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Newton's theory had triumphed yet again. In his Astronomical Tables, Halley had written, referring to the comets of 1531, 1607, and 1682:

You see therefore an agreement of all the elements in these three, which would be next to a miracle if they were three different comets ... . Wherefore if according to what we have already said it should return again about the year 1758, candid posterity will not refuse to acknowledge that this was first discovered by an Englishman.

Nicolas Louis de Lacaille referred to 'Halley's comet' in a session of the French Academy of Sciences in 1759, and it has borne Halley's name ever since.

### Aberration and nutation

In the Principia, Newton had asserted that 'the orbit of the earth is sensibly perturbed by the moon',35 but he did not provide any quantitative analysis. Newton claimed that the centre of gravity of the Earth-Moon system revolves around the Sun in an elliptical orbit (which is true to a high degree of approximation) and as the Earth and Moon take part in a monthly rotation about this point, the longitude of the Sun varies from its Keplerian value. In 1744, Euler calculated the inequality as 15'' sin 9, where 9 is the angular distance between the Sun and Moon, but this value is significantly in error due to the inaccurate values that he used for the ratio of terrestrial and lunar mass, and for the solar parallax -had he used the correct values he would have obtained a maximum inequality of nearer 6'' .36

The work of Euler, Clairaut, and d'Alembert on the three-body problem made it possible to perform a more systematic study of the orbit of the Earth, rather than simply assuming Keplerian motion for the centre of gravity. The first derivation of the perturbations of the orbit of the Earth due to the gravitational

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