3 or More Body Interactions: Difference between revisions
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==Main Idea== | ==Main Idea== | ||
Problems involving two bodies that are interacting gravitationally are relatively easy to solve. Once there are more than two bodies, however, this is no longer the case. Generally, three or more body problems require numerical integrations to solve, and are quite complex. It becomes difficult to predict the motion of the bodies under the influence of multiple other gravitational forces, and the system most often becomes chaotic. There are, however, a number of cases where motion is not chaotic and that thus can be studied. | Problems involving two bodies that are interacting gravitationally are relatively easy to solve. Once there are more than two bodies, however, this is no longer the case. Generally, three or more body problems require numerical integrations to solve, and are quite complex. It becomes difficult to predict the motion of the bodies under the influence of multiple other gravitational forces, and the system most often becomes chaotic. There are, however, a number of cases where motion is not chaotic and that thus can be studied. | ||
'''Restricted 3-Body Problem''' | |||
In the restricted three body problem, we assume that the third body has a negligible mass, and that it moves under the influence of two other massive bodies. This simplifies calculations, as we can treat the two massive bodies as though they are in a simple two body problem to predict their motion. We assume that these two bodies orbit around their mutual center of mass, and that the third body, being of negligible mass, does not affect this motion. | In the restricted three body problem, we assume that the third body has a negligible mass, and that it moves under the influence of two other massive bodies. This simplifies calculations, as we can treat the two massive bodies as though they are in a simple two body problem to predict their motion. We assume that these two bodies orbit around their mutual center of mass, and that the third body, being of negligible mass, does not affect this motion. | ||
The restricted 3-body problem is useful for analyzing motion for many objects in the solar system, chiefly the Earth-Moon-Sun system, and other such systems involving moons. Because the moon is much less massive than the Earth, which is in turn much less massive than the Sun, we can treat that problem as a restricted 3-body problem. | The restricted 3-body problem is useful for analyzing motion for many objects in the solar system, chiefly the Earth-Moon-Sun system, and other such systems involving moons. Because the moon is much less massive than the Earth, which is in turn much less massive than the Sun, we can treat that problem as a restricted 3-body problem. | ||
'''Other Solutions''' | |||
[[File:Three body problem figure-8 orbit animation.gif|250px|thumb|right|An example of a stable solution to the 3-body problem.]] | |||
There are also a number of stable orbits associated with three-body problems. One such example is a stable figure eight orbit, as depicted here. | |||
===A Mathematical Model=== | ===A Mathematical Model=== | ||
Revision as of 15:18, 14 June 2019
This page introduces the concept of n-body interactions (with 3 or more bodies). This is a basic overview of the concept. You do not have to know this material in detail.
Main Idea
Problems involving two bodies that are interacting gravitationally are relatively easy to solve. Once there are more than two bodies, however, this is no longer the case. Generally, three or more body problems require numerical integrations to solve, and are quite complex. It becomes difficult to predict the motion of the bodies under the influence of multiple other gravitational forces, and the system most often becomes chaotic. There are, however, a number of cases where motion is not chaotic and that thus can be studied. Restricted 3-Body Problem In the restricted three body problem, we assume that the third body has a negligible mass, and that it moves under the influence of two other massive bodies. This simplifies calculations, as we can treat the two massive bodies as though they are in a simple two body problem to predict their motion. We assume that these two bodies orbit around their mutual center of mass, and that the third body, being of negligible mass, does not affect this motion.
The restricted 3-body problem is useful for analyzing motion for many objects in the solar system, chiefly the Earth-Moon-Sun system, and other such systems involving moons. Because the moon is much less massive than the Earth, which is in turn much less massive than the Sun, we can treat that problem as a restricted 3-body problem. Other Solutions
There are also a number of stable orbits associated with three-body problems. One such example is a stable figure eight orbit, as depicted here.
A Mathematical Model
Examples
Connectedness
My research involves an n-body integrator. Using these types of simulations to predict the motion of the stars and other celestial bodies is important in understanding how systems came to form as they are today. The idea that we can use integrators to predict the motion, or to run backwards in time to see where bodies used to be is extremely interesting. Our ability to create mathematical models of space is incredibly useful in furthering our understanding of space.
I am a physics major and, as such