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Let the percentage of the total mass divided between these two particles vary from 100% P 1 and 0% P 2 through 50% P 1 and 50% P 2 to 0% P 1 and 100% P 2, then the center of mass R moves along the line from P 1 to P 2. The percentages of mass at each point can be viewed as projective coordinates of the point R on this line, and are termed ...
r 1 is the distance from body 1's center to the barycenter; a is the distance between the centers of the two bodies; m 1 and m 2 are the masses of the two bodies. The semi-major axis of the secondary's orbit, r 2, is given by r 2 = a − r 1.
In the center of mass frame the kinetic energy is the lowest and the total energy becomes = ˙ + The coordinates x 1 and x 2 can be expressed as = = and in a similar way the energy E is related to the energies E 1 and E 2 that separately contain the kinetic energy of each body: = = ˙ + = = ˙ + = +
The theorem tells us how different parts of the mass distribution affect the gravitational force measured at a point located a distance r 0 from the center of the mass distribution: [13] The portion of the mass that is located at radii r < r 0 causes the same force at the radius r 0 as if all of the mass enclosed within a sphere of radius r 0 ...
The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object in -dimensional space is the intersection of all hyperplanes that divide into two parts of equal moment about the hyperplane.
The two-body problem in general relativity (or relativistic two-body problem) is the determination of the motion and gravitational field of two bodies as described by the field equations of general relativity. Solving the Kepler problem is essential to calculate the bending of light by gravity and the motion of a planet orbiting its sun.
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A spherically symmetric body affects external objects gravitationally as though all of its mass were concentrated at a point at its center. If the body is a spherically symmetric shell (i.e., a hollow ball), no net gravitational force is exerted by the shell on any object inside, regardless of the object's location within the shell.