How does NASA determine the orbits an interplanetary spacecraft will have with given burns and gravitational assists?

This question has primarily come to me from playing Kerbal Space Program and understanding the orbital mechanics behind it all. However, in a game such as KSP, the nodes you set will display the future orbit after the burn. Does NASA have a simulation of our solar system in which they can simulate a spacecraft's future orbit, such as the Juno flyby with Earth and the effects afterward? Or is it simply all just vigorous math they use?

Submitted July 28, 2016 at 01:48AM by LethalTugboat http://ift.tt/2azvUiN