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—
and .
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.
