Astronomy Answers
Conjunctions

Once in a while there are rumors about upcoming conjunctions of "all" planets, which some people expect to have great consequences on Earth. For example, there was some (unwarranted) panic about the conjunction of some planets in May 2000. This essay explains about conjunctions of planets and other celestial bodies, and that those have no measurable influence on Earth, except for the tides that the Sun and Moon raise.

1. What is a conjunction of celestial bodies?

Fig. 1: Picture of Jupiter, Saturn & Pleiades

How close together must the celestial bodies be to be in conjunction? That depends on who you ask. If you think it is only a "real" conjunction if two planets are less than 10° apart, but your friend is satisfied already with 20°, then your friend will see more and longer lasting conjunctions than you will.

If there are more than two celestial bodies involved, then you must decide when all of them are in conjunction. Is that when they all fit within a circle of a certain diameter? Or when the distance between each pair of successive planets (from left to right) is less than a limit value? Or do you use still another measure?

It is clear that the meaning of the word "conjunction" is not very precise. By adjusting your definition you can find few, or instead many conjunctions.

2. What does a conjunction mean?

Only one conjunction in the sky has noticeable influence on Earth, and that is the conjunction of the Sun and the Moon. Such a conjunction happens whenever it is New Moon, and then the tidal forces of the Sun and Moon add up and we have spring tide with on average a larger difference between high and low tide than usual.

The distances and masses of the planets are such that they have no measurable tidal influence on Earth. This is clear from the following table, which lists the maximum tides due to the planets and the Sun, compared to the tides due to the Moon. The strength of the tide due to a planet or other body increases when the mass of the body increases, but decreases rapidly (as the third power) when the distance of the body increases. The tides due to the Moon are more important than the tides due to the Sun because the much smaller distance of the Moon outweighs the much greater mass of the Sun.

The column "Name" lists the name of the (celestial) body. The column "Mass" displays the mass; for the planets, Sun, and Moon these are compared to the mass of the Earth. The column "Distance" shows the typical least distance from the Earth; for the planets, Sun, and Moon these are measured in Astronomical Units. The column "Tides" provides the magnitude of the tides due to that body when it is at the indicated distance, compared to the tides due to the Moon. Usually, the planet is further away than the minimum distance listed in the table, so usually the tides due to the planets are even smaller than those listed in the table.

It follows from the table that the tides on Earth due to the Sun are about half as strong as the tides due to the Moon, and that the tides due to all other planets combined are at their greatest still some 15,000 times smaller than the tides due to the Moon. If the difference between high and low tides due to the Moon is 1.5 m (3 ft) somewhere, then the difference due to the Sun is about 0.7 m (1.5 ft), and the difference due to all other planets combined is at most about 0.1 mm (1/250th of an inch): so small that it cannot even be measured.

The table also lists the tides due to a person of 70 kg (155 lb) at 1 km (0.6 mi) distance: those tides are even larger than the tides due to any planet! And every time that the distance of that person is divided in two, the tides increase eightfold. The tidal forces due to a person at about 40 m (120 ft) is comparable to the tidal forces due to the Moon. The distribution of all people, cars, buildings, and other heavy bodies within about 1 km (or 1 mi) from you has more influence on you than the configuration of the planets.

Of the four fundamental forces in the Universe, only gravity (and the associated tidal forces) is effective at great distances. If the tidal forces of the planets are negligible on Earth, then the other fundamental forces due to the planets are even more negligible on Earth. In short, conjunctions of planets sometimes provide pretty sights in the sky, but are otherwise of no importance.

3. How can you measure the closeness of a conjunction?

There is no clear border between having a conjunction and not having a conjunction, so it is more useful to use a measure that indicates how close the conjunction is at any moment. With such a measure, you can also effectively compare different conjunctions.

An obvious measure for the closeness of a conjunction of planets is the diameter of the smallest circle that encloses all of the planets, but that circle can usually only be found after a tedious search, and does not depend on the distribution of the planets within the circle.

A better measure for calculating is what I call the conjunction spread. The calculation of the conjunction spread is fairly easy and requires no searching, and this measure changes whenever any one planet's location changes.

You calculate the conjunction spread as follows: Determine for each planet that is included the vector of length 1 that points from Earth to that planet. Call the length of the average of all of those vectors r. The conjunction spread w in degrees is then equal to

(Eq. 1) w = √(−26262.45*ln(r))

with ln the natural logarithm. For planets distributed randomly across the ecliptic, with standard deviation s in the ecliptic longitude, w equals twice s. For two planets that are close together, their conjunction spread is almost equal to their distance from one another. (The conjunction spread then overestimates the distance by less than one percent for distances less than 40 degrees.)

