Motion Of Comet Research Articles

A Method of Integrating the Equations of Motion in Special Coordinates and the Elimination of a Discontinuity in the Theory of the Motion of Periodic Comet Wolf

From the integration formulae of Numerov and Subbotin we have developed and programmed for an electronic computer a particular method for integrating the differential equations of cometary motion in special rectangular coordinates, with a variable step and allowing for all planetary perturbations and nongravitational effects over a time interval of 400 yr. Application of this method and our set of programmes to the investigation of the motion of P/Wolf permits us to eliminate the discontinuity that has hitherto existed in the theory on account of the comet's close approach to Jupiter in 1922.

The Solution of Problems of Cometary Astronomy on Electronic Computers

A series of standard programmes has been developed for numerical integration by Cowell's method of the differential equations of motion of minor bodies. A variable step is used, and perturbations by eight major planets and nongravitational effects are taken into consideration. Further programmes have been constructed as part of a general attempt at ITA to produce numerical theories of cometary motion. They include the reduction of observations, the comparison of the observations with theory and the improvement of orbits. The programmes make it possible to calculate (O–C) residuals of up to 2000 observations simultaneously.

Comets and Nongravitational Forces. II

view Abstract Citations (83) References (13) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Comets and Nongravitational Forces. II Marsden, B. G. Abstract The orbits of six short-period comets and one long-period comet are determined by the use of equations of motion that include terms for a nongravitational force. It appears that the radial component of this force is almost invariably outward from the sun, the transverse component is about an order of magnitude smaller, and there is no component perpendicular to the orbit plane. This result is completely consistent with Whipple's model of an icy-conglomerate comet nucleus, and indicates that the lag angle between the direction of the maximum mass ejection and the subsolar point is small. It also appears that the magnitude of the nongravitational force (at any rate the transverse component) decreases with time, with the volatile materials in the nucleus presumably being depleted. It seems all the more probable that P/Arend-Rigaux and P/Neujmin 1, comets that are decidedly asteroidal in appearance, represent a transition phase between a comet and an asteroid of the Apollo type. There is also some evidence that additional nongravitational forces, probably random and impulsive in nature, also affect the motions of comets. Publication: The Astronomical Journal Pub Date: June 1969 DOI: 10.1086/110848 Bibcode: 1969AJ.....74..720M full text sources ADS |

The sungrazing comet group

view Abstract Citations (100) References (23) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The sungrazing comet group Marsden, B. G. Abstract The principal effects of planetary perturbations on the orbit of a sungrazing comet are derived, both from a simplified general theory and by direct numerical integration of typical trajectories. New orbit determinations are made for the three most recently observed members of the Kreutz group: comets 1965 VIII, 1963 V, and 1945 VII. For comet 1965 VIII the results are obtained in terms of both general relativity theory and the Brans-Dicke theory, but the observations are insufficient to enable one to decide which theory is correct. Some remarks are made about the less certain members of the comet group, and evidence is provided for dividing the comets into two distinct subgroups. Studies on the past motions of comets 1882 II and 1965 VIII reveal it as virtually certain that these comets separated from each other at their previous perihelion passage, and it seems possible that they were then observed as the comet of 1106. Not all the members of each subgroup can be explained so simply, but it is probable that the subsidiary separations took place not more than two revolutions ago. The two subgroups can presumably be explained by a similar split some 10 to 20 revolutions ago, although a few other possible explanations are touched upon in the final section. An ephemeris is provided for use in searching for further members of the group. Publication: The Astronomical Journal Pub Date: November 1967 DOI: 10.1086/110396 Bibcode: 1967AJ.....72.1170M full text sources ADS |

The rôle of measurement in the downfall of a system: Some examples from sixteenth century comet and nova observations

While the “new” star of 1572 was still visible there were statements to the effect that it was further from the Earth than the Moon, and therefore refuted the Aristotelian doctrine of the immutability of the heavens. The same is true of the comet of 1577 which, in addition, was thought to move across the supposedly crystalline spheres, and these eventually were discarded. Very crude measurements, some made without any instrument or with a thread held before the eyes, sufficed to indicate the supra-lunar position of the two phenomena. Slightly more accurate observations attested to the comet's motion across the spheres. Tycho Brahe's compilation of all the available observations, including his own quite accurate measurements, such as those of the distance of the nova at upper and lower culmination from a known fixed star in nearly the same meridian, gave weight to the acceptance of the supra-lunar position of novae and comets by the next generation of astronomers. The downfall of a system cannot be complete without the adoption of a new one. Discarding the spheres, which for centuries had accounted for the motion of the planets, necessitated the discovery of some other cause for their motion. In addition, the two phenomena strengthened Tycho's determination to observe the heavenly bodies carefully, and his observations were of just the right degree of accuracy to enable Kepler to derive the laws of planet motion.

