We introduce a new method to perform preliminary orbit determination for space debris on low Earth orbits (LEO). This method works with tracks of radar observations: each track is composed by n ≥ 4 topocentric position vectors per pass of the satellite, taken at very short time intervals. We assume very accurate values for the range ρ, while the angular positions (i.e. the line of sight, given by the pointing of the antenna) are less accurate. We wish to correct the errors in the angular positions already in the computation of a preliminary orbit. With the information contained in a pair of radar tracks, using the laws of the two-body dynamics, we can write 8 equations in 8 unknowns. The unknowns are the components of the topocentric velocity orthogonal to the line of sight at the two mean epochs of the tracks, and the corrections ∆ to be applied to the angular positions. We take advantage of the fact that the components of ∆ are typically small. We show the results of some tests, performed with simulated observations, and compare this algorithm with Gibbs' method and the Keplerian integrals method.

We propose an adaptation of the semilinear algorithm for the prediction of the impact corridor on ground of an Earthimpacting asteroid. The proposed algorithm provides an efficient tool, able to reliably predict the impact regions at fixed altitudes above ground with 5 orders of magnitudes less computations than Monte Carlo approaches. Efficiency is crucial when dealing with imminent impactors, which are characterized by high impact probabilities and impact times very close to the times of discovery. The case of 2008 TC3 is a remarkable example, but there are also recent cases of imminent impactors, 2018 LA and 2019 MO, for which the method has been successfully used. Moreover, its good performances make the tool suitable also for the analysis of the impact regions on ground of objects with a more distant impact time, even of the order of many years, as confirmed by the test performed with the first batch of observations of Apophis, giving the possibility of an impact 25 years after its discovery.

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We propose a method to account for the Earth oblateness effect in preliminary orbit determination of satellites in low orbits with radar observations. This method is an improvement of the one described in [9], which uses a pure Keplerian dynamical model. Since the effect of the Earth oblateness is strong at low altitudes, its inclusion in the model can sensibly improve the initial orbit, giving a better starting guess for differential corrections and increasing the chances to obtain their convergence. The input set consists of two tracks of radar observations, each one composed of at least 4 observations taken during the same pass of the satellite. A single observation gives the topocentric position of the satellite, where the range is very accurate, while the line of sight direction is poorly determined. From these data we can compute by a polynomial fit the values of the range and range rate at the mean epochs of the two tracks. In order to obtain a preliminary orbit we wish to compute the angular velocities, that is the rate of change of the line of sight. In the same spirit of [9], we also wish to correct the values of the angular measurements, so that they fit the selected dynamical model if the same holds for the radial distance and velocity. The selected model is a perturbed Keplerian dynamics, where the only perturbation included is the secular effect of the J2 term of the geopotential. The proposed algorithm models this problem with 8 equations in 8 unknowns.

The interest in the problem of small asteroids observed shortly before a deep close approach or an impact with the Earth has grown a lot in recent years. Since the observational dataset of such objects is very limited, they deserve dedicated orbit determination and hazard assessment methods. The currently available systems are based on the systematic ranging, a technique providing a two-dimensional manifold of orbits compatible with the observations, the so-called Manifold Of Variations. In this paper we first review the Manifold Of Variations method, to then show how this set of virtual asteroids can be used to predict the impact location of short-term impactors, and compare the results with those of already existent methods.