...established this relation rigorously, and furthermore has made the mean longitude of the first satellite less three times that of the second plus twice that of the third equal to a semi-circumference. At the same time a periodic inequality has arisen which depended upon...

...these three bodies approached very near to the relation which renders the mean motion of the first, minus three times that of the second, plus twice that of the third, equal to nothing. Then their mutual attraction rendered this ratio rigorously exact, and it has moreover...

...extraordinary than the preceding, one which consists in this, that the mean longitude of the first, minus three times that of the second, plus twice that of the third, is constantly equal to two right angles. Laplace claims that these motions were brought within certain...

...equal to three times that of the second. And the mean sidereal or synodical longitude of the first, minus three times that of the second, plus twice that of the third, is generally equal to two right angles. It follows therefore that, for a great number of years at least,...

...Jupiter's principal three satellites [32], according to which law the mean longitude of the first, minus three times that of the second, plus twice that of the third, is exactly equal to IT [33]. The close fit of the mean motions of these heavenly bodies, since their discovery,...

...planet, occulted. He tried to remember Laplace's law regarding the first three Galilean moons: The longitude of the first satellite, minus three times...second, plus twice that of the third, is always equal to half of the circumference ... He had memorized that in high school, but it did him a fat lot of good...

...attraction rendered this ratio rigorously exact, and it has moreover made the mean longitude of the first minus three times that of the second, plus twice that of the third, equal to a semicircumference. At the same time, it gave rise to a periodic inequality, which depends...