\magnification=\magstep1


$$
GPE \quad = \quad - \sum_{i \neq j} {{ G m_i m_j} \over {r_{ij}}}
$$

$$
KE \quad = \quad \sum_i { {{1}\over{2}} m_i v_i^2 }
$$

$$
{\rm Initial\ Energy \ } \quad = \quad GPE \ + \  KE
$$

$$
{\rm Final\ Energy \ } \quad = \quad GPE \ + \  KE
$$

$$
 { {\Delta E}\over{E} } 
  \quad = \quad
  {{ \rm (Final\ Energy) \ - \ (Initial\ Energy) } \over 
           {\rm (Initial\ Energy) } }
$$

\bye
