I just finished looking over the chapter. It starts by talking about good vs evil, then goes on to describe (barely) the Dark Satellite, and the way it's written makes it sound like an actual orb which was closest to the Earth in 1881, and has been moving away since, or at least when this book was published. (1970, Nash Publishing) The orb is described as being filled with spiritual beings of high intelligence, who are responsible for influencing humanity in the direction of depravity, but that since the influence is waning as the orb moves away from us, now true spiritual knowledge would become more available to humanity. Some had suggested that the dark orb was our moon, but according to the author this is not our moon, but was a sort of "dustbin of the universe." It's orbit was mentioned, whether it orbits Earth, the sun, or something else was not specified in this chapter.

After that it goes into some dialogue about mortality and immortality, I flipped through the chapter and the orb wasn't brought up again. The implication was that a lot of suffering on Earth is caused by this Dark Satellite, but is blamed on human nature.