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A centripetal force (from Latin centrum, "center" and petere, "to seek" [1]) is a force that makes a body follow a curved path.The direction of the centripetal force is always orthogonal to the motion of the body and towards the fixed point of the instantaneous center of curvature of the path.
Problem 4 then explores, for the case of an inverse-square law of centripetal force, how to determine the orbital ellipse for a given starting position, speed, and direction of the orbiting body. Newton points out here, that if the speed is high enough, the orbit is no longer an ellipse, but is instead a parabola or hyperbola .
In classical mechanics, the central-force problem is to determine the motion of a particle in a single central potential field.A central force is a force (possibly negative) that points from the particle directly towards a fixed point in space, the center, and whose magnitude only depends on the distance of the object to the center.
A central-force problem is said to be "integrable" if this integration can be solved in terms of known functions. If the force is a power law, i.e., if F ( r ) = a r n {\displaystyle F(r)=ar^{n}} , then u {\displaystyle u} can be expressed in terms of circular functions and/or elliptic functions if n {\displaystyle n} equals 1, -2, -3 (circular ...
The forces acting on a body add as vectors, and so the total force on a body depends upon both the magnitudes and the directions of the individual forces. [ 23 ] : 58 When the net force on a body is equal to zero, then by Newton's second law, the body does not accelerate, and it is said to be in mechanical equilibrium .
All attractive central forces can produce circular orbits, which are naturally closed orbits. The only requirement is that the central force exactly equals the centripetal force, which determines the required angular velocity for a given circular radius. Non-central forces (i.e., those that depend on the angular variables as well as the radius ...
The n-body problem is an ancient, classical problem [19] of predicting the individual motions of a group of celestial objects interacting with each other gravitationally. Solving this problem – from the time of the Greeks and on – has been motivated by the desire to understand the motions of the Sun, planets and the visible stars.
In classical mechanics, the Kepler problem is a special case of the two-body problem, in which the two bodies interact by a central force that varies in strength as the inverse square of the distance between them. The force may be either attractive or repulsive.
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