recognisably modern terms. His groundbreaking work is shown for example in the Principia in all versions including the first edition published in 1687. Newton's biographer, David Brewster, reported that the complexity of Lunar Theory impacted Newton's health: "[H]e was deprived of his appetite and sleep" during his work on the problem in 1692-3, and told the astronomer John Machin that "his head never ached but when he was studying the subject". According to Brewster, Edmund Halley also told John Conduitt that when pressed to complete his analysis Newton "always replied that it made his head ache, and kept him awake so often, that he would think of it no more" [Emphasis in original]. Solar perturbation of lunar motion Newton identified how to evaluate the perturbing effect on the relative motion of the Earth and Moon, arising from their gravity towards the Sun, in Book 1, Proposition 66, and in Book 3, Proposition 25. The starting-point for this approach is Corollary VI to the laws of motion. This shows that if the external accelerative forces from some massive body happens to act equally and in parallel on some different other bodies considered, then those bodies would be affected equally, and in that case their motions (relative to each other) would continue as if there were no such external accelerative forces at all. It is only in the case that the external forces (e.g. in Book 1, Prop. 66, and Book 3, Prop. 25, the gravitational attractions towards the Sun) are different in size or in direction in their accelerative effects on the different bodies considered (e.g. on the Earth and Moon), that consequent effects are appreciable on the relative motions of the latter bodies. (Newton referred to accelerative forces or accelerative gravity due to some external massive attractor such as the Sun. The measure he used was the acceleration that the force tends to produce (in modern terms, force per unit mass), rather than what we would now call the force itself.) Thus Newton concluded that it is only the difference between the Sun's accelerative attraction on the Moon and the Sun's attraction on the Earth that perturbs the motion of the Moon relative to the Earth. Newton then in effect used vector decomposition of forces, to carry out this analysis. In Book 1, Proposition 66 and in Book 3, Proposition 25, he showed by a geometrical construction, starting from the