Now, the slightest error in the data, though hardly affecting the result for epochs near the present, leads to uncertainty which accumulates with extreme rapidity in the lapse of time; so that even the present uncertainty of the sun's distance, small as it is, renders precarious all conclusions from such computations when the period is extended more than a few hundred thousand years from the present time. If, for instance, we should find as the result of calculation with the received data that two millions of years ago the eccentricity of the earth's orbit was at a maximum, and the perihelion so placed that the sun was nearest during the northern winter (a condition of affairs which it is thought would produce a glacial epoch in the southern hemisphere), it might easily happen that our results would be exactly contrary to the truth, and that the state of affairs indicated did not occur within half a million years of the specified date—and all because in our calculation the sun's distance, or solar parallax by which it is measured, was assumed half of one per cent, too great or too small. In fact, this solar parallax enters into almost every kind of astronomical computations, from those which deal with stellar systems and the constitution of the universe to those which have for their object nothing higher than the prediction of the moon's place as a means of finding the longitude at sea.
Of course, it hardly need be said that its determination is the first step to any knowledge of the dimensions and constitution of the sun itself.
This parallax of the sun is simply the angular semi-diameter of the earth as seen from the sun; or, it may be defined in another way as the angle between the direction of the sun ideally observed from the centre of the earth, and its actual direction as seen from a station where it is just rising above the horizon.
We know with great accuracy the dimensions of the earth. Its mean equatorial radius, according to the latest and most reliable determination (agreeing, however, very closely with previous ones), is 3962.720 English miles [6377.323 kilometres], and the error can hardly amount to more than 1000000 of the whole—perhaps, 200 feet one way or the other. Accordingly, if we know how large the earth looks from any point, or, to speak technically, if we know the parallax of the point, its distance can at once be found by a very easy calculation: it equals simply [206,265 X the radius of the earth] ÷ [the parallax in seconds of arc].
Now, in the case of the sun it is very difficult to find the parallax with sufficient precision on account of its smallness—it is less than 9", almost certainly between 8.8" and 8.9". But this tenth of a second
- This number 206,265 is the length of the radius of a circle expressed in seconds of its circumference. A ball one foot in actual diameter would have an apparent diameter of one second at a distance of 206,265 feet, or a little more than 39 miles. If its apparent diameter were 10", its distance would, of course, be only 10 as great.