
170 Classical Mechanics
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It is obvious that r = r
min
when cos θ is a maximum, that is, when θ = 0. Thus, the choice of θ
0
=0
corresponds to measuring θ from r
min
. This position is called the pericenter. The position of r
max
is
called the apocenter. The corresponding terms for motion about the sun are perihelion and aphelion
and, for motion about the earth, perigee and apogee. The general term for these turning points is
apsides.
Let us return to the equation of orbit (Equation 6.39), a conic section. For attractive force, k > 0,
and so α (= l
2
/μk) > 0; it is then evident from Equation 6.39 that the conditions ...