Chapter 3: UNUSUAL ASTRONOMCAL ALIGNMENTS-PART I

Chapter 3: UNUSUAL ASTRONOMICAL ALIGNMENTS-PART I

This chapter explores phenomena which occur very rarely, are visible over small geographical regions or are of very short duration.

A. BRIGHT PLANETARY CONJUNCTIONS (THREE PLANETS)

Planet-to-planet conjunctions (in R.A.) occur quite often. Their rarity depends on three fundamental considerations; pairing distances, period intervals and the number of planets under consideration (table 3.1 explores dual pairings-planetary trios).

Table 3.1: Bright Tri-Planetary Conjunctions (1500-2500 A.D.) <=60' Radius

	MINIMUM SUM
	CONJUNCTIONS	CIRCLE OF RADIUS
YEAR	PAIR 1	DATE  	SEP  	PAIR 2	DATE	SEP  INSCRIBE CIRCUM	RATIO 	DATE	SUN'S SEP

1524	J-S 	JAN 31 	46'	M-S 	FEB 05  53'	15'	33'	2.2  	FEB 05	+1h05m
1563	V-S	AUG 12 	13	J-S  	AUG 25	 7	21	48 	2.2  	AUG 10	-2h29m
1564	V-S	JUN 02  86	M-S 	JUN 03  43 	19	49 	2.6  	JUN 03	+2h18m
1564	V-J	JUN 08  74	M-J 	JUN 13  32 	25  	54 	2.2  	JUN 08	+2h25m
1682	M-S	SEP 21  23	J-S  	OCT 24 	15 	20  	49 	2.4  	SEP 22 	-3h39m
1769	V-J	DEC 23 	20	M-J 	DEC 24 	46 	21  	48 	2.3  	DEC 26	-1h40m
1802	J-S	JUL 17  39	V-S  	JUL 26  17 	24  	59 	2.4  	JUL 26 	+1h36m
1819	M-S	APR 26 	45	V-S 	APR 28 	38 	18  	49 	2.7  	APR 28	-1h30m
1901	J-S	NOV 28 	26	M-S 	DEC 14 	78 	19  	54 	2.8  	DEC 17	+1h17m
1991	M-J	JUN 14  37	V-J  	JUN 18  69 	14  	60 	4.3  	JUN 22	+2h36m
2136	V-J	SEP 22  87	M-J  	SEP 29  68 	26  	56 	2.1  	SEP 22 	+1h20m
2159	V-S	DEC 03 	20	J-S  	DEC 20 	72 	20  	49 	2.4  	DEC 02	-2h52m
2277	V-J	AUG 02 	71	M-J  	AUG 03 	27 	16  	40 	2.5  	AUG 01	+0h59m
2301	M-J	DEC 05 	 6	V-J  	DEC 03 	45 	 8  	31 	3.9  	DEC 05	-3h37m
2318	V-S	APR 03 	27	J-S  	APR 27 	42 	17  	55 	3.2  	MAR 31	-1h01m
2333	V-M	APR 28 	17	M-J  	MAY 07	74	26  	58 	2.2  	MAY 02	+1h23m
2378	M-S	FEB 01  61	J-S  	FEB 18  49 	11  	51 	4.6  	JAN 28	+2h55m
2378	V-S	FEB 04  30	J-S  	FEB 18  49 	18  	44 	2.4  	FEB 02	+2h34m
2477	V-S	JUN 15  93	J-S  	JUL 06   6 	25  	55 	2.2  	JUN 14	+2h28m
Table 3.1 lists all occasions from 1500-2500 when Venus (V), Mars (M), Jupiter (J) and Saturn (S) are in very close dual pair conjunctions. Dates prior to 1580 are on the Julian calendar; the latter are Gregorian. Each line gives the approximate date based on (12h) Universal time of minimum separation. As depicted in figure 1 below, an inscribed circle of radius is the radius of a circle inside the triangle formed by connecting the three planets near conjunction. A circumscribed radius is the smallest circle which can fit the three planets on its circumference. The minimum sum of both radii are used as the date of tightest grouping although lesser values of each type of radius may occur near this date. The closer the ratio of circumscribed to inscribed radii is to 2, the more the configuration will appear as an equilateral triangle. A side to side ratio (largest to smallest sides) of 25:1 will yield a circle of radii ratio of 5.7:1. Sun's separation: (+) for time planets set after sunset, (-) for time planets rise before sunrise for trio as seen from northern mid-latitudes. All events on the table are considered easily visible for several days before and after minimum separation.