4. What conjunctions have been and are coming?

4.1. Mercury - Saturn

I've calculated the conjunction spread (as seen from Earth) for the planets Mercury through Saturn, which can be seen with the unaided eye, for a period of five million days between 4713 BC and AD 8977. To calculate the positions of the planets, I used the VSOP model of Bretagnon and Francou. The conjunction spread during this period shows periodic behavior with main periods of 378.09, 398.88, and 779.94 days, corresponding to the synodical periods of the Earth with Saturn, Jupiter, and Mars.

The next table shows for a few values of the conjunction spread during which fraction of time the conjunction spread of Mercury through Saturn (as seen from Earth) is less than or equal to that value.

For example, the conjunction spread is smaller than 10.8° during only one ten thousandth of the time, and the conjunction spread is less than 125.4° during half of the time (and greater than that during the other half of the time).

Fig. 2: Diagram of the Chance for Conjunctions

The conjunction spread w is shown along the horizontal axis, measured in degrees. The vertical axis measures the chance (1 = everything) that the conjunction spread at a randomly selected moment is not more than the value displayed along the horizontal axis. For example, if you go up straight from the 10 on the horizontal axis until you hit the solid line and then go left until you hit the edge of the graph, then you end up at about 0.0001, which means that the part of the time during which the conjunction spread is 10° or less is equal to about 0.0001 or 0.01% or one part in ten thousand.

This diagram is a so-called double logarithmic plot. Short and longer dashes are indicated along the horizontal and vertical axes. Each next longer dash represents a value that is ten times (an order of magnitude) greater than the previous one, as the associated numbers show. To get the values of the short dashes you should multiply the value of the next left or lower longer dash with 2, 3, 4 through 9. Then comes another longer dash which represents 10 times as much as the previous longer dash. The first couple of values associated with the longer and short dashes starting at the 1 in the lower left-hand corner of the diagram are: 1 (long), 2 (short), 3 through 9 (short), then 10 (long), 20 (short), 30 through 90 (in steps of 10), then 100 (long), 200 (short), and so on.

The dashes line shows the results of an approximation formula, equal to

(Eq. 2) P(<w) = 1.3*10(−8)*w(3.5)

Fig. 3: Conjunction Spread Diagram

The next reasonably close conjunction occurred in May 2002, with a conjunction spread of 23°. Conjunctions that are as close or closer than that one occur about 26 times per 1000 years during the investigated period (without a clear period of repetition).

Fig. 4: Conjunction Intervals Diagram

(Eq. 3) w = 75*(t − 0.35)(−0.34)

Below is a table with information about the top 30 of closest conjunctions (with the smallest conjunction spreads) of Mercury through Saturn during the period 4713 BC - AD 8977:

The column marked "JD" shows the Julian day number. The column "a" (annum) contains the number of the year in astronomical reckoning (which recognizes a year 0; year −2 corresponds to 3 BC). The columns "m" and "d" list the month number (January = 1, and so on) and the day number. The dates are given in the Julian calendar for years up to AD 1582, and in the Gregorian calendar for later years. The column marked "w" lists the smallest conjunction spread for the conjunction (in degrees), and column "r" the rank of the conjunction in this list (number 1 is the closest). The column marked "c" shows the location of the center of the group of planets in the sky, relative to the Sun (in degrees). A positive number for "c" means that (most of) the planets are East of the Sun and therefore visible in the evening. A negative number means that (most of) the planets are West of the Sun and therefore visible in the morning (before sunrise).

The narrowest conjunction of Mercury through Saturn during the investigated period will occur in January AD 5874, when the conjunction spread will be only 2.7°. The narrowest so far (since the beginning of the period) occurred in February 1953 BC, when the conjunction spread was 3.0°. The next future conjunction from the top 30 of the investigated period comes in September 2040, when the conjunction spread will be 7.7°. The last conjunction that was closer than that occurred around 25 June 710. The last top 30 conjunction happened around 19 february 1524, when the conjunction spread was 9.1°.

The conjunction of May 2000 happened too close to the Sun to be well visible, with some planets close and East of the Sun, and the others close and West of the Sun. In that respect, the conjunction of May 2002 was better, and the conjunction of September 2040 willl be better, with the planets on average 29 and 24° East of the Sun (and so visible in the evening).

Here is a table similar to the previous one, but showing the top-30 of the period from 1 January 1000 through 1 January 3000.

