iSyMBA: A symplectic massive bodies integrator with planets interpolation

A planetary instability occurring at time $<100$ My after formation of the giant planets in our solar system can be responsible for some characteristics of the inner solar system. However, the actual influence of the instability on the terrestrial planet formation is not well understood. The simulations of terrestrial planet formation are very CPU-expensive, and this limits the exploration of different instability scenarios. To include the effects of the giant planets instability in the simulations of terrestrial planets formation in a feasible way, we approach the problem in two steps. First, we model and record an evolution of the giant planets that replicates the present outer solar system in the end. Then, we use that orbital record, properly interpolated, as the input for a second step to simulate its effects on the terrestrial planet formation. For this second step, we developed iSyMBA, a symplectic massive bodies algorithm, where ``i'' stands for interpolation. iSyMBA is a very useful code to accurately evaluate the effects of planetary instabilities on minor body reservoirs, while accounting for close encounters among massive objects. We provide a detailed description of how iSyMBA was developed and implemented to study terrestrial planet formation. Adapting iSyMBA for other problems that demand interpolation from previous simulations can be done following the method described here.