respective distances at 42, 56 and 72 AU from the Sun. He gave no indication as to how he determined their existence, and no known searches were mounted to locate them. In 1911, Indian astronomer Venkatesh P. Ketakar suggested the existence of two trans-Neptunian planets, which he named after the Hindu gods Brahma and Vishnu, by reworking the patterns observed by Pierre-Simon Laplace in the planetary satellites of Jupiter and applying them to the outer planets. The three inner Galilean moons of Jupiter, Io, Europa and Ganymede, are locked in a complicated 1:2:4 resonance called a Laplace resonance. Ketakar suggested that Uranus, Neptune and his hypothetical trans-Neptunian planets were also locked in Laplace-like resonances. His calculations predicted a mean distance for Brahma of 38.95 AU and an orbital period of 242.28 Earth years (3:4 resonance with Neptune). When Pluto was discovered 19 years later, its mean distance of 39.48 AU and orbital period of 248 Earth years were close to Ketakar's prediction (Pluto in fact has a 2:3 resonance with Neptune). Ketakar made no predictions for the orbital elements other than mean distance and period. It is not clear how Ketakar arrived at these figures, and his second planet, Vishnu, was never located. Planet X In 1894, with the help of William Pickering, Percival Lowell (a wealthy Bostonian) founded the Lowell Observatory in Flagstaff, Arizona. In 1906, convinced he could resolve the conundrum of Uranus's orbit, he began an extensive project to search for a trans-Neptunian planet, which he named Planet X, a name previously used by Gabriel Dallet. The X in the name represents an unknown and is pronounced as the letter, as opposed to the Roman numeral for 10 (at the time, Planet X would have been the ninth planet). Lowell's hope in tracking down Planet X was to establish his scientific credibility, which had eluded him due to his widely derided belief that channel-like features visible on the surface of Mars were canals constructed by an intelligent civilization. Lowell's first search focused on the ecliptic, the plane encompassed by the zodiac where the other planets in the Solar System lie. Using a 5-inch photographic camera, he manually examined over 200 three-hour exposures with a magnifying glass, and found no planets. At that time Pluto was too far above the ecliptic to be imaged by the survey. After revising his predicted possible locations, Lowell conducted a second search