A comet model. I. The acceleration of Comet Encke

view Abstract Citations (678) References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS A comet model. I. The acceleration of Comet Encke Whipple, F. L. Abstract A new comet model is presented that resolves the chief problems of abnormal cometary motions and accounts for a number of other cometary phenomena. The nucleus is visualized as a conglomerate of ices, such as H,O, NH3, CH4, CO, or CO, (C,N,?), and other possible materials volatile at room temperature, combined in a conglomerate with meteoric materials, all initially at extremely low temperatures (<50 K). Vaporization of the ices by externally applied solar radiation leaves an outer matriz of nonvolatile insulating meteoric material. Quantitative and qualitative study shows that heat transfer through tiiin meteoric layers in a vacuum is chiefly by radiation, that the heat transfer is inversely proportional to the effective number of layers, and that an appreciable time lag in heat transfer can occur for a rotating cometary nucleus. Because of the time lag, such a cometary nucleus rotating in the "forward" sense will emit its vaporized ices with a component toward the antapex of motion. The momentum transfer from the kinetic velocity of the emitted gas will propel the nucleus in the forward sense, reduce the mean motion, and increase the eccentricity of the orbit. Such orbital effects occur for Comet D'Arrest; the mean daily motion of Comet Wolf I also appears to be decreasing. Retrograde rotation can produce an acceleration in mean motion and a decrease in eccentricity, as observed for Comet Encke. If the decelerating force component is taken as its maximum theoretical value, the present observed acceleration in the mean motion of Comet Encke can be produced by a loss of 0.002 of its mass per revolution. The corresponding mass loss for Comet D'Arrest is 0.005. For both comets the observed changes in eccentricity are obtained if the force acts proportionately to the solar energy flux but is cut off at a solar distance of about 2 A.U. A second paper (Part II) soon forthcoming will be concerned with the physical problems of comet structure, loss of meteoric and gaseous material, and correlations with observed meteoric phenomena. Publication: The Astrophysical Journal Pub Date: March 1950 DOI: 10.1086/145272 Bibcode: 1950ApJ...111..375W full text sources ADS | Related Materials (3) Commentary: 1999ApJ...525C.393B Part 2: 1951ApJ...113..464W Part 3: 1955ApJ...121..750W

AN ATTEMPT TO DETERMINE THE MASS OF PLUTO FROM ITS DISTURBING EFFECT ON HALLEY'S COMET

While glancing through some volumes of the Monthly Notices of the Royal Astronomical Society of thirty years ago, the writer's attention was attracted by a statement1 regarding a discrepancy in the predicted return of Halley's Comet. The time of perihelion passage had been fixed with extreme care by P. H. Cowell and A. C. D. Crommelin,2 the simplicity and high precision of their method having won for them the Lindemann3 prize of 1000 marks offered for the best essay on the return of Halley's Comet. Starting with perihelion passage on November 16, 1835, as their zero date, they had traced the comet's motion, step by step, backward to perihelion in 1759 and forward to 1910, considering it to move under the combined attraction of the sun and all the planets except Mercury. Although the other elements could be determined from the observations

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COMET 1915d (MELLISH).—The discovery of a second comet during the present year by Mr. J. E. Mellish, Madison, Wis., U.S.A., was announced last Thursday in a telegram from Copenhagen. On September 6, at 22h. 9.1m., the comet's position was α 6h. 30.2m., δ 8° 50′ (approx. 8° south of γ Geminorum). No information was supplied regarding the direction or rate of the comet's motion, or of its magnitude.