The first factor concerns the degree of separation between the planets. In the most extreme case, a planet occults another. No planet on planet occultations has occurred in the 20th Century (the last one on 3 January 1818 involved Venus and Jupiter), although on average three events per century take place during the 2nd, 3rd and 4th millennium. Basically, the closer the conjunction, the fewer the events.

The second factor relates to the time span under review. As noted, one has to wait longer to achieve a situation of very close separation. A very high positive linear correlation between planet separation and interval between events exists and is a function of planet orbital speed. The only notable exception occurs occasionally between Mercury and Venus. For example, on 26 August 1999 and 6 Apr 2001, both planets will be more than ten degrees apart in R.A.. Yet in late October 2001, both planets will be less than one degree apart for 11 days yet never attaining true conjunction (known as quasi-conjunction.

The third and final factor involves the number of planets in conjunction at one time. By increasing the number of planets, the frequency of events will decreases sharply. For example, the interval between the time when Mercury, Venus, Mars, Jupiter and Saturn are easily visible in close proximity span from March 3, 1953 BC to September 8, 2040 AD (table 3.2).. Even the close alignment of four bright planets are quite rare (from June 1564 to Feb 2378).

Table 3.2: Grand Planetary Conjunction of 2040 A.D.

Year	Date	UT	Mag.	       Mag.	Sep
2040	Aug 18	01:49	 1.7  Mar-Jup -1.7	35'
	Aug 31	01:31	 1.7  Mar-Sat  0.9	110' 
	Sep 01	17:39	-3.9  Ven-Jup -1.7	10'
	Sep 06	17:56  	-3.9  Ven-Sat  0.9	88'
	Sep 07	21:03	-0.2  Mer-Jup -1.7	88'
	Sep 11	12:09	-0.1  Mer-Sat  0.9	185'
	Sep 13	04:04	-3.9  Ven-Mar  1.7	13'
	Sep 20	15:43	-0.0  Mer-Mar  1.6	139'
Table 3.2 shows the conjunction pairs associated with the Grand Conjunction of 2040. Although this event occurs over a one month period, only around September 6-8 will the planets be most favorably aligned.

Any equilateral triangle will yield a ratio of circumscribed to inscribed radii of 2:1. Equilateral right triangles yield a ratio of 2.4:1. This ratio will increase as the ratio of the sides forming the right angle increases (i.e., 2:1 side ratio results in a 2.5:1 circumscribed to inscribed ratio. At 3:1, the radii ratio is 2.8:1; 4:1, the radii ratio is 2.9:1 and 10:1, the radii ratio is 3.9:1, at 25:1 the radii ratio is 5.7:1 and 33:1, the radii ratio is 6.4:1.

Although not directly visible from Earth, all the planets except Pluto are found in the same heliocentric quadrant (<= 90 degree sector) 25 times during the first 30 centuries of the Christian era. While the inferior planets are near conjunction with the sun, the superior planets are near opposition.

B. RARE PLANETARY OCCULTATIONS

During the evening of February 11, 1683, European explorers in South America had the unique opportunity to view a full moon occulting Jupiter and Saturn in a mere 15 minute time span! Did anyone took notice of this magnificent display? Even today when the -12.7 magnitude full moon dominates the night, amateur and professional astronomers resign themselves to very limited visual sky observing (the full moon is actually up to 25 percent brighter than even one day before or after (known as the "opposition effect")) . Fortunately, the mechanics of our solar system allow us to periodically yet briefly glimpse and admire unusual planetary occultations even when the moon is full.

