History of Astronomy From Roman Empire to the Present, part 10
The fundamental principle of parallactic angles is unsound, while it is at the same time in conflict with quite a host of other astronomical theories, because the theories of Atmospheric Refraction, Perpendicularity, Geocentric Parallax, and the Aberration of Light, combined with the use of Sidereal Time, all go to prove that every observation taken from the surface of the earth to a star is exactly parallel with a line from the centre of the earth to the same star, and that B’s line to x is parallel to that of A.
Consequently if Mars were on the line O X (in diagram 15), as Dr. Hailey presumed when he invented this method, it would be perpendicular to both A and B, therefore neither one observer or the other would see it at any angle at a 11; as shown in diagram 17.
It is not possible for any observer on earth to see Mars to the right or left of a star that is perpendicular unless the planet is in reality to the right or left of that perpendicular. No apparent displacement could occur, but the displacement must be physical; and so the theory of parallactic angles is exploded.
Of course there will be some ready to contend that Sir David Gill really did measure an angle. That is true; but it will prove to be an actual (physical) deviation of the planet from the perpendicular, which is a very different thing than an angle of parallax.
But it was believed to be a parallactic angle, that is to say— it was supposed to be only an optical or apparent displacement due to the change in the position of the observer from A to B, hence a world of romance is built upon that little angle in this fashion: Angle of Mars 23″ = 35,000,000 miles, 35,000,000×2.6571 =93,000,000= solar parallax 8.80’ = distance of the sun; the sun’s diameter is 875,000 miles; weight X Y Z lbs., age 17,000,000 years, and will probably be burnt out in another 17 million years. 93,000,000 x 2 = 186,000,000 miles diameter of earth’s orbit, the distance to the stars must be billions of miles or even more, they must be a terrific size, and the earth is only like a speck of dust in the Brobdinagian Universe, &c., &c., &c.
But we have not yet done with that angle. Regarded as an angle of parallax, and considered to be equivalent to just such an angle as a surveyor would use in measuring a plot of land, it was of course presumed that the two lines of sight converged so as to meet at a point thirty-five million miles away. (See diagram 18.) This, however, is a mistake, for the two lines of observation, when placed in their proper relations to each other, and in the order as they were taken, should be as in diagram 19, which shows that they diverge.
We will prove this in diagram 20. A study of our earlier diagram 6— which gives a suggestion of a
small section mapped out with dotted lines to indicate latitude and longitude in universal space— reveals the fact that twelve hours’ rotation of the earth does not transfer the observer from A to the point B in space, because— according to Copernican astronomy— the earth is not only rotating on its axis during those twelve hours, but also rushing through space in a gigantic orbit round the sun at the rate of sixty-six thousand miles an hour, or thereabouts, and so when the observer takes his second observation he is something like three-quarters of a million miles away from where he started. He is at latitude G in diagram 6.
Now let us study diagram 20, which has been made as simple as possible in order to illustrate the principle involved the more clearly. The letter C is used in this diagram to take the place of G in the earlier diagram 6, because it is simpler to describe the movements of the observer by A, B, C than it is by A, B, G ; easier to convey my meaning.
All the principles and theories of modern astronomy have been carefully observed, and the parallelism of the lines is strictly in accordance with the theories of Greenwich. As I anticipate that in the course of time a battle-royal will wage around this question of the measurement to Mars, I wish to make it quite clear that diagram 20 is designed only to illustrate the principles; it is to clarify the whole proceeding so that the layman can follow the argument. If the Royal Astronomical Society have any objection to make, I will be happy to discuss these questions with them in a manner worthy of the subject. The discussion may then, perhaps, be more refined, indeed.
I foresee a very pretty debate, wherefore I advise them that I know that Sir David did not really take his observations with a twelve hours’ interval as proposed by Dr. Hailey— because it was impossible—but that he actually waited only seven and a half hours (hence my use of C in place of G in diagram 20), but that only elevates the discussion to a higher plane, while the principle and the net results remain the same. In the appointed time and place I will discuss the actual practice if desired, but here I am dealing with the principle; and talking to the layman and the judge.
Now let us get on with this diagram 20. The first observation is taken at A and the second at C. It was evening when the observer was at A, but it is morning when he arrives at C, so that his east and west are reversed, the sun remaining fixed far below the bottom of this page. (The sun is at the observer’s west in the evening, and to his east in the morning, while Mars is in the opposite direction to the sun.)
In this example I have placed the planet exactly on the perpendicular from A to the star of reference, thus “A MARS X.” That is the starting point, or first observation; taken in the evening to the observer’s eastward. Twelve hours later the observer is at C, and sees the same star and the planet both to his west; but Mars is at this time not exactly on the perpendicular, but a little, a very little, to the left of the star.
The planet is not quite as much west as the star, that is to say— being to the left— it is to the eastward in universal geography ; and to the eastward of the perpendicular line C X.
Now if we were not particularly careful, and had not this diagram to guide us, it would be quite natural to think that the first observation (to the east) should be on the left hand, and the other (west) on the right, so as to face each other, so that any angle that might appear, such as an angle of parallax, would be between the two perpendiculars to the star. In that case they would seem to be as shown in diagram 18; but that is wrong!
Referring again to diagram 20, where the observations are illustrated in the proper order as they were actually taken, and all in accordance with the theories of Copernican astronomy, we find that the angle of Mars is to the EASTWARD! outside of the two perpendiculars. This is more simply shown in diagram 19. A being the first observation, on the right, and C, the second observation, on the left; that is correct.
Starting, as we did, with Mars on the perpendicular at A, we know that whenever we shall see it again it must be to the eastward of the star which marks that perpendicular, because, while the star remains fixed in space the planet is moving every hour along its orbit to the eastward round the sun, and so, when we see it from C the next morning, it is as we have shown in diagrams 19 and 20. It has moved from the line A X to a position a little further east in universal space than the line C X.
Whatever displacement there is, is outside the two perpendiculars; so that the second line of sight to Mars diverges from the firs t; consequently no triangulation occurs, and nothing of any material value is accomplished.
The so-called angle of parallax was a displacement due to a real movement of the planet during the night.
In conclusion, as A X and C X are one and the same perpendicular, and no angle, either real or apparent, occurs between them, the first observation A X and the base-line are entirely without value, and may be discarded as useless. (Diagram 21.) This leaves us with only the perpendicular C X and the second observation, which proves to be a narrow inverted triangle “ C X Mars,” where the displacement of the Diagram 21. planet X M— (hitherto known as the parallax of Mars) — indicates how much the planet has moved to the left of the star during the night; while the observer at C is at the apex. Just that, and no more.