A Note on the Development of the Reciprocal Distance in Planetary Theory

Abstract

In a development of the reciprocal distance (1/Δ) between two planets, their orbital inclinations, in a sense, improve the convergence, though the development is carried out in powers of the inclinations. This is most clearly shown in the Neptune-Pluto case: if their inclinations, 2° and 17°, are assumed to be 0°, the two orbits cross each other. The development in the actual case ought to be easier than in the assumed case with vanishing inclinations.