Popular Science Monthly/Volume 19/October 1881/About Comets

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ABOUT COMETS.
By AARON NICHOLS SKINNER,
UNITED STATES NAVAL OBSERVATORY, WASHINGTON, D. C.

THE study of astronomy reaches back to the very beginnings of history, and through all the ages the ablest intellects have been directed to the wellnigh impossible task of unraveling the celestial motions. The terrestrial observer not being located at the center of the motions of the solar system, the complexity arising from this compounding of the motion of the observer with the motion of the planet observed rendered the problem very difficult.

Copernicus furnished the key, by showing that the sun and not the earth is the center of the solar system. Tycho Brahe soon followed, and furnished an extensive series of accurate observations that afforded Kepler the material upon which he based his studies that developed those immortal laws defining the forms of the orbits of the planets, the character of their motions, and the relation between the dimensions of their orbits and their periods of revolution.

It remained for Newton to discover the existence of the law of universal gravitation, of which Kepler's laws are an immediate sequence.

Thus the secrets of the motions of the planets were explained. But comets, those erratic visitants of our system, whose advent in olden time filled the mind with universal awe, were still an unfathomed mystery. Suddenly they would blaze out in the sky, and as suddenly pass out of sight, and no astronomer could tell whence they came or whither they went, or the laws which governed their motions.

Newton first showed that comets also were obedient to the attraction of gravitation. He demonstrated this fact by means of the comet of 1680. The orbit of this comet he found not to differ perceptibly from a parabola.

After Newton, Edmund Halley, from a careful study of the comets of 1531, 1607, and 1682, ventured the assertion that these were only different appearances of one and the same body, whose period of revolution was about seventy-five years. Halley, consequently, predicted a reappearance of this comet in 1759. This comet was shown to move in a very elongated ellipse. In accordance with prediction, reappearances of this comet occurred in 1759 and 1835.

Since the time of Newton all the comets which have come to view have been submitted to a careful study. To determine the orbit of any newly discovered member of our system, it is necessary that its direction in space from the earth at three dates, as nearly equidistant as may be, should be determined by observation.

The data for the problem are, then, as follows: the positions of the earth with reference to the sun at three different dates, and the positions of the heavenly body with reference to the earth at the same dates. The unknown elements which describe the character of the orbit and its position in space are as follows:

 I. The mean longitude of the body at any convenient epoch.
 II. The semi-major axis of the orbit.
 III. The eccentricity of the orbit.
 IV. The longitude of the perihelion.
 V. The longitude of the ascending node.
 VI. The inclination between the orbit-plane and the plane of the earth's orbit.

Of the above, I indicates the position of the body in the orbit at some definite time; II gives the greatest semi-diameter of the ellipse; III gives the ratio of the distance of the focus from the center divided by the semi-major axis; IV, with VI, gives the position in space of the greatest diameter of the ellipse; Y gives the position of the line of intersection between the plane of the unknown orbit and the plane of the earth's orbit.

From II may be determined immediately the period of revolution by means of Kepler's law as follows: if a and a′ are respectively the semi-major axis of the unknown orbit and the earth's orbit, and t and t′ the respective periods of revolution, then we have from Kepler's law—

\scriptstyle \frac{t^2}{a^3} = \frac{t'^2}{a'^3} and \scriptstyle t = \left(\frac{a^3t'^2}{a'^3}\right)^{\frac{1}{2}}.

If the eccentricity of the orbit is very large, the portion of the ellipse in the vicinity of the perihelion approximates to a parabola, which it becomes when the eccentricity equals unity.

As a matter of history, the great majority of comet orbits hitherto studied are either parabolas or are portions of excessively elongated ellipses, so as to be indistinguishable from parabolas, at least in the part of the orbit traversed during visibility. This portion of the orbit is always adjacent to the perihelion.

From the foregoing fact, and moreover because the computation of a parabolic orbit is much simpler, there being one less unknown quantity, preliminary comet orbits are always parabolic. Subsequent investigations show whether the comet deviates perceptibly from the parabola computed.

On October 10, 1880, Lewis Swift, of Rochester, New York, discovered a comet which has proved to be of peculiar interest. From its first discovery it has presented no brilliancy of appearance, for, during its period of visibility, a telescope of considerable power was necessary to observe it. Since this comet when in close proximity to the earth was very faint indeed, its dimensions must be quite moderate.

