n-body problem

In <a href="/facts/Physics/a7aH2y08">physics</a>, the n-body problem is the problem of predicting the individual motions of a group of <a href="/facts/Astronomical_object/BCHLa0Q2">celestial objects</a> interacting with each other <a href="/facts/Gravitation/bqAN7DdQ">gravitationally</a>. Solving this problem has been motivated by the desire to understand the motions of the <a href="/facts/Sun/CadPCVHh">Sun</a>, <a href="/facts/Moon/zKHqEMPb">Moon</a>, <a href="/facts/Planet/rbPjE6Bx">planets</a>, and visible <a href="/facts/Star/PFbd6ICx">stars</a>. In the 20th century, understanding the <a href="/facts/Dynamics_(physics)/JLk81H71">dynamics</a> of <a href="/facts/Globular_cluster/FL0EERJU">globular cluster</a> star systems became an important n-body problem. The n-body problem in <a href="/facts/General_relativity/jVsoIg8X">general relativity</a> is considerably more difficult to solve due to additional factors like time and space distortions.
The classical physical problem can be informally stated as the following:

<blockquote>Given the quasi-steady orbital properties (instantaneous position, velocity and time) of a group of celestial bodies, predict their interactive forces; and consequently, predict their true orbital motions for all future times.</blockquote>
The <a href="/facts/Two-body_problem/YCG4geSH">two-body problem</a> has been completely solved and is discussed below, as well as the famous restricted <a href="/facts/Three-body_problem/58dES4YL">three-body problem</a>.

n-body problem open-in-new

n-body problem