text: The velocity equation for a hyperbolic trajectory has either + , or it is the same with the convention that in that case a is negative.
  Orbital period
  Under standard assumptions the orbital period () of a body travelling along an elliptic orbit can be computed as:
  where:
  is the standard gravitational parameter.
  is the length of the semi-major axis.
  Conclusions:
  The orbital period is equal to that for a circular orbit with the orbital radius equal to the semi-major axis (),
  For a given semi-major axis the orbital period does not depend on the eccentricity (See also: Kepler's third law).
  Energy
  Under standard assumptions, the specific orbital energy () of an elliptic orbit is negative and the orbital energy conservation equation (the Vis-viva equation) for this orbit can take the form:
  where:
  is the orbital speed of the orbiting body,
  is the distance of the orbiting body from the central body,
  is the length of the semi-major axis,
  is the standard gravitational parameter.
  Conclusions:
  For a given semi-major axis the specific orbital energy is independent of the eccentricity.
  Using the virial theorem to find:
  the time-average of the specific potential energy is equal to −2ε
  the time-average of r−1 is a−1
  the time-average of the specific kinetic energy is equal to ε
  Energy in terms of semi major axis