Planetary alignments

Recently I received a few email questions about a special planetary alignment that is supposed to occur in May of 2000. Here I explain about planetary alignments.

What is an alignment?

In everyday use, when things are "aligned", then they are in the same orientation and their centers are exactly on a straight line. If you look at such things along the straight line, then they all seem to be in the same place, and part or all of the things that are in the back are obscured by the things that are in the front (unless the things are transparent). Most of the time, things get out of alignment already when they are moved sideways over just a small fraction of their size.

If aligments of planets were judged the same way, then a planetary alignment would mean that one planet was eclipsing part or all of another planet, but the planets are almost never lined up like that, as seen from any particular location. If alignments of planets were judged as strictly as that, then alignments between just two planets would happen very rarely, maybe once or twice in a lifetime, and alignments between three or more planets would be much rarer still. I expect that no human ever (past or present) has witnessed such an alignment between all five planets visible to the unaided eye.

Because eclipses between planets or other things in the sky that seem small are so very rare, it does not make much sense to reserve the word "alignment" for them. So, alignments in the sky are much more relaxed than alignments in everyday life. When two or more things in the sky are aligned, then they are visible in about the same direction. How close do they have to be for it to be considered an alignment? That depends on who you talk to. If you demand that two planets be separated by not more than thirty degrees (for example) to be declared "aligned" and your friend is satisfied already with a separation of sixty degrees, then your friend will see more alignments and for longer periods than you will.

Also, you can measure the distance between the planets along the sky in different ways. A very common way is to measure the distance only along the ecliptic, and to disregard the relatively small distance that the planets may wander away from the ecliptic. The position of a planet is then indicated by its geocentric ecliptical longitude only, disregarding its ecliptical latitude. This is similar to how you specify your position along a highway: you mention the mile marker nearest you but not how many feet you are from the edge of the road.

When more than two planets are involved, then you must also decide when all of them are in alignment with each other. Is that when the distance between any two planets (going from left to right) is less than your limit value, or when the distance between any two planets in any order is less than the limit value, or do you use yet another criterion?

There is a vagueness about the word "alignment". By judicious selection of the rules of what is and what is not an alignment, you can either find very many, or hardly any alignments.

What do alignments mean?

Alignments of planets sometimes yield pretty pictures for sky gazers, but are otherwise totally unimportant. Astrologers read more into planetary alignments, but in scientific studies astrology (which is based on planetary alignments and such) has proven as unreliable a source of predictions as dice rolls or coin tosses. The other planets are much too far away to have any significant influence on our planet, and planetary alignments do not cause disasters such as floods or droughts.

Alignment quality

Here I shall study alignments in a different way. Rather than deciding beforehand what distance separates an alignment from something that is not an alignment (which, as we saw above, is rather arbitrary), I'll define some measure for how good the alignment of the planets is at any given moment. This allows me to compare different alignments and see which one is the more close one.

I measure the quality of the alignment by a number which is fairly simple to calculate and that indicates over how many degrees the directions of all the considered planets are scattered around the sky. If this number, which I call the alignment width, is small, then all the planets are closely aligned.

Another measure of alignment quality is the greatest distance in the sky between any two of the considered planets. This measure is more difficult to determine, has sudden changes of direction when one of the furthest-separated planets is replaced in that capacity by another planet, and this measure does not care about the distribution of the planets that are not the two furthest separated ones.

Mercury through Saturn

I've studied the alignment (as seen from the Earth) of the planets Mercury through Saturn for a period of 3,000,000 days between 4713 BC and AD 3501. The alignment width shows periodic behavior with main periods of about 10.9, 20.1, and 200 years. The length of time that an alignment lasts is a fraction of the shortest synodical period that is involved; when Mercury is involved it is of the order of a few weeks.

