text: The angular momentum is related to the vector cross product of position and velocity, which is proportional to the sine of the angle between these two vectors. Here  is defined as the angle which differs by 90 degrees from this, so the cosine appears in place of the sine.
  Equation of motion
  From initial position and velocity
  An orbit equation defines the path of an orbiting body  around central body  relative to , without specifying position as a function of time.  If the eccentricity is less than 1 then the equation of motion describes an elliptical orbit.  Because Kepler's equation  has no general closed-form solution for the Eccentric anomaly (E) in terms of the Mean anomaly (M), equations of motion as a function of time also have no closed-form solution (although numerical solutions exist for both).
  However, closed-form time-independent path equations of an elliptic orbit with respect to a central body can be determined from just an initial position () and velocity ().
  For this case it is convenient to use the following assumptions which differ somewhat from the standard assumptions above:
  The central body's position is at the origin and is the primary focus () of the ellipse (alternatively, the center of mass may be used instead if the orbiting body has a significant mass)
  The central body's mass (m1) is known