Nonlinearity in Inverse Problems of Asteroid Dynamics

Abstract

A collision of an asteroid with the Earth in the future is always considered as a probabilistic event because the asteroid orbit determined from observations with random errors inevitably contains an uncertainty in its parameters. To establish the probability of collision, the parametric uncertainty as a probabilistic distribution of virtual objects is mapped by the orbital model into the physical space for the period of the asteroid rendezvous with the Earth, and then the probabilistic mass penetrating into the planet body is estimated. The asteroid impact on the Earth is a very significant phenomenon because it can have fatal consequences for mankind. Therefore, probabilistic estimation of collision with potentially hazardous asteroids must be carried out very carefully with allowance for various subtle aspects. In this work, nonlinearity in inverse problems of asteroid dynamics under different observation conditions for various types of determined orbits is studied. The main problem we set ourselves is to examine to what extent nonlinearity can affect the accuracy of a probabilistic estimation when the parametric uncertainty is simulated using classical linear stochastic methods. To study the total, parameter-effect, and intrinsic nonlinearities, we introduce original indices with justified threshold values determined from the maximum tolerable biases of probabilistic estimates due to nonlinearity. The general analysis of nonlinearity is carried out for potentially hazardous asteroids observed in one appearance before June 2020. In particular, it is shown that main factors of strong nonlinearity are the short observed orbital arc (less than one degree) and the small observation period (less than ten days). Moreover, the situation is aggravated if the asteroid moves during the observation along the ecliptic and near it on an arc with small curvature. It is also established that, due to strong nonlinearity in problems of probabilistic estimation, nonlinear stochastic methods are required to simulate the orbital uncertainty for almost half of the potentially hazardous asteroids (44%).