Figure 2 presents time evolution of the mean orbital elements and the mean position of the ascending and descending nodes orbital nodes of the 21 VAs of the asteroid (101955) Bennu 5000 yr backwards and 1000 yr forward from the osculating epoch 2014 May 23.0 = JDT 2456800.5.
Generally, values of all orbital elements and positions of the ascending and descending nodes of all VAs of Bennu have greater dispersion 1000 yr in the future than in backwards because of the CAs with the earth in that time--see Section 8.
This has been the case for several millennia and it will continue long into the future, but after many more millennia, eventually, for transits taking place at Venus' descending node the southward displacement of the chord is replaced by a northward one.
The paths are parallel, but at the second transit the chord is displaced by about 24' to the south at the ascending node or by about 20' to the north at the descending node. After two returns the displacement is either 48' or 40', which exceeds the Sun's diameter of 32'; hence it is not possible for three transits to occur within sixteen years.
A list of transits from -2999 to 3000 was given by Meeus, (10) who introduced the alphabetical system for identifying each series, which uses upper case characters for transits occurring at the ascending node and the lower case for those at the descending node. This system has been retained here and in my earlier paper.
The present transit belongs to series c and we can tell at a glance that it takes place at the descending node. Table 4 presents a 'panorama' of transits between 1283 and 3000, grouped according to their series.
At present the Earth passes about 0.25 AU outside the descending node
and the orbital evolution will slowly decrease this distance, raising the possibility of a meteor shower from this comet in a few hundred years time.
The good news is that we are still on the inside of Giacobini-Zinner's orbit at the descending node. The gap has widened since 1985, but not by much, to 0.0383 a.u.
The first columns give the date (in Universal Time) when Earth arrives at the descending node of Comet Giacobini-Zinner's orbit.
These are the years when Earth follows Comet Giacobini-Zinner to its descending node just inside the comet's orbit.
If the node in SRM (goal) is OR node, then the DS for that node will be calculated based on sum of the descending nodes
. Otherwise if it is AND node, the DS will be calculated based on production of the descending nodes