
160 Classical Mechanics
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Because
must be positive, that is,
, the possible values of r for the given E and 1 are deter-
mined by the inequality
Ur Vr
l
r
E() ()=+ ≤
2
2
2µ
, (6.20)
and the maximum and minimum values of r, for which
, are given by the equality sign in
Equation 6.20. They are the turning points or the apsidal distances of the orbit. When U(r) has a
minimum and is equal to this minimal value, then
during the entire motion. The motion is
therefore circular. No motion is possible for values of F less than this.
To illustrate the preceding points, consider motion in an attractive inverse ...