The limiting radii of direct and retrograde satellite orbits, with applications to the solar system and to stellar systems

Simple expressions are derived for the limiting radii of direct and retrograde orbits of planetary satellites in the presence of the sun's gravitational field. The formulas may also be used for computing tidal radii of stellar systems. A revision of the King (1962) formula is suggested, and results for a satellite in the general two-body problem are also given. As illustrations, the formulas are applied to the solar system and to the Sculptor dwarf galaxy. On the basis of this theory, it is argued that an ancient single encounter between two protogalaxies could lead to objects such as M104 or even NGC 5128 or NGC 2685.