An alternative to the conventional method for determining impact probability by an asteroid is presented that utilizes the positional uncertainty ellipsoid. This method is used commonly for Earth-orbiting satellite collision probability. In the scaling up process, the gravitational influence of one of the bodies in the collision is taken into account, namely that of the Earth. The restricted three-body problem is sufficient to provide a backdrop for the probability analysis, while making sure to note that the results are only hypothetical given a simplified dynamic model. Uncertainty is represented mathematically by the covariance matrix and is propagated into the future. Encounter regions are defined as regions along the nominal trajectory of the asteroid where the propagated uncertainty encloses the Earth. Probability is calculated by a triple integral of the probability density function (pdf) over the volume swept out by the Earth through the encounter region. The trend in probability calculated vs. initial uncertainty is investigated, and it is found that higher probabilities result from initial uncertainties that are tighter in the radial, in-track and out-of-plane directions.
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