"In physics and classical mechanics, the three-body problem is the problem of taking the initial positions and velocities (or momenta) of three point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's law of universal gravitation."
A problem in which three point masses interact with each other gravitationally.
Planetary Motion: Describes the behavior of planets in their orbits around the sun and the gravitational forces that govern them.
Kepler’s Laws: Describes the three laws of planetary motion that were first proposed by Johannes Kepler in the early 17th century.
Newton’s Laws of Motion: Describes the three laws of motion proposed by Isaac Newton that are fundamental in understanding the behavior of celestial bodies.
Gravitational Forces: Describes the forces that govern the movement of celestial bodies, including the force of gravity between two objects.
Celestial Mechanics: Describes the motion and behavior of celestial bodies such as planets, asteroids, and comets.
Perturbation Theory: Describes the mathematical technique for analyzing the behavior of systems that are subject to small, yet persistent, disturbances.
Lagrangian Mechanics: Describes the mathematical framework for analyzing the behavior of systems with multiple degrees of freedom.
Hamiltonian Mechanics: Describes the mathematical framework that is based on the concept of energy to analyze the behavior of systems.
Orbits: Describes the different types of orbits that celestial bodies can assume, such as elliptical, circular or hyperbolic.
Stability: Describes the stability of celestial systems, including the concept of stable and unstable orbits.
Chaos Theory: Describes the phenomenon of chaos that can occur in systems such as the Three-Body Problem and the complexity of analyzing systems that exhibit chaos.
Numerical Methods: Describes the numerical techniques used to model and solve the equations that govern the behavior of celestial bodies.
N-body Problem: Describes the mathematical challenge of predicting the behavior of a group of celestial bodies as they interact with one another.
Binary Star Systems: Describes the behavior of binary star systems, which are two stars that orbit around a common center of mass.
Planetary Rings: Describes the behavior of rings around planets, including the dynamics of the particles that make up the ring.
Circular Restricted Three-Body Problem (CRTBP): This is one of the simplest types of three-body problem, where two massive bodies are assumed to be moving in circular orbits around their common centre of mass while a third much smaller body moves in their plane of motion, experiencing gravitational forces from the two massive bodies. This problem is also known as the 'restricted problem', as it assumes that the small body's mass is negligible compared to that of the two massive bodies.
Elliptic Restricted Three-Body Problem (ERTBP): This is similar to the CRTBP, except the two massive bodies move in elliptical orbits instead of circular ones. The third body is still assumed to be much smaller than the two massive ones.
General Three-Body Problem: This type of problem does not make any assumptions about the masses or orbits of the three bodies, and is usually solved numerically. It is one of the most complex problems in orbital mechanics, and is still an active area of research.
Gravitational Capture: This occurs when a small body enters the gravitational field of two massive bodies and is captured into orbit around one of them. This can happen when the small body's initial velocity is less than the escape velocity of either of the two massive bodies.
Triangular Lagrange Points: These are points in space where the gravitational forces from the two massive bodies cancel out the centrifugal forces experienced by a small body. There are five such points in any three-body system, and they are named after Joseph-Louis Lagrange who first discovered them.
Binary Orbit: This occurs when two of the three bodies are much more massive than the third, and are in close proximity to each other, while the third body orbits around the two of them. This type of problem is often used to model the orbits of binary stars or the Earth-Moon system.
Chaos in the Three-Body Problem: Due to the complexity of the general three-body problem, there are many instances where small changes in initial conditions can lead to vastly different outcomes. This can result in chaotic behaviour, where the three bodies exhibit seemingly random motions over time. Chaos in the three-body problem is still an active area of research.
Perturbations: The perturbations in the three-body problem are disturbances that affect the orbits of the three bodies. These can be caused by external forces such as other celestial bodies, or by slight changes in the masses or velocities of the three bodies themselves. These perturbations can result in long-term changes in the orbits of the bodies, and can have significant effects on celestial mechanics.
"The three-body problem is a special case of the n-body problem."
"No general closed-form solution exists."
"The resulting dynamical system is chaotic for most initial conditions."
"Numerical methods are generally required."
"The first specific three-body problem to receive extended study was the one involving the Moon, Earth, and the Sun."
"In an extended modern sense, a three-body problem is any problem in classical mechanics or quantum mechanics that models the motion of three particles."
"...solving for their subsequent motion according to Newton's laws of motion and Newton's law of universal gravitation."
"A three-body problem is any problem in classical mechanics or quantum mechanics that models the motion of three particles."
Yes, it is considered a fundamental problem in physics.
"Unlike two-body problems, no general closed-form solution exists."
"The three-body problem falls under the domain of physics and classical mechanics."
"For most initial conditions, the resulting dynamical system is chaotic."
"Numerical methods are generally required."
"No general closed-form solution exists."
"No, the term 'three-body problem' can be applied to any problem that models the motion of three particles in classical mechanics or quantum mechanics."
"The initial positions and velocities (or momenta) of three point masses."
"The resulting dynamical system is chaotic for most initial conditions."
"Newton's laws of motion and Newton's law of universal gravitation."
"The first specific three-body problem to receive extended study was the one involving the Moon, Earth, and the Sun."