[745] Ibid., t. xi., p. 505.
[746] Comptes Rendus, t. cxii., p. 1200.
[747] Wied. Ann., Bd. xxxix., p. 294; Scheiner, Temperatur der Sonne, pp. 36, 38.
CHAPTER VI
THE SUN'S DISTANCE
The question of the sun's distance arises naturally from the consideration of his temperature, since the intensity of the radiations emitted as compared with those received and measured, depends upon it. But the knowledge of that distance has a value quite apart from its connection with solar physics. The semi-diameter of the earth's orbit is our standard measure for the universe. It is the great fundamental datum of astronomy—the unit of space, any error in the estimation of which is multiplied and repeated in a thousand different ways, both in the planetary and sidereal systems. Hence its determination was called by Airy "the noblest problem in astronomy." It is also one of the most difficult. The quantities dealt with are so minute that their sure grasp tasks all the resources of modern science. An observational inaccuracy which would set the moon nearer to, or farther from us than she really is by one hundred miles, would vitiate an estimate of the sun's distance to the extent of sixteen million![748] What is needed in order to attain knowledge of the desired exactness is no less than this: to measure an angle about equal to that subtended by a halfpenny 2,000 feet from the eye, within a little more than a thousandth part of its value.
The angle thus represented is what is called the "horizontal parallax" of the sun. By this amount—the breadth of a halfpenny at 2,000 feet—he is, to a spectator on the rotating earth, removed at rising and setting from his meridian place in the heavens. Such, in other terms, would be the magnitude of the terrestrial radius as viewed from the sun. If we knew this magnitude with certainty and precision, we should also know with certainty and precision—the dimensions of the earth being, as they are, well ascertained—the distance of the sun. In fact, the one quantity commonly stands for the other in works treating professedly of astronomy. But this angle of parallax or apparent displacement cannot be directly measured—cannot even be perceived with the finest instruments. Not from its smallness. The parallactic shift of the nearest of the stars as seen from opposite sides of the earth's orbit, is many times smaller. But at the sun's limb, and close to the horizon, where the visual angle in question opens out to its full extent, atmospheric troubles become overwhelming, and altogether swamp the far more minute effects of parallax.
There remain indirect methods. Astronomers are well acquainted with the proportions which the various planetary orbits bear to each other. They are so connected, in the manner expressed by Kepler's Third Law, that the periods being known, it only needs to find the interval between any two of them in order to infer at once the distances separating them all from one another and from the sun. The plan is given; what we want to discover is the scale upon which it is drawn; so that, if we can get a reliable measure of the distance of a single planet from the earth, our problem is solved.
Now some of our fellow-travellers in our unending journey round the sun, come at times well within the scope of celestial trigonometry. The orbit of Mars lies at one point not more than thirty-five million miles outside that of the earth, and when the two bodies happen to arrive together in or near the favourable spot—a conjuncture which occurs every fifteen years—the desired opportunity is granted. Mars is then "in opposition," or on the opposite side of us from the sun, crossing the meridian consequently at midnight.[749] It was from an opposition of Mars, observed in 1672 by Richer at Cayenne in concert with Cassini in Paris, that the first scientific estimate of the sun's distance was derived. It appeared to be nearly eighty-seven millions of miles (parallax 9·5′); while Flamsteed deduced 81,700,000 (parallax 10′) from his independent observations of the same occurrence—a difference quite insignificant at that stage of the inquiry. But Picard's result was just half Flamsteed's (parallax 20′; distance forty-one million miles); and Lahire considered that we must be separated from the hearth of our system by an interval of at least 136 million miles.[750] So that uncertainty continued to have an enormous range.