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{\LARGE Conic Sections - General Equations}\\
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These general formulae govern all types of
orbital motion in the gravitational two body problem, 
including both bound and unbound conics. More specialized formulae,
valid only for certain types of orbits, can be derived from these.

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\begin{tabular}{|c|c|c|c|c|} 
\hline
Specific & Specific  & Distance & Speed  & Pericenter \\
Energy & Angular Momentum &  & & Distance\\
\hline
$ C = - {GM \over 2a}$  &  $h=\sqrt{GMa(1-e^2)}$ &
{\Large $ r = {a(1-e^2) \over 1 + e\cos f}$} &  $v = \sqrt{GM\biggr({2 \over r} - {1 \over a}}\biggr)$   & $q = a(1-e)$ \\
\hline


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{\LARGE Conic Sections - Equations for Specific Orbits}\\
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Energy determines whether an orbit is bound or not. Circles and ellipses are the only bound orbits; parabolas and hyperbolas are the only unbound ones.
Note that $e=1$ orbits (rectilinear or straight-line orbits) may be elliptical, parabolic, or hyperbolic.

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~~~~~~~~~~~~Bound Orbits  $(C<0)$~~~~~~~~~~~ Unbound Orbits $(C\ge 0)$   \\

\begin{tabular}{|l|l|l|l|l|} \hline
& Circle  &  Ellipse   &  Parabola  & Hyperbola  \\ 
\hline
Semimajor Axis: & $a=r$  &  $a>0$   &  $a\rightarrow\pm\infty$  & $a<0$  \\
\hline
Eccentricity: & $e=0$   &  $0<e\le1$   & $e=1$   & $e\ge1$  \\
\hline
Distance & $r=a$  &  $r\ge a(1-e)$   &  $r\ge a(1-e)$   & $r\ge a(1-e)$  \\
         &        &  $r\le a(1+e)$   &  $r\rightarrow\infty$ & $r\rightarrow\infty$ \\
\hline         
Speed: & $v=\sqrt{GM \over a}$  &  $v\le\sqrt{GM(1+e)\over a(1-e)}$  &  $v=\sqrt{2GM \over r}$  &  $v\le\sqrt{GM(1+e)\over a(1-e)}$  \\
          &  & $v\ge\sqrt{GM(1-e)\over a(1+e)}$   & $v(r\rightarrow\infty)=0$   & $v(r\rightarrow\infty) \rightarrow \sqrt{-GM \over a}$\\
\hline
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