determined by observing the difference of declination of the upper and lower limb; he adopts the mean diameter 33′. With these data he now calculates the real diameters of the sun and moon, making use of the old value of the solar parallax of 3′, which neither Copernicus nor he thought of discarding. The distance of the sun being 1150 semi-diameters of the earth, the semi-diameter of the sun will be 5.2 times that of the earth, and similarly the distance of the moon is 60 and its semi-diameter 0.29. For the planets he assumes apparent diameters from 2′ to 3′, and calculates from these their diameters and volumes in parts of those of the earth.[1] For the fixed stars Tycho assumes smaller apparent diameters than other astronomers did before the invention of the telescope.[2] With regard to the distance of the stars, he believes the greatest distance of Saturn to be 12,300 semidiameters of the earth (to arrive at which he sketches the theory of Saturn as mentioned above[3]); and as he does not believe that there is a great void between the orbit of Saturn and the fixed stars, he places these at
- ↑ The diameters of the planets are measured by pointing with the armillæ or a quadrant alternately to the upper and lower edge of the planet. See, e.g., Historia Cœlestis, p. 429, for a number of measures of Saturn. The diameters assumed are (Prog., pp. 475-76):
Mercury 2′ 10″ at mean distance, 1,150
Venus 3′ 15″„„ 1,150
Mars 1′ 40″„„ 1,745
Jupiter 2′ 45″„„ 3,990
Saturn 1′ 50″„„ 10,550 - ↑ First mag. diameter 120″, second 90″, third 65″, fourth 45″, fifth 30″, sixth 20″ (ibid., pp. 481–82). Magini took the stars of the first mag. to be 10′ in diameter; Kepler made the diameter of Sirius 4′ (Opera, ii. p. 676); the Persian author of the Ayeen Akbery put the diameter of stars of the first mag. = 7′ (Delambre, Moyen Age, p. 238), so that Tycho's estimates were more reasonable than any of these.
- ↑ The ratio of the semidiameters of the deferent of Saturn and of the solar orbit he borrows from Copernicus. Compare above, p. 181, footnote 1.
some observations made at Hveen in March and June 1578, giving 30′ 35″ and 29′ 53″. About the diopters of Hipparchus, see Halma's preface to the Almegist, vol. ii. p. lviii.
