 2034, 2036, and 2039. Based on the 101 observations of 1999 AN10 from 1999 Jan. 13 - May 16, we show that its collision with the Earth in 2027 is impossible, but in 2039 it would be more probable. We made also a numerical simulation of the fictitious asteroid which would certainly collide with the Earth. We show that in this case we can easily find the impact orbit, and the rms value evidently does not allow us to exclude a possibility of the collision.
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