4.2. Venus - Saturn

Mercury is a bit difficult to see from Earth, because it is never far from the Sun and does not get particularly bright. The four other planets that are visible to the unaided eye, Venus - Saturn, have their closest conjunction in the investigated period around 8 January 6728 (2.4°). The next top-30 conjunction of these planets occurs around 4 February 2378 (2.4°), and the most recent one from the top 30 occurred around 6 June 1564 (4.2°). During the conjunction of September 2040 the spread is 5.9°, but that one is not in the top-30.

4.3. Mercury - Neptune

The seven planets Mercury - Neptune have their closest conjunction (in the investigated period) around 28 October 7838 (16.3°). The next top-30 conjunction of these planets occurs around 21 March 2673 (25.1°), and the most recent one was around 2 January 1665 (28.4°). It is clear that the more planets are included in the conjunction, the wider most of them are. With these seven planets the closest conjunction has a spread of 16.3°, whereas with the four planets mentioned before the smallest spread is only 2.4°.

4.4. Mercury - Pluto

The orbital periods (around the Sun) of Uranus, Neptune, and Pluto are 84, 165, and 248 years. Formulas for accurate calculation of the position of Pluto are available to me for only a few centuries around 2000, so I cannot easily include Pluto in the investigation of the standard period of over 13000 years. It appears, however, that Pluto is caught in a 3:2 orbital resonance with Neptune, such that each two orbits that Pluto completes around the Sun are on average exactly as long as three orbits of Neptune. This means that Neptune and Pluto return to approximately the same relative positions every 496 years.

My (rough) calculations for one such period show that Pluto and Neptune never get closer to each other in the sky than about 11° (the Redshift 3 planetarium program yielded 8.9° as the smallest separation), and that the next time for this to happen is in September 2383 (and about every 496 years after that, because of the orbital resonance). Comparison with the top-30 conjunctions of Mercury - Neptune shows that a close Neptune-Pluto conjunction always occurs 20 to 25 years after a fairly narrow conjunction of Mercury through Neptune. (This happens mostly because the orbital period of Uranus fits 496 years almost a whole number of times.) During such a Mercury - Neptune conjunction, Neptune and Pluto are about 28 - 34° apart, which is comparable to the conjunction spread of Mercury - Neptune during that period. Three of the top-30 conjunctions of Mercury - Neptune may have an accompanying Neptune - Pluto conjunction: those of 1099 BC, AD 969, and AD 5455.

It appears, then, that there is some sort of conjunction of all planets about once every 500 years, but that the conjunction spread is at least about 30° (and probably often a lot more).

5. How close together can the planets get?

In movies (such as Lara Croft: Tomb Raider from 2001) they sometimes show conjunctions of all (or at least many) planets where these planets line up exactly, or at least appear so close together in the sky that you can see them all as big disks close together through a powerful telescope, but in reality such an alignment never happens. We saw earlier that the smallest conjunction spread of Mercury - Saturn (as seen from Earth) between 4713 BC and AD 8977 is 2.7°, which is about 5 times the apparent size of the Moon, and 180 times as large as the apparent diameter of Jupiter in the sky.

Fig. 5: Planet Orbits

Fig. 6: Diagram of the Closest Possible Conjunctions

The smallest possible conjunction spreads (of Mercury - Saturn) is never greater than 1.21° (as is approached on 23 May and 26 November), and is never smaller than 0.30° (as is approached on 13 March near ecliptic coordinates 325°, −1° and elongation 29° east, and on 3 September near ecliptic coordinates 145°, +1° and elongation 18° east). These closest possible conjunctions always occur at least 6° and at most 29° from the Sun. If such conjunctions happen between about 10 December and 19 February or between about 9 June and 15 August, then they happen east of the Sun (so they are visible after sunset), and otherwise west of the Sun (so they are visible before sunrise).

The best visible of the closest conjunctions of Mercury through Saturn would happen near a 13 March at 29° east of the Sun, with a conjunction spread of 0.3°. The planets would then appear in the sky strung out along a line with a length of about 0.4°, which is only slightly less than the apparent diameter of the Moon, but is still 40 times greater than the apparent diameter of Jupiter, which would then appear biggest of the planets. So, even in the most favorable case (which has not occurred during the last 6500 years, and will not occur during the coming 6500 years, either) the planets are still far apart, compared to their apparent sizes.

The following table shows the closest conjunctions of all pairs of planets from Mercury through Pluto in the Earth's sky between the years −4712 and +8977. The VSOP model is used for all planets except Pluto, at a resolution of 1 day. For Pluto, a certain fixed elliptical orbit is assumed. The top right half of the table displays the smallest distance, measured in degrees. The bottom left half of the table shows the corresponding date in the Gregorian or Julian Proleptic calendar (in the order year month day).

