**Minakov E.P., Sokolov B.V., Shaldaev S.E., Aleksandrov M.A.** Calculation and Research of Space-Temporal Characteristics of Attack Abrases of Asteroids by Orbital Means // SPIIRAS Proceedings. 2019. Vol.18. No.6. P.1462–1490.

https://doi.org/10.15622/sp.2019.18.6.1462-1490

### Abstract

A development of work to combat the asteroid hazard requires construction and study of areas of outer space in which moving spacecraft-interceptors can affect asteroids. In this paper, such areas are called attack lines, the spatio-temporal characteristics of which depend on the parameters of the asteroid’s orbits and the phase coordinates of the nodal points. At these points the trajectory intersects the asteroids and the orbital planes of the spacecraft-interceptors. In the case of the impact of spacecraft-interceptors on asteroids at nodal points, the study of the spatio-temporal characteristics of the lines of attack, taking into account restrictions on the relative speeds between asteroids and spacecraft-interceptors, is of particular importance. Building and analyzing the corresponding zones of reverse reach are suggested.

In the article, the developed models include a simulation model, using which random angles between the projections of the velocity vectors of asteroids on a plane of the orbits of spacecraft interceptors and the current directions on the hodographs of their velocity vectors at nodal points, as well as an analytical model for estimating the spatio-temporal characteristics of boundaries are simulated attacks of asteroids, including: the radii of their external and internal boundaries for certain values of the latitude arguments and arrival time of spacecraft-interceptors at modal points.

Testing these models and the corresponding characteristics of the attack lines were carries out during computational experiments on two cyclic modeling of the angles between the projections of the velocity vectors of asteroids on the plane of the orbits of interceptor spacecraft and the current directions on the hodographs of their velocity vectors at nodal points. The results obtained made it possible to verify and validate the developed models, on the basis of which a conclusion was drawn about the required degree of their applicability. In the paper also a procedure for estimating the parameters of attack lines, depending on the values of the arguments of the latitudes of interceptor spacecraft and their altitudes above the Earth’s surface is proposed. At the same time, an approach is substantiated for estimating the spatio-temporal characteristics of the boundaries of attack of asteroids by spacecraft-interceptors for any inside the planar parameters of their orbits.

In the article, the developed models include a simulation model, using which random angles between the projections of the velocity vectors of asteroids on a plane of the orbits of spacecraft interceptors and the current directions on the hodographs of their velocity vectors at nodal points, as well as an analytical model for estimating the spatio-temporal characteristics of boundaries are simulated attacks of asteroids, including: the radii of their external and internal boundaries for certain values of the latitude arguments and arrival time of spacecraft-interceptors at modal points.

Testing these models and the corresponding characteristics of the attack lines were carries out during computational experiments on two cyclic modeling of the angles between the projections of the velocity vectors of asteroids on the plane of the orbits of interceptor spacecraft and the current directions on the hodographs of their velocity vectors at nodal points. The results obtained made it possible to verify and validate the developed models, on the basis of which a conclusion was drawn about the required degree of their applicability. In the paper also a procedure for estimating the parameters of attack lines, depending on the values of the arguments of the latitudes of interceptor spacecraft and their altitudes above the Earth’s surface is proposed. At the same time, an approach is substantiated for estimating the spatio-temporal characteristics of the boundaries of attack of asteroids by spacecraft-interceptors for any inside the planar parameters of their orbits.