PATH OF COMETS

Evening Post, Volume CXXV, Issue 21, 26 January 1938, Page 19

PATH OF COMETS

DIFFICULT TO CHART

INFLUENCE OF THE PLANETS

MAY DRIVE THEM AWAY

There is a fairly general idea that astronomers can forecast the return of a comet, such as Halley's Comet, for instance, with accuracy, so that it will make its, closest approach to the sun within a day or so of the predicted time. But even in the case of a comot which has been observed over so long an interval as Halley's Comet at its last appearance, when the first and last photographs were separated by over twenty-two months, such an accuracy is hardly to be hoped for, says a writer in the .Melbourne "Age."

In the case of most comets the observations extend over a much shorter period; the orbit cannot be determined so accurately as that of Halley's Comet, and there will be an increased uncertainty in the knowledge of its motion. The date of return will naturally be more uncertain for the comets of longer period. Suppose a comet has beer, well observed over an interval of two or three months, so that a fairly good determination of its orbit can be made. If the time taken, by the comet to describe its orbit is short, say. six or eight years, the uncertainty in the time of its return is a week ov two. If the period of its revolution round the sun is fifty or a hundred years the uncertainty in the period derived from the observations is a year or more. If the period is very long, say one thousand years, the uncertainty in the' time of its return is likely to be one hundred years. • DIFFICULTY OF OBSERVATION. The uncertainty in the orbit arises from the limited accuracy of the observations. As a general rule the comet's' head appears as a diffuse object on the photograph, and it is not possible to measure the position of this with the same accuracy as if the image were a sharp stellar point. The portion of the orbit over which' observations extend is generally only a very small portion near the sun. The problem of_ the computing astronomer is to find^an orbit which will pass through the observed positions as closely "as possible. He makes the assumption at first that the orbit is a parabola, with the sun in the focus. This gives a preliminary orbit, which serves for.following the comet for a short period. - But as the arc of the orbit gets longer a parabolic orbit may not give a sufficiently good fit for all -the observations, and it becomes necessary to compute an elliptic orbit. We know from Kepler's laws that the orbit of a comet round the sun, neglecting the effect of the attraction of the planets, must be a conic section. The parabola is chosen for the first • orbit because the computation is much shorter. It is only when the observed arc becomes longer that it is advisable to proceed to the computation of the elliptic orbit. • .- ■ ■ ■..--■ The preliminary orbit is computed as soon as observations on three days_ become available. This, of course, gives a very short arc, and a slight inaccuracy in one of the observations may ; have a very great, influence on the predicted position of the comet. For July 4 of this 'year by Finsler,-of Zur-. ich. As soon as the necessary obseiv vations became available a parabolic orbit was computed, and the position in which the comet would appear in the sky was predicted from the computed orbit. ■; •■■:'■. A SECOND ORBIT. „. A few dayss-later.a.second orbit was published'!frp'm observations -made on' July,1 4,6, and 7. The position predicted for August 11 from the second orbit, differed by fen degrees from that predicted from the first- orbit. Using' observations from July 4, 10, and 14, a third orbit was computed. The position for August 11 from the orbit computed from this longer arc differs by two degrees from the position from the second orbit. " Later, if the observed position of the comet differs much from the position predicted from this third orbit, another orbit will be, computed from observations extending over a longer arc. Finally, when the cornet has disappeared all the. observations will be collected and an orbit will be computed in which the attraction of the planets is allowed for. ■ From this final orbit, again making allowance for the attractions of the planets, the date of return, if it should be a short-period comet, will be computed,/ But this is a long and very tedious task and one not to be undertaken lightly. . The two difficulties in determining exactly the time of return of a periodic comet are, then, first, the difficulty arising from the small inaccuracies of observation and the short arc overwhich the observations .extend; arid,: second, the disturbance in -the orbit produced by the attraction of the planets. That these disturbances are by no means negligible is shown iby Halley's comet, to quote the most familiar case. The average interval between returns of this comet is 77 years, but the actual, interval'between returns may be two and a'half years on either side of this average, the longest interval being that ending in 530 A.D., and the shortest that • ending at the last return in 1910. ATTRACTION BY PLANETS. The effect of a planet in producing a disturbance depends on the mass of the planet and on the distance of the comet from it; it is proportional to the mass and inversely proportional to the square of the distance. The two planets that will have greatest effect will be Jupiter and Saturn, the most massive of the planets. If the comet approaches close to either of these, the disturbing effect will be very large, and increases rapidly with closer approach. A remarkable example of an orbit greatly changed by the attraction of Jupiter is that -of the comet discovered by Schwassmann and Wachmann at Hamburg in 1929. The orbit of this was unusual, as it lay entirely within the orbit of Jupiter. A diagram shows the orbit of this comet lying between the orbits of the earth and Jupiter, with the sun in the centre of the earth's orbit. The motion of each was from right to left in the upper part of the diagram. In tracing back the position of the comet before its discovery, it was found that in 1926 the comet was close to Jupiter, so that Jupiter would cause a large disturbance in the comet's orbit. Computing back, step by step, always allowing for the attraction of Jupiter it was found that on March 26, 1926, the comet was less than 17.000,000 miles from Jupiter.

Amongst the large number of comet? for which, orbits have been computed, the great majority have elliptical or parabolic orbits; there are a few, however, for which hyperbolic orbits have been computed. This raises the interesting question of: the origin ok comets, whether they have been permanently members of the solar system, or have entered the solar system from without.

In the latter case we would expect to find a number of orbits which were

markedly hyperbolic—the comet would approach the sun, and then recede, never to return. But in actual fact the hyperbolic orbits differ little from parabolas, none being conspicuously hyperbolic. The hyperbolic orbits have been investigated, chiefly at Copenhagen, under the leadership of Stromgren. The orbits have been traced backward step by. step,. and it has been found that the present hyperbolic form of the orbits had been produced by disturbances arising from the planetary attractions, the original orbits at great distances from the sun being distinctly elliptical. As far as our present knowledge goes, there is no case in which it can be shown that the original orbit was hyperbolic. There are, indeed, a few cases in which the orbit as computed is hyperbolic, but the departure from the parabola is so slight that it may be looked on as illusory, arising from lack of sufficient observations to enable an accurate orbit to be computed.

It appears, then, that the comets have always been members of the solar system, moving in elliptical orbits round the sun, including the parabolic orbit as a limiting case. Occasionally the orbit may be changed by the attraction of the planets into a hyperbolic orbit, in which case the comet will leave the solar system never to return. But the total number of comets in the solar system may run into hundreds of thousands, so that the supply is not likely to be exhausted soon.