Astronomy for Amateurs

by Camille Flammarion

Fig. 83.—Measurement of the distance of the Sun.

Thus, it has been found that the half-diameter of the Earth viewed from the Sun measures 8.82″. Now, we know that an object presenting an angle of one degree is at a distance of 57 times its length.

The same object, if it subtends an angle of a minute, or the sixtieth part of a degree, indicates by the measurement of its angle that it is 60 times more distant, i.e., 3,438 times.

Finally, an object that measures one second, or the sixtieth part of a minute, is at a distance of 206,265 times its length.

Hence we find that the Earth is at a distance from the Sun of 206265⁄8.82—that is, 23,386 times its half-diameter, that is, 149,000,000 kilometers (93,000,000 miles). This measurement again is as precise and certain as that of the Moon.

I hope my readers will easily grasp this simple method of triangulation, the result of which indicates to us with absolute certainty the distance of the two great celestial torches to which we owe the radiant light of day and the gentle illumination of our nights.

The distance of the Sun has, moreover, been confirmed by other means, whose results agree perfectly with the preceding. The two principal are based on the velocity of light. The propagation of light is not instantaneous, and notwithstanding the extreme rapidity of its movements, a certain time is required for its transmission from one point to another. On the Earth, this velocity has been measured as 300,000 kilometers (186,000 miles) per second. To come from Jupiter to the Earth, it requires thirty to forty minutes, according to the distance of the planet. Now, in examining the eclipses of Jupiter's satellites, it has been discovered that there is a difference of 16 minutes, 34 seconds in the moment of their occurrence, according as Jupiter is on one side or on the other of the Sun, relatively to the Earth, at the minimum and maximum distance. If the light takes 16 minutes, 34 seconds to traverse the terrestrial orbit, it must take less than that time, or 8 minutes, 17 seconds, to come to us from the Sun, which is situated at the center. Knowing the velocity of light, the distance of the Sun is easily found by multiplying 300,000 by 8 minutes, 17 seconds, or 497 seconds, which gives about 149,000,000 kilometers (93,000,000 miles).

Another method founded upon the velocity of light again gives a confirmatory result. A familiar example will explain it: Let us imagine ourselves exposed to a vertical rain; the degree of inclination of our umbrella will depend on the relation between our speed and that of the drops of rain. The more quickly we run, the more we need to dip our umbrella in order not to meet the drops of water. Now the same thing occurs for light. The stars, disseminated in space, shed floods of light upon the Heavens. If the Earth were motionless, the luminous rays would reach us directly. But our planet is spinning, racing, with the utmost speed, and in our astronomical observations we are forced to follow its movements, and to incline our telescopes in the direction of its advance. This phenomenon, known under the name of aberration of light, is the result of the combined effects of the velocity of light and of the Earth's motion. It shows that the speed of our globe is equivalent to 1⁄10,000 that of light, i.e., = about 30 kilometers (19 miles) per second. Our planet accordingly accomplishes her revolution round the Sun along an orbit which she traverses at a speed of 30 kilometers (better 291⁄2) per second, or 1,770 kilometers per minute, or 106,000 kilometers per hour, or 2,592,000 kilometers per day, or 946,080,000 kilometers (586,569,600 miles) in the year. This is the length of the elliptical path described by the Earth in her annual translation.

The length of orbit being thus discovered, one can calculate its diameter, the half of which is exactly the distance of the Sun.

We may cite one last method, whose data, based upon attraction, are provided by the motions of our satellite. The Moon is a little disturbed in the regularity of her course round the Earth by the influence of the powerful Sun. As the attraction varies inversely with the square of the distance, the distance may be determined by analyzing the effect it has upon the Moon.