SP-345 Evolution of the Solar
System
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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