Systematic and random deformations of long-period comet orbits

A system of differential equations for the evolution of the orbital elements of a comet subject to regular galactic forces has been derived, assuming a circular orbit for the sun around the Galaxy. The general solution to the equations indicates that an initial straight-line orbit lying either in the galactic plane or along the z-axis will not evolve. If the straight-line orbit is inclined to the galactic plane by a 27.65 deg angle, it will become a circular orbit only after an infinite time span. A formula has been obtained for the dispersion in the incremental angular momentum of an initially degenerate orbit due to the cumulative effect of irregular galactic forces. Formulas are presented which can be used to calculate the changes in the parameter of a highly elongated orbit over various time intervals for various values of the semimajor axis.