  In this paper, we overlay a continuum of analytical relations which
essentially serve to compute the arc-length described by a celestial body in an
elliptic orbit within a stipulated time interval. The formalism is based upon a
two-dimensional heliocentric coordinate frame, where both the coordinates are
parameterized as two infinitely differentiable functions in time by using the
Lagrange inversion theorem. The parameterization is firstly endorsed to
generate a dynamically consistent ephemerides of any celestial object in an
elliptic orbit, and thereafter manifested into a numerical integration routine
to approximate the arc-lengths delineated within an arbitrary interval of time.
As elucidated, the presented formalism can also be orchestrated to quantify the
perimeters of elliptic orbits of celestial bodies solely based upon their
orbital period and other intrinsic characteristics.