According to my criterion, there is a close alignment (for a few weeks) around 11 May 2000 with an alignment width of 15.4 degrees, i.e., the planets are spread over about 15 degrees in the sky. During the investigated period of 8213 years, there are 71 alignments that are at least as close as the one of May 2000, so an alignment as close or closer than the one in May 2000 occurs on average about 8.6 times per 1000 years (but without any apparent periodicity). The last alignment before 2000 that was at least as close occurred on 5 February 1962 (alignment width 15.0 degrees). The next reasonable alignment after 2000 occurs on 14 May 2002 with an alignment width of 23 degrees. There are 212 alignments at least as close as that one during the investigated period, so such alignments occur at a rate of 25.8 per 1000 years (without apparent periodicity). The closest alignment during the investigated period occured around 25 February 1953 BC, with a smallest alignment width of 3.0 degrees. The next alignment that is in the top 30 of the investigated period occurs around 8 September 2040 (width 7.7 degrees), and the most recent one was around 31 August 1624 (10.4 degrees).

Below follows a table displaying information about the 30 closest alignments involving Mercury through Saturn (i.e., the planets visible to the naked eye) during the period 4713 BC - AD 3501.

Year	Mo	D	r	w	m		Year	Mo	D	r	w	m
-4434	11	29	20	10.0	-31		-582	8	21	30	12.1	+9
-4116	8	5	14	9.0	+12		-184	3	24	4	6.1	-29
-4018	12	7	18	9.7	-1		-144	7	27	7	7.8	-4
-3917	6	12	15	9.1	-13		-46	11	28	9	8.6	-18
-3720	1	27	27	10.9	-24		133	12	1	29	11.6	+8
-3242	4	19	26	10.7	-2		332	10	4	5	7.2	-13
-3063	5	22	12	8.9	+7		710	6	25	3	5.3	+22
-2726	10	23	8	7.8	+7		1186	9	17	11	8.8	+6
-2249	1	2	25	10.6	-3		1524	2	18	13	9.0	+6
-2209	5	4	21	10.2	+24		1624	8	31	24	10.4	-5
-1952	2	25	1	3.0	-27		2040	9	8	6	7.7	+24
-1436	9	8	17	9.5	-11		2297	7	11	23	10.4	-23
-1197	11	6	19	9.9	-18		2478	8	8	28	11.4	+18
-1058	5	27	2	5.1	+25		2954	11	2	10	8.6	+2
-958	11	19	16	9.3	+5		3292	4	6	22	10.2	+6

The dates are in the Julian (proleptic) calendar before 1582 and in the Gregorian calendar after 1582. The year is listed in astronomical reckoning, i.e., year 1 equals 1 AD, year 0 equals 1 BC, year -1 equals 2 BC, and so forth. Then follow the month and day numbers. The columns headed "r" show the rank of the alignment (based on the alignment width) in the investigated period. The columns headed "w" show the alignment width in degrees, and the columns headed "m" the distance of the center point of all considered planets relative to the Sun. A positive number means that the central point is to the east of the Sun, a negative number that it is to the west.

For example, the alignment of September 2040 is closest on 8 September 2040. It is the 6th closest alignment in the 8213-year period at an alignment width of 7.7 degrees, and the central point is about 24 degrees to the east of the Sun, i.e., the planets are all to the east of the Sun (that is, visible during the early evening).

Unfortunately, the alignment of May 2000 happens too close to the Sun (average distance 1.2 degrees) to be well visible from Earth, with some of the planets to the East and some to the West of the Sun. The alignment of 2002 is better situated at 29 degrees from the Sun, with all planets East of the Sun.

The following table lists what fraction of the time the alignment width of Mercury through Saturn is less than certain values.

width (degrees)	6.7	12.5	29.3	52.6	68.6	134.4
fraction	1/10,000	1/1,000	1/100	1/20	1/10	1/2

For instance, the width is less than 29 degrees about one percent of the time, and is greater than 134 degrees during about half of the time.

For the greatest distance between any two of the planets, the list is as follows:

max dist (deg)	8.6	16.0	37.4	67.0	86.1	152.9
fraction	1/10,000	1/1,000	1/100	1/20	1/10	1/2

Fully half of the time two of the planets Mercury through Saturn are more than 152 degrees apart in the Earth sky.

