In his paper “ON LAPLACE AND THE 3-BODY PROBLEM” Miles gives an argument for why the distance between Saturn’s and Jupiter’s orbit should be shrinking with time if only gravity was present as a force. He writes:
Let us look at four positions of the two planets, in four diagrams, in a straight 3-body problem.
With gravity as a force of attraction, and no other force fields playing a part, we find that we would expect the gap between Jupiter and Saturn to be getting smaller. Because, while Jupiter is sometimes being pulled away from the Sun by Saturn and sometimes toward it, Saturn is always being pulled toward the Sun by Jupiter. I challenge you to find a relative position of the two planets where Saturn is not being pulled into a lower orbit by Jupiter.
(Diagrams created by Miles Mathis.)
It seems to us that this argument does not make any sense. Consider for example the following similar diagram where the big dot represents the Sun and the smaller dot represents the earth:
If Mathis’s arguments were valid, a two-body system could certainly not be stable because the earth could only fall into orbits closer to the sun. The (mathematical) two-body problem however exhibits stable solutions – we are, approximately, living on one!