Search results
Results From The WOW.Com Content Network
The concept of center of gravity or weight was studied extensively by the ancient Greek mathematician, physicist, and engineer Archimedes of Syracuse.He worked with simplified assumptions about gravity that amount to a uniform field, thus arriving at the mathematical properties of what we now call the center of mass.
The three-body problem is a special case of the n-body problem, which describes how n objects move under one of the physical forces, such as gravity. These problems have a global analytical solution in the form of a convergent power series, as was proven by Karl F. Sundman for n = 3 and by Qiudong Wang for n > 3 (see n-body problem for details
If Jupiter had Mercury's orbit (57,900,000 km, 0.387 AU), the Sun–Jupiter barycenter would be approximately 55,000 km from the center of the Sun ( r 1 / R 1 ≈ 0.08). But even if the Earth had Eris's orbit (1.02 × 10 10 km, 68 AU), the Sun–Earth barycenter would still be within the Sun (just over 30,000 km from the center).
The most prominent example of the classical two-body problem is the gravitational case (see also Kepler problem), arising in astronomy for predicting the orbits (or escapes from orbit) of objects such as satellites, planets, and stars. A two-point-particle model of such a system nearly always describes its behavior well enough to provide useful ...
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.
The Euler three-body problem is known by a variety of names, such as the problem of two fixed centers, the Euler–Jacobi problem, and the two-center Kepler problem. The exact solution, in the full three dimensional case, can be expressed in terms of Weierstrass's elliptic functions [ 2 ] For convenience, the problem may also be solved by ...
A common misconception occurs between centre of mass and centre of gravity.They are defined in similar ways but are not exactly the same quantity. Centre of mass is the mathematical description of placing all the mass in the region considered to one position, centre of gravity is a real physical quantity, the point of a body where the gravitational force acts.
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.