The above plot shows a measure for the quality of the alignment of Mercury through Saturn between 1980 and 2020. The higher the number r, the better the alignment.

The above plot shows the alignment width between 1980 and 2020, as derived from the previous plot. The smaller the width, the better the alignment. The periodicity of the results is clearly visible.

The third plot shows the alignment width and the largest distance between any two of the planets between the beginning of 1997 and the end of 2000.

[LS 9 February - 17 October 1997]

Venus through Saturn

Mercury is fairly hard to see from the Earth. The remaining planets that can be seen with the unaided eye, Venus through Saturn, show the closest alignment in the investigated period on 3 February 2378 AD (2.4 degrees). The next top-30 alignment of Venus through Saturn after today occurs around 4 September 2040 (5.9 degrees), and the most recent top-30 one was around 5 June 1564 (4.1 degrees).

Mercury through Neptune

The planets Mercury through Neptune have their closest alignment during the investigated period around 20 June 3502 BC (16.8 degrees). The next top-30 alignment of Mercury through Neptune after today occurs around 20 March 2673 (25.1 degrees), and the most recent top-30 one was around 1 January 1665 (28.4 degrees).

Mercury through Pluto

Formulas for calculating the position of Pluto in the distant past or future are not readily available, so I cannot easily include Pluto in the calculations. However, it appears that Pluto is caught in a 3:2 orbital resonance with Neptune, such that Pluto's orbital period is on average exactly 3/2 times that of Neptune. This means that Neptune and Pluto repeat their relative positions about every 494.3 years. My approximate calculations over one such period show that Pluto and Neptune are always separated by at least 11.2 degrees as seen from the Sun (which is practically the same as seen from the Earth), and that the next such closest encounter occurs in September 2383. Because of the orbital resonance, similar close encounters occur about every 494.3 years before or after 2383.

Comparison of the close-encounter dates for Neptune and Pluto with the top-30 alignments dates of Mercury through Neptune reveals that close Neptune-Pluto encounters are always 20 - 25 years after the corresponding Mercury-through-Neptune encounters. The separation between Neptune and Pluto during such close Mercury-through-Neptune encounters is about 28 - 34 degrees, which is about as large as the alignment widths of Mercury through Neptune during such alignments. Five of the top-30 Mercury-through-Neptune alignments in the 8213-year interval have a corresponding Neptune-Pluto encounter: the ones in 1597 BC, 1099 BC, 561 BC, 2854 AD, and 3352 AD.

It seems, then, that an alignment of some sort between all nine planets occurs about once every 500 years with an alignment width that gets down to about 30 degrees or so about 1 in 3 of such periods.

[LS 9 February - 19 March 1997]

Vertical alignment

We might call it another sort of "alignment" when all considered planets are on the same side of the ecliptic. Since each planet spends approximately half of the time on either side of the ecliptic, the fraction of the time that we can expect n planets to all be on one particular side of the ecliptic is equal to 2^-n.

Here are some characteristics of the planet's wanderings away from the ecliptic during the investigated 8213 years, as seen from the Earth:

Planet	Merc.	Venus	Mars	Jup.	Sat.	Uranus	Nep.
North	0.4559	0.4969	0.5517	0.5271	0.5286	0.4738	0.5064
South	0.5441	0.5031	0.4483	0.4729	0.4714	0.5262	0.4936
Limit	0.0000	0.0001	0.0002	0.0014	0.0036	0.0100	0.0201
Max N	4.08	8.91	5.27	2.09	2.97	0.94	2.43
Max S	-5.11	-8.95	-6.88	-2.10	-3.04	-0.94	-2.43

The rows marked "North" and "South" show the fractions of the time (in the 8213 years) that the planets spend north or south of the ecliptic. The row marked "Limit" shows how much the fractions can differ from 0.5 because the investigated time period does not cover an integral number of the planet's periods, even if the planet spends on average exactly half its time on either side of the ecliptic. The actual length of the investigated time period was not used in determining these limits, and if it was then some of the limits would become smaller. The rows marked "Max N" and "Max S" show the maximum values in degrees of the geocentric ecliptic latitude relative to the equinox of the date that the planets achieve during the investigated 8213 years.