As soon after its apparition as the necessary observations of position were obtained, its parabolic elements were computed by several astronomers. After carefully comparing these elements with those of previous comets, Mr. S. C. Chandler, of Boston, remarked the striking similarity between them and those of Comet III of 1869. He immediately suspected them to be one and the same body, revolving in an elongated ellipse, having a period of eleven years, or a sub-multiple of eleven years.

Mr. Chandler hereupon made some extended investigations, to determine which period was the more probable. He showed that the observed positions could be satisfied more closely with a period of five and one half years.

It seemed very desirable that elliptic elements should be determined for this comet without making any previous assumptions in reference to any of the elements; this was undertaken independently by two astronomers of the United States Naval Observatory, each from different data. Professor Frisby made use of observations of October 25th, November 7th, and November 20th. Mr. Upton selected the following dates: October 25th, November 23d, and December 22d.

The results of these two computations agree very closely: the resulting period is only a few days less than six years. The inclination of the plane of the orbit to the plane of the ecliptic is about five and one half degrees.

To show more strikingly the remarkable situation of the comet's orbit with reference to the earth's orbit, the attention of the reader is directed to the accompanying diagram (Fig. 1), which, for the sake of

Fig. 1.
PSM V19 D813 Comet orbit between earth and jupiter.jpg

simplicity, shows the two orbits as if in one plane, when in reality the angle of inclination between them is about five and one half degrees. The line marked "line of nodes" is the line of their mutual intersection, the part of the comet's orbit in the vicinity of the perihelion being north of the plane of the ecliptic.

The relative situations of the earth and comet are shown by their positions in orbit at the date of discovery of the comet, October 10; the date of the perihelion passage, November 8, 1880, and January 1, 1881.

The nearest approach of the comet to the earth was about November 18, 1880, when it was distant from the earth 0·13 of the earth's distance from the sun. The period, as determined by Professor Frisby and Mr. Upton, is probably somewhat too large, owing to the uncertainty arising from the shortness of the arc of observation. The length of the period of revolution affords a reason for the fact that the comet escaped observation at its last return; since then it must have been in the direction of the sun.

It will be seen, from the drawing, that at aphelion the comet passes beyond the orbit of the planet Jupiter.

About the 22d of June last, a comet flashed into view which was unexpected as it was brilliant. It was seen with the unassisted eye by a multitude of persons in widely separated localities. Among the earliest

Fig. 2.
PSM V19 D814 Comet orbit in relation to earth.jpg

of those who discovered its presence in the northern sky was Mr. G. W. Simmons, of Boston, Massachusetts, who chanced to be in camp at Morales, Mexico. This gentleman first saw it on the morning of June 20th. It had, however, been discovered nearly one month earlier by Mr. Tebbutt, of New South Wales, Australia, on May 22d. During the interval between these two dates it had moved northward through an arc of more than 60°, which rapid motion accounts for its sudden apparition in our northern sky.

The relative situation of the orbits of the comet and the earth will be best understood by the perspective view of a model of the two orbits constructed to scale (Fig, 2). This model was executed, from elements computed by Messrs. Chandler and Wendell, of Harvard College Observatory, by Ensign S. J. Brown, U.S.N., who kindly placed it at the service of the writer.

In this cut, the horizontal plane represents the position of the earth's orbit, and the plane cutting this at a large angle represents the plane of the comet's orbit. The comet moved from below, which is the southern side, up through the plane of the earth's orbit to the northern side. The dates indicate the positions of the earth and comet at different times in their respective orbits. It passed its perihelion point just before passing through the plane of the earth's orbit.

The orbit of the comet is inclined to the plane of the earth's orbit at an angle of 63°. Its perihelion distance is 0·77 of the earth's distance from the sun. It arrived at its perihelion June 16th, and was nearest the earth June 19th, when its distance from the earth was 0·28 of the earth's distance from the sun.

The nucleus attained fully the brightness of a first-magnitude star, and the length of the tail was variously estimated at from 20° to 30°. This comet is still faintly visible to the naked eye (August 22d).

At first it was suspected that this comet was identical with that of 1807, but later investigation disproved this supposition.

 
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