Commonly, N-body simulations will be systems based on some type of equations of motion ; of these, most will be dependent on some initial configuration to "seed" the simulation. In systems such as those dependent on some gravitational or electric potential, the force on a simulation entity is independent on its velocity. Hence, to seed the forces of the simulation, merely initial positions are needed, but this will not allow propagation- initial velocities are required. Consider a planet orbiting a star- it has no motion, but is subject to gravitational attraction to its host star. As a time progresses, and time steps are added, it will gather velocity according to its acceleration. For a given instant in time, t n , the resultant acceleration of a body due to its neighbouring masses is independent of its velocity, however, for the time step t n + 1 , the resulting change in position is significantly different due the propagation's inherent dependency on velocity. In basic propagation mechanisms, such as the symplectic euler method to be used below, the position of an object at t n + 1 is only dependent on its velocity at t n , as the shift in position is calculated via