  The Product of Exponentials (PoE) formulation is most commonly used in the
field of robotics, but has recently been adapted for use in describing orbital
motion. The PoE formula for orbital mechanics is an alternate method for
defining and drawing an orbit based on its orbital elements set. Currently the
PoE formula for orbital mechanics has only been derived through the first
derivative (velocity). This work explores the second derivative of the adapted
PoE formula for orbital mechanics, which gives a more complete description of
the orbital motion of a satellite in a two-body system. This comprehensive
approach employs a unified approach to account for all six time-varying orbital
elements, therefore broadening the scope of the research and applications.