It appears, then, that all considered planets with the possible exception of Neptune spend unequal amounts of time on either side of the ecliptic. Mercury, Venus, and Uranus spend most time to the south, and Mars, Jupiter, and Saturn to the north of the ecliptic. Yet all planets except Uranus reach farther south of the ecliptic than north (when the numbers are investigated at more than two decimals). The greatest difference occurs for Mars, which reaches 1.51 degrees further south of the ecliptic than it does north.

These results occur because the orbits of the planets are not circles but ellipses. If the orbits were circles then the planets would on average spend equal amounts of time to the north and to the south of the ecliptic, and would get as far north as south of the ecliptic. Because the orbits are in fact ellipses, the planets spend more time near their aphelion than near their perihelion, and spend unequal amounts of time on either side of the ecliptic. The same effects are seen to a much more extreme degree in the orbits of comets: Comets spend by far most of their time on one side of the Sun, and only go to the other side during the brief interval when they swing by the Sun.

Mercury through Saturn are all north of the ecliptic as seen from the Earth on average 3.48 % of the time and all south of the ecliptic 2.73 % of the time (compared to 3.13 % if everything were exactly balanced). For Venus through Saturn the similar numbers are 7.62 % and 5.02 % (6.25 % when balanced), and for Mercury through Neptune 0.82 % and 0.74 % (0.78 % when balanced). Having these groups of planets all to the north of the ecliptic is more common than having them all south of the ecliptic.

The next period that Mercury through Saturn are all to the south occurs between 1 and 14 September 1997, and then off and on until 30 December 2001, after which the planets move north. The next period that these planets are all north of the ecliptic is between 9 and 12 January 2005.

The next time that Mercury through Neptune are all to the south of the ecliptic occurs around 20 June 2020, and the next time they are all to the north of the ecliptic occurs around 12 December 2122.

[LS 26 March 1997]

Where are the planets right now?

The above plot shows you where the planets Mercury - Neptune are, measured from the Sun, in the years 1997 through 2000. The year is indicated along the horizontal axis, and the time difference with the Sun along the vertical axis. The Sun is indicated by the horizontal solid line at height zero. The planets are indicated by variously dotted and dashed lines. The planets Mercury and Venus never stray far from the Sun as seen from the Earth, so their curves always stay between -4 and +4.

If a planet is above the horizontal line at zero, then the occurrences of that planet follow those of the Sun. If the planet is below the horizontal line, then its occurrences precede those of the Sun. For example, at the beginning of 1997, Mars precedes the Sun by about 7 hours: Mars rises about 7 hours before the Sun does, passes through the South about 7 hours before the Sun does (that is, around 5 AM standard time, 6 AM daylight savings time), and sets about 7 hours before the Sun does.

Planets just below the horizontal line at zero are visible in the morning hours before sunrise. Planets just above the horizontal line are visible in the evening hours after sunset. Planets at the top or bottom edges of the plot are in opposition, and above the horizon all night long. When the curves of two planets intersect, then those planets are very close together in the sky. When a planet crosses the horizontal line at zero then it is in conjunction with the Sun and not visible at all.

From this plot you can see that all planets (from Mercury through Neptune) are reasonably close together in the sky toward the beginning of 1998, and quite close together in September 2000.

The above plot shows the distances of the nearest planets (Mercury through Mars) and the Sun to the Earth, measured in Astronomical Units, from 1997 through 2000. It shows that around the beginning of 1997, and again in the second half of 1999, Venus is the planet closest to the Earth. During the second half of 1997 and almost all of 1998 Mars is the furthest planet from the Sun (of the ones that are displayed).

Of all the planets and the Sun, during the investigated period between 4713 BC and AD 3501, the Sun is the closest to the Earth during 27.1 percent of the time. Mercury is closest during 27.7 percent of the time, Venus during 31.3 percent of the time, and Mars during 14.0 percent of the time.

[LS 20-21 October 1997, 1 March 1999]