Onset Of Chaotic Behaviour

The Minimum Orbit Intersection Distance, or MOID, between two orbits evolves under orbital precession. During epochs when its value is very small, close approaches between objects moving on the two orbits are possible if the objects reach their near-intersection point at a similar time.

The MOID between 55P/Tempel-Tuttle and Earth is moderately small for some millennia about the present. This means that at any given time there are some particles in the Leonid stream with a small enough MOID to permit close enough approaches to be substantially deflected by the Earth's gravity. Of course, the closest approaches of all are impacts, resulting in meteors, and the comet's small MOID is the reason why meteor storms are possible, since just a small perturbation of the nodal position is required to bring orbits to Earth intersection.

Some breaks in the smooth, slowly varying behaviour of the trail are evident in Figure 1 (easiest to see in the last of the 4 plots as the gaps progressively widen). For example, parts of the trail at Aa0 ~ —0.04, +0.17, +0.38, etc. came close to the Earth at one year intervals in the 1830s epoch (—0.04 in 1832, +0.17 in 1833, etc.). There is a similar sequence corresponding to the 1860s epoch, e.g., +0.09 in 1866, +0.20 in 1867, +0.31 in 1868, although some gaps are smaller (and may not be noticeable at the resolution plotted in Figure 1) because the approach distance to the Earth was greater.

Therefore after a close approach, a break is present at that point in the trail at subsequent times. Although trails are generally disrupted because of approaches to the giant planets [1], the most noticeable gaps in Figure 1 are identifiable with Earth approaches. This is consistent with the fact that for the past several centuries, the MOID between 55P/Tempel-Tuttle (aphelion near orbit of Uranus) and Jupiter and Saturn has been well above zero. Precession in the argument of perihelion means that the MOID to Saturn approached zero ~0.9 kyr ago. At present we are approaching an epoch when the orbit of Uranus is intersected, although currently a near-commensurability keeps the comet, and parts of trails not too distant from the comet, safe from the closest possible Uranus approaches [7]. Thus Leonid trails that have formed during recent centuries have evolved under circumstances where the only very close approaches have been to Earth.

Particles ejected in 1800

S 1500 oo

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