tokens: gravitational influences, it is possible to include the Yarkovsky drift. The orbfit has additional programs for determination of the orbits of Solar system bodies and could compute their positions on the celestial sphere. Also, orbfit has tools for the computation of Lyapunov exponents and proper elements (analytic and synthetic). 2.2 <sc>mercury</sc> The mercury package (Chambers Migliorini 1997 ) includes different algorithms, and it is written using the fortran 77 programming language. The mercury package is publicly available at https://github.com/4xxi/mercury . mercury has the following N -body algorithms: second-order mixed-variable symplectic integrator, general Bulirsh–Stoer integrator, conservative Bulirsh–Stoer, Everhart's RA15 (RADAU) algorithm and Hybrid symplectic/Bulirsh–Stoer integrator. For the purpose of our analysis, we chose the explicit Hybrid symplectic integrator (Chambers 1999 ) that could compute close encounters. Symplectic integrators (for complete theory of symplectic integrators, see e.g. Sanz-Serna 1991 ; Yoshida 1993 ) do not have a long-term build-up of energy error, and they are significantly faster with problems in which most of the mass is contained in a single body. The idea behind symplectic integrators is to split the Hamiltonian () of a system into pieces, each of which can be solved on its own. Symplectic integrator use a fixed time-step that makes calculating close encounter difficult due to the necessity of changing the step size. One of the possible solutions is to use a smaller step size or to split the perturbing terms, and to set a different step size for each term (SYMBA integrator; Duncan, Levison Lee 1998 ). Chambers ( 1999 ) described an alternative solution – a hybrid integrator that has symplectic and non-symplectic components. That alternative solution keeps the best properties of both symplectic and non-symplectic integrators. 3 METHODOLOGY AND DATA To study the limitations of the BIM, first a fictional family is going to be created based on the Veritas asteroid family. In this respect, all adopted values of the fictitious family are the same as of Veritas. Families are formed from the disruption of the target asteroid during a high-velocity impact. Escape speed ( v esc ) is much smaller than orbital speed ( v orb ≈ 15–20 km s −1 ), and, consequentially, all the orbits of family members are similar immediately after their creation. To create the initial orbital distribution of the simulated family members, we have used Gauss equations. These equations describe changes in the osculating elements due to the components of the ejection velocity: where a , e , i , f and ω are the semimajor axis, eccentricity, inclination, true anomaly and argument of perihelion, respectively; na is the mean orbital velocity; and δ V T , δ V R and δ V W are the components of ejection velocity along the direction of the motion, the radial direction and perpendicular to the orbital plane, respectively. The
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