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Newton's laws are often stated in terms of point or particle masses, that is, bodies whose volume is negligible. This is a reasonable approximation for real bodies when the motion of internal parts can be neglected, and when the separation between bodies is much larger than the size of each.
In physics, a number of noted theories of the motion of objects have developed. Among the best known are: Classical mechanics. Newton's laws of motion; Euler's laws of motion; Cauchy's equations of motion; Kepler's laws of planetary motion ; General relativity; Special relativity; Quantum mechanics
So long as the force acting on a particle is known, Newton's second law is sufficient to describe the motion of a particle. Once independent relations for each force acting on a particle are available, they can be substituted into Newton's second law to obtain an ordinary differential equation, which is called the equation of motion.
Newton's proof of Kepler's second law, as described in the book. If a continuous centripetal force (red arrow) is considered on the planet during its orbit, the area of the triangles defined by the path of the planet will be the same. This is true for any fixed time interval. When the interval tends to zero, the force can be considered ...
Gauss's law for gravity – Restatement of Newton's law of universal gravitation; Jordan and Einstein frames – different conventions for the metric tensor, in a theory of a dilaton coupled to gravity; Kepler orbit – Celestial orbit whose trajectory is a conic section in the orbital plane
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
Newton was a pretty smart guy. Much of what we’re taught in high school physics and calculus can be tracked back to him. And apparently, he had a pretty good track record as a diversified, buy ...
In 1679, he returned to his work on celestial mechanics by considering gravitation and its effect on the orbits of planets with reference to Kepler's laws of planetary motion. Newton's reawakening interest in astronomical matters received further stimulus by the appearance of a comet in the winter of 1680–1681, on which he corresponded with ...