The Babylonians (c1000 BC) recorded the comings and goings of the Moon arithmetically without understanding the geometry. The Greeks (c200 BC) went further; they viewed the solar system as sitting in an immense vacuum surrounded by the fixed stars. But even the clever Greeks knew nothing about the underlying physics of the solar system. This fell to Newton (1687) in the "Principia," and the 18th century mathematician/physicists such as Laplace. These thinkers proposed the principle of universal gravitation and tried to check it out on the complicated Moon-Earth-Sun system. In many physics problems, the dynamics of two interacting bodies (a planet and a star or two electrical charges, say) is easy. Add a third body and things get complicated, indeed chaotic, which is why Newton and his 18-century followers were largely stumped in their efforts to nail down the Earth-Sun-Moon dynamics.
The amassing of positions, orbits, times (the kinds of things published in tables) corresponds to the "Babylonian phase," while the advent of a model of the solar system represents the "Greek phase." The third, or Newtonian, age is when the underlying forces are deduced.