text: It can be helpful to know the energy in terms of the semi major axis (and the involved masses). The total energy of the orbit is given by
  ,
  where a is the semi major axis.
  Derivation
  Since gravity is a central force, the angular momentum is constant:
  At the closest and furthest approaches, the angular momentum is perpendicular to the distance from the mass orbited, therefore:
  .
  The total energy of the orbit is given by
  .
  Substituting for v, the equation becomes
  .
  This is true for r being the closest / furthest distance so two simultaneous equations are made, which when solved for E:
  Since  and , where epsilon is the eccentricity of the orbit, the stated result is reached.
  Flight path angle
  The flight path angle is the angle between the orbiting body's velocity vector (equal to the vector tangent to the instantaneous orbit) and the local horizontal. Under standard assumptions of the conservation of angular momentum the flight path angle  satisfies the equation:
  where:
  is the specific relative angular momentum of the orbit,
  is the orbital speed of the orbiting body,
  is the radial distance of the orbiting body from the central body,
  is the flight path angle
  is the angle between the orbital velocity vector and the semi-major axis.  is the local true anomaly. , therefore,
  where  is the eccentricity.