For example: the closest conjunction of Mercury and Mars (in the chosen period) happened on 25 December −1255 (in the Julian Proleptic calendar) when those planets were only 0.0006 degrees apart in the sky.

Warning: The accuracy of the VSOP model is finite. The accuracy decreases when one goes further away from the year 2000. The accuracy is estimated at about 0.0003 degrees at about 2000 years from the year 2000 for the inner planets, at about 4000 years from the year 2000 for Jupiter and Saturn, and at about 6000 years from the year 2000 for Uranus and Neptune. If we assume that the inaccuracy increases as the square of the time distance from the year 2000, then the accuracy at the beginning and end of the calculation period that the above table is based on would be about 0.003 degrees for the inner planets, about 0.001 degrees for Jupiter and Saturn, and about 0.0003 degrees for Uranus and Neptune. Some of the distances listed in the above table are smaller than that. If those distances belong to dates near the ends of the calculation period, then they are not trustworthy.

The smallest distances between Pluto and the other planets are not nearly as accurate as the smallest distances between the other planets, because the orbit of Pluto is not known very well (to me).

The smallest distances between the planets as seen from Earth are in some cases small enough that one of those planets might (partially) obscure (occlude) the other planet. This might be the case for Mercury with Venus, Mars, or Jupiter; for Venus with Mars, Jupiter, Uranus, or Neptune; for Mars with Jupiter or Uranus; for Jupiter with Uranus or Neptune; and for Saturn with Neptune.

Below is a table that shows three close conjunctions before 1 January 2005 and one close conjunction after 1 January 2005 for all pairs of planets, as seen from Earth. Each row of the table displays the name of the two planets, followed by four pairs of a date in the Gregorian calendar and the distance that those planets reach on that date, measured in degrees. The last column lists the distance limit above which no occultation can happen. If the mutual distance is not less than or approximately equal to that limit value, then the two planets won't occlude each other. If the mutual distance is less than the limit value, then there is a chance that the two planets will (partially) occlude each other. The only conjunction from the below table for which an occultation is possible is the one of Jupiter and Neptune on 19 September 1702, for which a separate calculation at greater resolution indicates that the smallest mutual distance is only 0.00066 degrees, which is small enough that an occultation will take place.

6. Where are the planets now in the sky?

Through the Planet Positions Page you can find diagrams of the positions of the planets relative to the Sun, as seen from Earth, for some years before and after the year 2000. The diagrams below show the positions of the planets Mercury through Neptune for the years 2000 through 2003 and for 2040 and 2041, relative to the Sun. Find the desired time of the year on the horizontal axis, and then go straight up until you cross the line of the planet of interest. Then go straight to the left to find the associated time on the vertical axis. That number is the time difference between the planet and the Sun, measured in hours: the planet is due South that many hours earlier (for a negative number) or later (for a positive number) than the Sun, and the rising and setting of the planet are also approximately that much sooner or later than those of the Sun.

If a planet is in the top part of the diagram, then it is visible after sunset. If the planet is in the bottom part of the diagram, then it is visible before sunrise. If the planet is close to the upper or lower edge of the diagram, then it is visible (almost) all night, and hence in opposition. If the planet crosses the center horizontal line (the location of the Sun), then the planet is in conjunction with the Sun. If the trajectories of two planets cross in the diagram, then those planets are in conjunction with each other. If a number of planets are close together in the diagram, then they are all in conjunction with each other.

For example, midway through the year 2000, Mercury lags the Sun by about 2 hours, and Mars and Venus are in conjunction with the Sun. Jupiter and Saturn are close together during all of 2000, and are in opposition towards the end of 2000. Around May 2000 (near 2000.4 on the horizontal axis) Mercury and Saturn are all reasonably close together (in conjunction), but Uranus and Neptune do not participate. Midway through 2001, Mars, Uranus and Neptune are in opposition, Jupiter and Saturn are in conjunction with the Sun, and Venus is the morning star. The conjunctions of Mercury through Saturn around May 2002 and around September 2040 in the evening sky are also visible, and again Uranus and Neptune do not participate.

Fig. 7: Planets Diagram 2000-2001

Fig. 8: Planets Diagram 2002-2003

Fig. 9: Planets Diagram 2040-2041

languages: [en] [nl]

http://www.astro.uu.nl/~strous/AA/en/samenstand.html;
Last updated: 2007-12-02