Unformatted text preview: 4 Classical Dynamics
4.1 Newtonian gravity 4.1.1 Basic law of attraction
Two point masses, with mass M1 and M2, lying at r1 and r2, attract one
another. M1 feels a force from M2 F 12 =
where r12 = r1 force on M1 from M2 = GM31 M2 r12
r12 r2 = vector from 2 to 1 and r12 = jr12j
M1
F12 r1 F21
Coordinate
Origin r2 M2 Similarly M2 feels a force from M1 F 21 = force on M2 from M1 = GM32M1 r21 = + GM31 M2 r12 = F 12
r21
r12
where r21 = r2 r1 is the vector from 1 to 2. We have used r21 = r12, and
jr21j = jr12j. Thus, the gravitational forces are equal and opposite. This is in
accordance with Newton's 3rd law and ensures that the composite system of
(M1 + M2) does not suddenly start moving as a whole and violating Newton's
1st law.
Notice also that the gravitational force at M1 from M2 is directed exactly
at M2 . It is a \central" force: F 12 is parallel to r 12 . This remark causes us
to digress and mention: : :
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 Fall '09
 dion
 Force, Mass, General Relativity

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