(meteorobs) The Ursids, Part 2

An Upcoming Outburst of the Ursids?
Part 2: The Analysis
By Gary W. Kronk, Rainer Arlt, and Richard Taibi

Abstract----------------------------------------------------------------

An investigation of the evolution of the Ursids has been conducted. The purpose of the investigation was to look at how the meteoroids would disperse within the orbit of the parent comet 8P/Tuttle. As with the studies which successfully predicted the appearance of the Leonid meteor showers in 1999 and 2000, the formation of ringlets were looked for. Of primary interest was why outbursts of meteors were detected from the Ursids in 1945 and 1986, some six years after the parent comet had passed perihelion.

Analysis----------------------------------------------------------------

[Heavily summarized by key points]

*As of 2000 December 20, six different integration sets, involving a total of 107 imaginary particles moving in the Tuttle/Ursid orbit have been run for periods as short as 3 years and as long as 500 years. These generated a total of 2700 orbits. In addition, two different orbits for 8P/Tuttle were integrated with the particles in two different sets in order to double-check accuracy.

*With respect to the 8P/Tuttle integration, the 1900 December 29 Jupiter encounter was duplicated with a 3-day error after a 97-year integration from 1803, and the 1994 December 29 Jupiter encounter was duplicated with an error of 4 days after a 55-year integration from 1939. These errors are well within the range of acceptability considering that nongravitational forces were not taken into account in the calculations. 8P/Tuttle does experience nongravitational effects.

*An important beginning point in the analysis was the determination of how long it would take for meteors to completely spread throughout the orbit of 8P/Tuttle. In order to derive a time-scale on which particles spread along the orbit of the Comet, we may assume an ejection velocity of 10 m/s in the direction of motion of 8P/Tuttle. The original semi-major axis of a=5.672 will increase to a=5.700 due to the speed up from 40.22 km/s at perihelion to 40.23 km/s. The orbital period increases accordingly from P=13.508 yr to Pnew=13.609 yr. The slight difference will cause particles to lay half an orbit BEHIND the Comet after about 67 revolutions, or roughly 900 yr. We can estimate the number of revolutions n by n = 1/2 P/(Pnew - P). This time gives an indication for time needed to fill the orbit of the 8P/Tuttle with particles. Radiation pressure will additionally increase the orbital period and shorten the filling time-scale.

*As soon as orbital integrations began, a new factor became apparent in the spread factor. Encounters between Jupiter and material within the Tuttle/Ursid orbit could play an important role in a more rapid distribution of the material throughout the orbit. A time scale of 500-600 years is not out of the question for complete dispersion of a particular cometary apparition dust cloud; however, the dispersion can not be homogenous.

*Jupiter can not presently approach to within 0.75 AU of the comet orbit, so the gravitational effects are never drastic. Nevertheless, alterations of about 0.2 years in the orbital period of objects within the Tuttle/Ursid orbit are possible during a Jupiter encounter. As Jupiter passes this point of closest approach Tuttle/Ursid particles that have already moved beyond this point will have their orbital periods decreased as Jupiter tugs on them. Those that have not reached this point will have their orbital periods increased as Jupiter pulls them. Particles that experience the closest possible approach will essentially end the encounter with an unchanged orbital period, because Jupiter will have increased the period early in the encounter and decreased it during the latter half of the encounter. This whole scenario puts the affected region into a state of expansion and, in a sense, the area of closest approach to Jupiter eventually becomes a "dead zone" virtually devoid of particles. The whole effect is like a boat cutting through water, with the sides of the boat's wake steadily moving away from each other. Of course the region will eventually be trespassed by other particles moving within the Tuttle/Ursid orbit.

*Jupiter passes close to the Tuttle/Ursid orbit once every 11.86 years. Assuming an average orbital period of 13.6 years, this indicates the center of the next affected area within the Tuttle/Ursid orbit will occur about 1.7 years ahead of the center of the last affected region; however, it will occur only 1.5 years ahead of the particles that had been perturbed into a shorter period orbit. These shorter period particles will be referred to here as "condensation A". Condensation A will also be affected by the new Jupiter perturbation, the result of which will be an increase in its orbital period. This can virtually stop the advance of this group away from the "dead zone" created by the last Jupiter encounter. It also sets up a situation where the particles that have their orbital periods increased by the new Jupiter encounter could advance toward condensation A, causing a denser pocket of particles. Back-to back encounters is the limit for any group of particles. Thereafter they will experience virtually no perturbations for another 90 to 100 years. We believe this scenario could explain the large variations in the observed rates for the Ursids.

*What happened to the meteoroids that caused the 1945 outburst? The condensation responsible would have passed perihelion on 1946 January 12. A total of 19 imaginary particles were integrated from 1945 December 15 to 2001 January 15. These particles covered a wide range of perihelion dates spanning 80 days, centered on the 1946 January 12 date. The imaginary cloud of material would have been strongly affected by Jupiter in 1948 and 1960. The result was the span of perihelion dates was reduced from 80 days in 1945 to only 13 days by 2001, indicating a strong focusing affect. As it turns out, the 1945 meteoroids would not have encountered Earth again during this period, although the highly concentrated knot probably just missed encountering Earth in 1999. Integrating backwards to 1850, revealed a double Jupiter encounter in 1853 and 1865 which would also have compressed the distances of material in those areas of the orbit. It was probably these two early encounters that set the stage for Earth's encounter with a dense cloud of meteoroids in 1945. Another integration was run involving 10 particles with different orbits and orbital periods ranging from 13.3 to 13.7 years, but with the perihelion dates set at 1946 January 12. Interestingly, these particles went through the same two strong Jupiter encounters, which altered the range of orbital periods to 13.5 to 13.7 years by 2001. This indicates the group was not only focused over time, as were the other 19 integrated particles, but the alteration of the orbital periods gave the group some permanance.

*What are the chances of a strong meteor shower in 2000? A total of 12 particles were integrated backwards, including 8 with random orbits and orbital periods (these were pulled from one of the other long-term integrations). The location of this swarm brought only minor perturbations by Jupiter in 1960 and 1948. The four particles moving in identical orbits in 2001 changed little in their orbital separation back to 1940. Interestingly, the random objects did move far away from one another as the orbits were integrated backwards. In addition, where the random orbits had periods of 13.50 to 13.62 years in 2001, their periods ranged from 13.20 to 13.26 back in 1940. This displays the reverse effect as was seen with the 1945 particles, indicating the Jupiter perturbations have had more of a dispersing effect during the last 60 years. Because of this, it is believed that no strong Ursid shower will be observed on 2000 December 22.