So delicate were these measures that Gill detected a minute periodic error of theory of twenty-seven days, owing to a periodically erroneous position of the centre of gravity of the earth and moon to which the position of the observer was referred. This led him to correct the mass of the moon, and to fix its ratio to the earth’s mass = 0.012240.
Another method of getting the distance from the sun is to measure the velocity of the earth’s orbital motion, giving the circumference traversed in a year, and so the radius of the orbit. This has been done by comparing observation and experiment. The aberration of light is an angle 20” 48, giving the ratio of the earth’s velocity to the velocity of light. The velocity of light is 186,000 miles a second; whence the distance to the sun is 92,780,000 miles. There seems, however, to be some uncertainty about the true value of the aberration, any determination of which is subject to irregularities due to the “seasonal errors.” The velocity of light was experimentally found, in 1862, by Fizeau and Foucault, each using an independent method. These methods have been developed, and new values found, by Cornu, Michaelson, Newcomb, and the present writer.
Quite lately Halm, at the Cape of Good Hope, measured spectroscopically the velocity of the earth to and from a star by observations taken six months apart. Thence he obtained an accurate value of the sun’s distance.[[5]]
But the remarkably erratic minor planet, Eros, discovered by Witte in 1898, approaches the earth within 15,000,000 miles at rare intervals, and, with the aid of photography, will certainly give us the best result. A large number of observatories combined to observe the opposition of 1900. Their results are not yet completely reduced, but the best value deduced so far for the parallax[[6]] is 8".807 ± 0".0028.[[7]]
FOOTNOTES:
[1] In 1480 Martin Behaim, of Nuremberg, produced his astrolabe for measuring the latitude, by observation of the sun, at sea. It consisted of a graduated metal circle, suspended by a ring which was passed over the thumb, and hung vertically. A pointer was fixed to a pin at the centre. This arm, called the alhidada, worked round the graduated circle, and was pointed to the sun. The altitude of the sun was thus determined, and, by help of solar tables, the latitude could be found from observations made at apparent noon.
[2] See illustration on p. 76.
[3] See Dreyer’s article on these instruments in Copernicus, Vol. I. They were stolen by the Germans after the relief of the Embassies, in 1900. The best description of these instruments is probably that contained in an interesting volume, which may be seen in the library of the R. A. S., entitled Chinese Researches, by Alexander Wyllie (Shanghai, 1897).
[4] Sir George Airy was very jealous of this honourable title. He rightly held that there is only one Astronomer Royal at a time, as there is only one Mikado, one Dalai Lama. He said that His Majesty’s Astronomer at the Cape of Good Hope, His Majesty’s Astronomer for Scotland, and His Majesty’s Astronomer for Ireland are not called Astronomers Royal.