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ay45c4-page1 - 4 Classical Dynamics 4.1 Newtonian gravity...

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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: : : 60 ...
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