Jupiter Saturn Neptune Venus "Saros" Cycle

Robert Tulip · #1 (**permalink**) 09-August-2008, 01:01 AM

Jupiter, Saturn, Neptune and Venus (JSNV) follow 179 year cycles which overlap in a similar way to the Saros cycle of eclipses, due to the interaction of several factors with similar orbital wavelengths.

An example of the overlapping cycles of the conjunctions of these four planets is as follows. In 54AD, a Jupiter Saturn conjunction followed their conjunctions with Neptune by two months for Jupiter and a year for Saturn. In successive 179 year repeats of this event, in 232-3, 411, 590, 769, 948, 1127, 1306-7, 1484-7, 1663-7, 1842-6, and 2021-5, the gap between the JS conjunction and their respective conjunctions with Neptune steadily decreases to a point where these three are near exactly conjunct in 769, after which JS meet an increasing time before they reach Neptune. This pattern overlaps with other families of JSNV conjunctions, for example 1344-5, 1523-4, 1702-3, 1881-2, 2060-1. This 1344-2060 group has 1523 as the year of closest JSN alignment, with the JS conjunction precessing against the JN and SN dates as in the 54-2021 series. In all cases each event is about 30° further along the ecliptic than its predecessor 179 years before. These families of repeating conjunctions, of which Venus is also a part, are produced by the small difference in orbital periods with 9 x JS=178.7 ~= 14 x JN = 178.9 ~= 5 x SN = 179.3 years. Interestingly, these orbital JSN periods produce a clear gravitational pattern in the wave function of the solar system barycentre as shown here.

The similarity with the Saros cycle is that eclipse families begin with inexact alignments producing short eclipses near the earth’s poles, but as the alignment improves each family of eclipses grows in length and width and migrates towards the equator and the other pole. Each family returns every 18 years, and there are about 40 simultaneous Saros eclipse families.

grant hutchison · #2 (**permalink**) 09-August-2008, 01:59 AM

Jupiter and Saturn reach heliocentric conjunction in a cycle of 7253.45 days, on average. Multiply by nine, and you have 65281 days = 178.73 years. In that time period, Jupiter travels through 15 revolutions + 24.28 degrees, Saturn through 6 revolutions + 24.28 degrees, and Neptune through 1 revolution + 30.50 degrees. So after nine Jupiter-Saturn conjunctions (~179 years), Neptune returns to almost the same relative position - the error is 30.50-24.28 = ~6 degrees. Uranus hits tolerably close to the same period: 2 revolutions and 45.80 degrees during nine Jupiter-Saturn conjunctions, so it accumulates an error of ~21 degrees per 179-year cycle. The inner planets go around sufficiently quickly that they can be accommodated to the same rhythm with only a little tweaking.

Hence the famous 179-year cycle that is always mentioned in discussions of the Voyager 2 "Grand Tour" incorporating Earth, Jupiter, Saturn, Uranus and Neptune.

Grant Hutchison

Robert Tulip · #3 (**permalink**) 09-August-2008, 03:36 AM

Thank you Grant, I had not seen information on the Voyager Grand Tour use of the outer solar system via this once-in-179-year launch window. This site states

Quote:

In the late 60's and early 70's a Grand Tour of the Outer Planets was being advocated by the Jet Propulsion Laboratory, in particular, and by other planetary enthusiasts who were advising NASA on new programs. JPL had shown that the forthcoming configuration of the outer planets Jupiter, Saturn, Uranus, and Neptune (a once-in-179-year phenomenon) would make it ballistically feasible to have a single spacecraft fly by all four of these remote planets. The Grand Tour, as such, was a budgetary casuality of late 1970. Soon, thereafter, I was asked by JPL to chair a Science Working Group to develop a more modest-sounding mission, tentatively called MJS (Mariner/Jupiter Saturn). The two-spacecraft mission that we developed was eventually approved and came to life in 1974. It was later renamed Voyager. Although the term Grand Tour was now eschewed in polite conversation, it did not escape our attention that the configuration of the outer planets was independent of budgetary-political considerations in the White House and the Congress.

To explain further on the similarity with the Saros cycle, wikipedia states

Quote:

repeat occurrences of ... lunar phases are controlled by the Moon's synodic period, which is about 29.53 days. ... The period of time for two successive passes of the ecliptic plane at the same node is given by the draconic month, which is 27.21 days. Finally, if two eclipses are to have the same appearance and duration, then the distance between the Earth and Moon must be the same for both events. The time it takes the Moon to orbit the Earth once and return to the same distance is given by the anomalistic month, which has a period of 27.55 days. The origin of the Saros cycle comes from the recognition that 223 synodic months is approximately equal to 242 draconic months, which is approximately equal to 239 anomalistic months (this approximation is good to within about 2 hours). What this means is that after one Saros cycle, the Moon will have completed an integer number of synodic, draconic, and anomalistic months, and the Earth-Sun-Moon geometry will be nearly identical: the Moon will have the same phase, be at the same node, and have the same distance from the Earth. If one knew the date of an eclipse, then one Saros later, a nearly identical eclipse should occur. However, the Saros cycle (18.031 years) is not equal to the precessional period of the lunar orbit (18.60 years). Therefore, even though the relative geometry of the Earth-Sun-Moon system will be nearly identical, the Moon will be in a different position with respect to the fixed stars. A complication with the Saros cycle is that its period is not an integer number of days, but contains a fraction of ⅓ of a day. Thus, as a result of the Earth's rotation, for each successive Saros cycle, an eclipse will occur about 8 hours later in the day. In the case of an eclipse of the Sun, this means that the region of visibility will shift westward by 120°, or one third of the way around the globe, and the two eclipses will thus not be visible from the same place on Earth. In the case of an eclipse of the Moon, the next eclipse might still be visible from the same location as long as the Moon is above the horizon. However, if one waits three Saros cycles, the local time of day of an eclipse will be nearly the same. This period of three Saros cycles (54 years 1 month, or almost 19756 full days), is known as a Triple Saros or exeligmos (Greek: "turn of the wheel").

In looking at the 179 year period of the major planets, a similar 'integer' relation exists between JSx9=JNx14=SNx5=179yrs as with the three factors of the eclipse cycle, and we can see a similar slow drift of emergence and departure.

Robert Tulip · #4 (**permalink**) 11-August-2008, 02:52 AM

The attached pictures show five successive examples of a family of Jupiter Saturn Neptune Venus conjunctions, separated by 179 year periods, in 53-4, 232-3, 411, 590 and 769 AD. The circled points show five near-exact SNV alignments. Venus meets Saturn and Neptune about a week after their 53 conjunction, and about a week before their 769 meeting. This very slow drift of only two weeks over the 716 year period illustrates that the VS, VN and SN periods are integer fractions of near-identical 179 year periods. The drift of the JS conjunction towards this stable SNV group is also clear in the illustrations. Data here is tropical and geocentric, but is readily available in sidereal and heliocentric formats as well.

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