Numerical model of the Solar System: Difference between revisions

Revision as of 09:21, 25 February 2023

Revision as of 22:53, 1 April 2025

Line 9:

==Modern method==

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 Lawlaw of Gravitationgravitation]]. 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 Secondsecond Lawlaw of Motionmotion]]. 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.

The result is a new value for position and velocity for all bodies. Then, using these new values one starts over the whole calculation for the next time-step Δ''t''. Repeating this procedure often enough, and one ends up with a description of the positions of all bodies over time.