Giovanni Battista Riccioli

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Giovanni Battista Riccioli : biography

17 April 1598 – 25 June 1671
  1. the celestial sphere and subjects such as celestial motions, the equator, ecliptic, zodiac, etc.;
  2. the earth and its size, gravity and pendulum motion, etc.;
  3. the sun, its size and distance, its motion, observations involving it, etc.;
  4. the moon, its phases, its size and distance, etc. (detailed maps of the moon as seen through a telescope were included);
  5. lunar and solar eclipses;
  6. the fixed stars;
  7. the planets and their motions, etc. (representations of each as seen with a telescope were included);
  8. comets and novae ("new stars");
  9. the structure of the universe—the heliocentric and geocentric theories, etc.;
  10. calculations related to astronomy.

Riccioli envisioned that the New Almagest would have three volumes, but only the first (with its 1500 pages split into two parts) was completed.

Pendulums and Falling Bodies

Riccioli is credited with being the first person to measure the acceleration due to gravity of falling bodies.Koyré 1955 (p. 349). Within Books 2 and 9 of the New Almagest Riccioli included a significant discussion of and extensive experimental reports on the motions of falling bodies and pendulums.

He was interested in the pendulum as a device for precisely measuring time. By counting the number of pendulum swings that elapsed between transits of certain stars, Riccioli was able to experimentally verify that the period of a pendulum swinging with small amplitude is constant to within two swings out of 3212 (0.062%). He also reported that a pendulum’s period increases if the amplitude of its swing is increased to 40 degrees. He sought to develop a pendulum whose period was precisely one second – such a pendulum would complete 86,400 swings in a 24 hour period. This he directly tested, twice, by using stars to mark time and recruiting a team of nine fellow Jesuits to count swings and maintain the amplitude of swing for 24 hours. The results were pendulums with periods within 1.85%, and then 0.69%, of the desired value; and Riccioli even sought to improve on the latter value. The seconds pendulum was then used as a standard for calibrating pendulums with different periods. Riccioli said that for measuring time a pendulum was not a perfectly reliable tool, but in comparison with other methods it was an exceedingly reliable tool.Meli 2006 (pp. 131-134); Heilbron 1999 (pp.180-181).

With pendulums to keep time (sometimes augmented by a chorus of Jesuits chanting in time with a pendulum to provide an audible timer) and a tall structure in the form of Bologna’s Torre de Asinelli from which to drop objects, Riccioli was able to engage in precise experiments with falling bodies. He verified that falling bodies followed Galileo’s "odd-number" rule so that the distance travelled by a falling body increases in proportion to the square of the time of fall, indicative of constant acceleration.An algebra-free explanation of the "odd-number" rule and distance increasing as the square of time: An object accelerating from rest (or zero speed) so that its speed steadily increases by 2 feet per second with every passing second, will, after one second has elapsed, be moving at 2 ft/s. Its average speed will be 1 ft/sec (the average of zero and 2 ft/s); therefore, having averaged 1 ft/s for 1 second, it will have traveled one foot. After two seconds have elapsed, the object will be moving at 4 ft/s, its average speed will be 2 ft/sec (the average of 0 ft/s and 4 ft/s); and, having averaged 2 ft/s for 2 seconds, it will have traveled four feet. After three seconds have elapsed the object will be moving at 6 ft/s, its average speed will be 3 ft/sec, and it will have traveled nine feet. After four seconds it will have traveled sixteen feet. Thus the distance the object travels increases as the square of elapsed time: (1 sec, 1 ft); (2 sec, 4 ft); (3 sec, 9 ft); (4 sec, 16 ft). Moreover, since, during the first second the object travels 1 ft, and during the next second it travels 4 ft – 1 ft = 3 ft, and during the third 9 ft – 4 ft = 5 ft, and during the fourth 16 ft – 9 ft = 7 ft, then the distance the object travels during each subsequent second follows an "odd-number" rule: 1 ft; 3 ft; 5 ft; 7 ft. According to Riccioli, a falling body released from rest travels 15 Roman feet (29.57 cm) in one second, 60 feet in two seconds, 135 feet in three seconds, etc.Meli 2006 (pp. 131-134); Heilbron 1999 (pp.180-181); Koyré 1955 (p. 356). Other Jesuits such as the above-mentioned Cabeo had argued that this rule had not been rigorously demonstrated.Meli 2006 (p. 122). His results showed that, while falling bodies generally showed constant acceleration, there were differences determined by weight and size and density. Riccioli said that if two heavy objects of differing weight are dropped simultaneously from the same height, the heavier one descends more quickly so long as it is of equal or greater density; if both objects are of equal weight the denser one descends more quickly.