On the Effects of Radiation on the Motion of Comets: (Second Note)

On the Effects of Radiation on the Motion of Comets: (Second Note)

On the Possible Effects of Radiation on the Motion of Comets, with special reference to Encke's Comet

On the Possible Effects of Radiation on the Motion of Comets, with special reference to Encke's Comet

The deduction of planetary masses from the motions of comets

The deduction of planetary masses from the motions of comets

Our Astronomical Column

THE THIRD COMET OF 1869.—This comet, the orbit of Which has so close a resemblance to that of the comet discovered by Mr. Swift on October 11, was detected at Marseilles by M. Tempel on November 37, 1869, in the constellation Pegasus, and appears to have been Inst observed on December 31 at Leipsic and Kremsmunstw, the hope of seeing it after the next period of moonlight not having been verified. On November 29 Dr. Vogel, observing at Leipsic, described it as a very faint large object elongated in the direction of the declination circle; in the comet-seeker its diameter was about 6′. On December 7 it was still very faint, large, and elongated in the direction 333°, the central condensation very slight. On the following night its diameter was 5′ it had “a peculiar milky appearance” and hardly any central condensation, so that observations were attended with difficulty. On the 21st it was seen only with much exertion of the eye, but on the 31st, though the comet was very faint, Prof. Bruhns considered his separate comparisons certain to about ten seconds of arc. At Kremsmunster Prof. Strasser found it “extraordinarily faint” during its entire visibility, and in consequence of wanting central condensation, very difficult to observe, and hence considered that his positions would not possess the ordinary degree of accuracy. The elements of the orbit werd calculated by Tiele, Oppolzer, Schulhof, and Bruhns, the parabolic orbit published by the latter in No. 1788 of the Astronomiscke Nachrichten being founded upon nearly the whole extent of observation; he remarks with respect to it:—“Eine angestellte Vergleichung hieslgen Beobachtungen scheint aber doch auf eine Abweichung der Bahn yon der Para bel hinzudeuten …” We are not aware that any farther examination of this point was made. If the period of revolution be really something less than eleven years, the circumstance of the comet having escaped observation prior to 1869 will not nevertheless occasion surprise, considering that both in 1869 and 1889 it has approached near the earth and has yet been very faint and diffused, so that when the perihelion passage has occurred at other seasons of the year it might be beyond reach of the telescope. it will be most essential for the theory of the comet's motion that observation should be continued as long as possible at the present appearance that if it prove to be one of short period its next return to perihelion may be closely predicted: the computation of the planetary perturbations during the period 1860–80 will of course be a necessary process with this object in view.

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WINNECKE'S COMET.—In No. 2,314 of the Astronomische Nachrichten Prof. v. Oppolzer has a note of more than ordinary interest on the motion of this body as investigated by his own calculations. He states that it results from his computation of the perturbations with the object of connecting the three appearances of 1858, 1869, and 1875 that a satisfactory agreement cannot be found without one of two hypotheses; either the mass of Jupiter must be diminished to 1/1051, or there is a necessity of admitting the existence of a similar extraordinary influence upon the motion of this comet to that first pointed out by Encke in the motion of the comet which bears his name. Prof. Oppolzer finds an acceleration in the mean daily sidereal motion of 0″.01439 after one revolution, a result which, he remarks, is in close accordance with his earlier one, deduced by a provisional calculation of the perturbations, from the observations made at the comet'S appearance in the summer of 1819. He infers from his researcheS upon Winnecke's comet a value for Encke's force designated by U, differing little from that assigned by Encke from his discussion of the motion of his comet, the more satisfactory considering that much latitude must be allowed in this direction. He further observes that with U = 1/900 the effect upon the motion of Faye's comet would be so small that it is necessarily mixed up with uncertainty in the values of the perturbations; it will be remembered that Prof. Axel-Möller, who has laboured so admirably to follow up with every precision the motion of Faye's comet, has not, since his computations assumed their present refined form, been able to detect any abnormal effect upon it.

An account of another small treatise, written in the High-Dutch and printed at Bazil, Anno 1681. Containing a new theory about the comets, invented by James Bernoully, the title whereof is thus expressed: A new introduction, shewing how the motions of comets may be reduced to some certain and geometrical rules, so that their appearance may be predicted.

Before he cometh to explain his Theory, he thinks it very convenient to say something of the Original cause of Comets, of their course and motion, of their place and tail.