SP-345 Evolution of the Solar System

 

FIGURE 6.4.1.-Longitudinal apparent attraction.

FIGURE 6.4.1.-Longitudinal apparent attraction. A particle initially moving along the arc ab with radius r0 is suddenly perturbed by a tangential gravitational force fper due to the mass mper. The new motion consists of a retrograde epicycle motion in an ellipse, the center of which ("guiding center") moves in a circle with radius r0 + x0 (above). The perturbed motion of three particles, originally situated at a, b, and c, describes three epicycles (right). The numbers 1 through 9 indicate the positions of the particles at intervals of (TK/4). The unperturbed particles form the line abc (left). The perturbation makes this line turn and first lengthen and then shorten. The quantity n in eq. (6.4.16) is equal to 2 in this case and consequently after the time 2TK has elapsed all particles simultaneously arrive at the point x = o, y = o. Hence there is a longitudinal apparent attraction of the particles to the guiding center of the unperturbed motion. (From Alfvén, 1971.)

 
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