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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 ...
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. One then seeks to predict the motion of the single remaining mobile object.
Euler's second law states that the rate of change of angular momentum L about a point that is fixed in an inertial reference frame (often the center of mass of the body), is equal to the sum of the external moments of force acting on that body M about that point: [1] [4] [5]
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.
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.
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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 ...
where G is the gravitational constant and m is the mass of the body. As long as the total force is nonzero, this equation has a unique solution, and it satisfies the torque requirement. [12] A convenient feature of this definition is that if the body is itself spherically symmetric, then r cg lies at its center of mass.