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\begin{question}{30} \comment{by John Brown}
Give the equations of motion for $i=1,\ldots, N$  particles of
masses $m_i$ and positions  $r_i(t)$ under the action of mutual
gravity alone in an arbitrary inertial frame.
\partmarks{4}

Use these to derive the following conservation laws of the system:

\part Constancy of linear momentum -- i.e., centre of mass fixed in a
suitable inertial frame. \partmarks{4}
 \part Constancy of angular momentum. \partmarks{6}
 \part Constancy of total energy.  \partmarks{8}

How many integrals of motion exist in total?
\partmarks{2}

Derive the moment of inertia   of the system and demonstrate its
relevance to criteria for escape of particles from the system.
\partmarks{6}
\end{question}
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