CELESTIAL MOTIONS CONSIDERED ON THE 

 PRINCIPLE OE RELATIXITY. 



Bv Col. II. E. MAKKW K K, C.B., F.R.A.S. 



In astronomical text-books and po[)ukir works on the 

 science one frequently, and naturally, meets with 

 references to the enormously swift motions of 

 celestial bodies, as compared with terrestrial 

 experience. We read of the great comet of 1882 

 " rushing through the part of its orbit closest to 

 the Sun," and the fixed stars are described as in 

 reality "flying through space" at enormous velocities 

 of varying direction and amount. One recalls how, 

 in old schoolda}S, when "doing globes," the master 

 would ask the question, " How fast is the Earth 

 moving in its orbit?" and the pupil would answer, 

 '■ Rather more than sixty thousand miles an hour." 

 The first time one heard this it sounded as some- 

 thing startling, but the youthful mind cannot easily 

 apprehend such an enormous speed, and by repeti- 

 tion the fact got to lose its significance. All these 

 statements of high speeds are, of course, true, being 

 based on a solar parallax which is now almost 

 certain to the first decimal, combined with observed 

 motions of the heavenly bodies. 



Sir R. S. Ball, a most lucid expositor of celestial 

 facts and figures, remarks in " The Storj' of the 

 Heavens," on the motion of the Earth : " It will 

 appear that the earth must actually complete 

 eighteen miles every second. Pause for a moment 

 to think w hat a velocitv of eighteen miles a second 

 really implies. Can we realize a speed so 

 tremendous ? " He then goes on to compare the 

 motion of the Earth with that of an express train, 

 travelling at the regulation text-book speed of sixty 

 miles an hour, so that the speed of the train " is not 

 even the one-thousandth part of the velocity of the 

 Earth in its orbit." But he continues : " View ed in 

 another way, the stupendous speed of the Earth does 

 not seem immoderate. The Earth is a mighty globe, 

 so great, indeed, that even when moving at this speed 

 it takes about eight minutes to pass over its own 

 diameter. If a steamer required eight minutes to 

 traverse a distance equal to its own length, its pace 

 would be less than a mile an hour." .A figure is 

 given, showing two equal circles joined by a straight 

 line, the distance between the centres being about 

 six times a diameter of the circle. If this represents 

 the Earth at two stages in its path, then " the time 

 required to pass from one position to another is 

 about forty-eight minutes." 



The particular point now is to consider some of 

 these enormous, and, to our experience, utterly 

 transcendental speeds, relatively to the size of the 

 moving body, because they then begin to assume 

 a different aspect. A sense of proportion must be 

 brought to bear on the matter, and actual terrestrial 

 motions and dimensions must be more or less kept in 



their proper sphere when studying the order of 

 motions and dimensions of the solar system as a 

 whole. Apparent motions, however, are common to 

 whatever position wc are in, or ma\' imagine our- 

 selves to be in. Apparent motion, or, as it may here 

 be termed, angular motion, is the speed at which a 

 bod\' moves across the field of view, irrespective of 

 its distance. If we imagine anyone (call anyone an 

 " ether-man," someone above an " air-man " in 

 powers and qualifications), occupying an isolated 

 position in space, it must still be with this corporeal 

 frame, with a pair of eyes to see, and a celestial 

 object to be seen. The rotation of the ether- 

 man's body round its longer axis still sweeps out a 

 field which is measured by three hundred and sixt}- 

 degrees for a complete rotation. This conception 

 holds good, even if deprived of the terrestrial 

 horizon. 



For the present purpose it seems convenient to fix 

 on some limit of angular speed, below which, at the 

 first glance or so, a body seems to have no motion. 

 It is rather an arbitrary proceeding, but may serve 

 for illustration. Put this limit at a rate of transit 

 of 10° in five minutes of time, or 2' of arc in 

 one second ; i.e., three hours for the tour of the 

 \\hole horizon. With this angular speed, a terrestrial 

 object at one hundred yards distant from the 

 observer would have to move at the rate of two 

 hundred and thirty-one yards per hour ; at two 

 hundred yards, four hundred and sixty-two yards 

 per hour ; at one mile distant about two and one- 

 third miles per hour ; and at ten miles distant 

 twenty-three miles per hour. For celestial observ- 

 ation, consider an object moving at a less angular 

 speed than this, as seen with the naked eye, to be 

 devoid of visible motion ; if it moves faster, then 

 sav it has visible motion. 



The angular motions of the planets round the Sun, 

 and of the satellites round their primaries, are, of 

 course, far below the limit just fixed. Seen from 

 the sun. Mercury moves about 0"-17 in one second, 

 the Earth 0"-04, Neptune 0"- 00025. Turning to 

 the satellites, the rapid Phobos, with its period of 

 seven hours thirty-nine minutes fourteen seconds, 

 moves 47" in one second. Take, again, the case of a 

 comet moving very close round the Sun. The comet 

 of 1843 is stated to have described the whole of the 

 segment of its orbit North of the plane of the ecliptic, 

 in a little more than two hours. This implies an 

 angular velocity of about 90" per second. All these 

 rates of motion are below, and most far below, the 

 hypothetical limit. 



What then, would a view of the solar system 

 reveal to the ether-man, placed in space at a point 



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