The modern method consists of numerical integration in 3-dimensional space. One starts with a high accuracy value for the position (x, y, z) and the velocity (v x, v y, v z) for each of the bodies involved. When also the mass of each body is known, the acceleration (a x, a y, a z) can be calculated from Newton's Law of Gravitation. Each body attracts each other body, the total acceleration being the sum of all these attractions. Next one chooses a small time-step Δ t and applies Newton's Second Law of Motion. The acceleration multiplied with Δ t gives a correction to the velocity. The velocity multiplied with Δ t gives a correction to the position. This procedure is repeated for all other bodies.