Determination of the parabolic orbit for a body moving in the plane of the ecliptic, by the Laplace method.

A modification of the Laplace method for the determination of a preliminary orbit of a body moving in the plane of the ecliptic is presented. It is shown that on the basis of three close positions on the celestial sphere, the parabolic orbit can be determined in cases, when the classical Laplace method is not suitable. The numerical estimation of the number of possible solutions is carried out, and their spatial distribution depending on initial conditions is shown. An example of the determination of an orbit for the comet C/2007 N3 (Lulin) is given. [ABSTRACT FROM AUTHOR]