"In classical mechanics, the two-body problem is to predict the motion of two massive objects which are abstractly viewed as point particles."
A problem in which two point masses interact with each other gravitationally.
Kepler's laws: These are three laws that describe the motion of planets around the sun in our solar system. They can also be applied to other two-body systems.
Gravity: Gravity is the force that holds two bodies together in orbit. Understanding gravity is essential to understanding the two-body problem.
Newton's laws: Newton's laws of motion describe how objects move in response to forces acting on them. They are also fundamental to understanding the two-body problem.
Orbital elements: Orbital elements are parameters that describe the shape, orientation, and position of an orbit. These are used to calculate the motion of a two-body system.
Energy and momentum: Energy and momentum are conserved in a two-body system. Understanding how they are transferred between the two bodies is important for understanding the motion of the system.
Escape velocity: Escape velocity is the minimum velocity required to escape the gravitational pull of a planet or other celestial body. It is important when considering the motion of satellites and spacecraft.
Perturbations: Perturbations are small disturbances in the motion of a two-body system. They can be caused by the presence of additional bodies in the system, or by other factors.
Lagrange points: Lagrange points are points in a two-body system where the gravitational forces of the two bodies cancel out. They are important in satellite placement and other applications.
Tides: Tides are caused by the gravitational attraction of the moon and sun on the earth's oceans. They can also affect the motion of satellites and other celestial bodies.
Orbital maneuvers: Orbital maneuvers are changes in the velocity and/or direction of a spacecraft in orbit. These maneuvers are necessary to maintain or change the orbit of a satellite or spacecraft.
Orbital transfers: Orbital transfers involve changing the orbit of a spacecraft from one orbit to another. This is done using a combination of orbital maneuvers and gravity assists.
Hohmann transfer: The Hohmann transfer is a particular type of transfer orbit that provides the most efficient way to transfer between two circular orbits.
N-body problem: The N-body problem involves the motion of three or more bodies in a system. It is much more complex than the two-body problem and requires advanced mathematical techniques to solve.
Multi-body gravitational dynamics: Multi-body gravitational dynamics is the study of the motion of multiple bodies in a system, taking into account the gravitational forces between all the bodies.
Celestial mechanics: Celestial mechanics is the branch of mechanics that deals with the motion of celestial bodies, such as planets, moons, and asteroids. It encompasses all of the topics listed above, as well as others.
Circular orbit: The two objects move around each other in a perfect circle, with constant distance between them.
Elliptical orbit: The two objects move around each other in an ellipse, with varying distance between them. The distance between the two objects is greatest at the apogee and closest at the periapsis.
Parabolic orbit: This occurs when the two objects are moving at the exact escape speed, resulting in an open and unbound trajectory.
Hyperbolic orbit: The two objects move around each other in a hyperbola, with varying distance between them. The distance between the two objects is greater than the distance at the apogee, and the orbit is unbound.
Transfer orbit: A spacecraft undergoes a sequence of two or more orbits, with each orbit being a stepping stone to reaching the final orbit. This type of orbit is widely used for space travel between planets.
Restricted three-body problem: A complex problem that considers three bodies in orbit around each other, with one body being negligible in mass compared to the other two. Examples include the Earth, Moon, and Sun, or Jupiter, Europa, and the Sun.
Satellite orbit: An object in orbit around a much larger object. Satellites can be natural, such as our Moon orbiting the Earth, or a human-made satellite.
Binary star system: Two stars that are in orbit around each other. The orbital mechanics of binary star systems is important in studying the evolution of stars.
Planetary Ring System: A set of rings in orbit around a planet, composed of dust, rock, and ice particles. The most notable example is the ring system of Saturn.
Tidal locking: This is a phenomenon where one object in orbit around another becomes locked so that it always presents the same face to its partner, such as the Moon always showing the same face to the Earth.
"The problem assumes that the two objects interact only with one another."
"The only force affecting each object arises from the other one."
"The most prominent case of the classical two-body problem is the gravitational case arising in astronomy."
"A two-point-particle model of such a system nearly always describes its behavior well enough to provide useful insights and predictions."
"A simpler 'one body' model, the 'central-force problem' treats one object as the immobile source of a force acting on the other."
"Such an approximation can give useful results when one object is much more massive than the other."
"However, the one-body approximation is usually unnecessary except as a stepping stone. For many forces, including gravitational ones, the general version of the two-body problem can be reduced to a pair of one-body problems, allowing it to be solved completely."
"The three-body problem (and, more generally, the n-body problem for n ≥ 3) cannot be solved in terms of first integrals, except in special cases."
"Objects which are abstractly viewed as point particles."
"The problem assumes that the two objects interact only with one another."
"Predicting the orbits (or escapes from orbit) of objects such as satellites, planets, and stars."
"A simpler 'one body' model, the 'central-force problem' treats one object as the immobile source of a force acting on the other."
"Such an approximation can give useful results when one object is much more massive than the other."
"However, the one-body approximation is usually unnecessary except as a stepping stone. For many forces, including gravitational ones, the general version of the two-body problem can be reduced to a pair of one-body problems, allowing it to be solved completely."
"The three-body problem (and, more generally, the n-body problem for n ≥ 3) cannot be solved in terms of first integrals, except in special cases."
"A two-point-particle model of such a system nearly always describes its behavior well enough to provide useful insights and predictions."
"A two-point-particle model of such a system nearly always describes its behavior well enough to provide useful insights and predictions."
"Such an approximation can give useful results when one object is much more massive than the other (as with a light planet orbiting a heavy star, where the star can be treated as essentially stationary)."
"For many forces, including gravitational ones, the general version of the two-body problem can be reduced to a pair of one-body problems, allowing it to be solved completely."