according to Bode's law, it was very nearly at the position the law had designated for Neptune. The subsequent discovery of the Kuiper belt – and in particular the object , which is more massive than Pluto, yet does not fit Bode's law – further discredited the formula. Possible earlier version In 1760 Tomàs Cerdà taught a renowned astronomy course, which led to a textbook Tratado de Astronomía. In Tratado de Astronomía, Cerdà obtains the planetary distances from the orbital periods by applying Kepler's third law, with an accuracy of 10−3 . Scaling the average distance of the Earth from the Sun as 10, and rounding to whole numbers, one can express the geometric progression as Using the uniform circular movement of Kepler's fictitious mean anomaly, values of corresponding to each planet's ratios may be obtained as resulting in 1.82, 1.84, 1.86, 1.88, and 1.90, in which the ratio between Keplerian succession and Titius–Bode Law, would be a numerical coincidence. The ratio is close to 2, but increases harmonically from 1.82 . The planet's average speed from to decreases moving away the Sun and differs from uniform descent in to recover from (orbital resonance). Data The Titius–Bode law predicts planets will be present at specific distances in astronomical units, which can be compared to the observed data for the planets and two dwarf planets in the solar system: Blagg formulation In 1913, Mary Blagg, an Oxford astronomer, re-visited the law. She analyzed the orbits of the planetary system and those of the satellite systems of the outer gas giants, Jupiter, Saturn and Uranus. She examined the log of the distances, trying to find the best 'average' difference. Her analysis resulted in a different formula: Note that in her formulation, the Law for the solar system was best represented by a progression in 1.7275, not 2. Blagg examined the satellite systems of Jupiter, Saturn, and Uranus, and discovered the same progression ratio (1.7275) in each. However, the exact formulation of the function f was not finalized in Blagg's 1913 paper, with Blagg noting that the figures given are only illustrative. An empirical form of the curve was provided in the form of a graph (the reason that points on the curve are such a close match for empirical data, for objects discovered prior to 1913, is that they are empirical data). Finding a formula closely fitting the curve turned out to