1. DUAL PLANETARY OCCULTATIONS

Although each planet on average is occulted by the moon more than 200 times per century, a total of only seven events per hundred years occur when two planets are occulted within 30' (R.A.) of each other. In one hour, the moon travels on average its own diameter thus enabling it to occult two planets that are separated by that distance at the same time. Planets in nearly the same R.A. however can be degrees apart in declination. The moon will occult each at about the same time but as viewed from widely separated geographical locations. Optimal viewing is further challenged since many dual occultations occur in daylight or when elongation from the sun is less than 15 degrees (twilight interferes). Thus on average, only one in 16 dual occultations are actually visible from one specific location.

Table 3.3:  Exceptionally Favorable Dual Planetary Occultations (1-4000 A.D.)
	DATE	UT 	               PLANETS 	       SL% 	          REGION

	35	Apr.  	6  	4h	Jup-Sat	     74+ 	Central/South America
 	629	Apr.	14	20	Jup-Nep	     92+ 	S. Atlantic Ocean
 	662	Jul. 	31  	0	Mars-Nep     69+ 	S. Atlantic Ocean
	1030	Jul.	7  	6	Ven-Mars     14+ 	Antarctic
	1164	Jun.	7  	4	Sat-Nep	     100 	Antarctic
	1374	Oct.	30  	3	Jup-Ura      40-  	N. Africa
	1375	Jan.	19	21	Jup-Ura	     97-  	S. Indian Ocean
	1580	Jul. 	26	12	Sat-Ura	     100 	Mid Pacific Ocean 
	1683	Feb.	11  	5	Jup-Sat	     100 	South America
	1998	Apr.	23  	5	Ven-Jup	     15-  	Africa, India
        2000  Mar.  4    xx  Ven-Ura      xx            S. Indian Ocean, New Zealand 
	2038	Feb.	16	20	Jup-Ura      90+ 	Central Africa
	2038	Mar.	16	5	Jup-Ura      71+ 	Central/South America
	2444	Apr.	30	6	Jup-Nep	     97+       North America (north of 35N)
	2509	Jan. 	24	19	Ura-Nep	     11+ 	S. Africa
	3073	May	15	4	Mars-Ura     98-  	Mid North Atlantic
	3262	Apr.	25	1	Jup-Nep	     98+ 	S. Atlantic Ocean 
Table 3.3 lists all occasions during 4000 years when two planets (excluding Mercury and Pluto) are occulted by the moon at the same time. Dates prior to 1582 are on the Julian calendar; the latter are Gregorian. Each line gives the approximate Universal time when both planets are invisible due to occultation. Sunlit percent (SL%) indicates (-) for waning and (+) for waxing lunar phases. Regional visibility pertains to locale where both planets are behind the moon. Occultation of one or both planets are generally visible up to 30 degrees in longitude and 15 degrees in latitude from occultation mid-point provided that the occultation is central to the moon's diameter. Most of these events occur in night (dark) skies for part of their track.

2. BRIGHT PLANETS OCCULTED DURING LUNAR TOTALITY

One should remember that when planets lie near a full moon, they too are near opposition and are significantly brighter than if near a slender crescent moon. Mars benefits with full moon occultations by shining nearly 3 magnitudes brighter as compared to a close encounter with a 40% sunlit moon. Even Jupiter and Saturn show a modest half magnitude gain in brightness under a similar scenario. However, viewing dramatically improve when an occultation occurs during a total eclipse. Just how unusual is this alignment? Very!

As the moon moves from conjunction to opposition with the sun (new to full moon), planets that are occulted by the moon will also increase in brightness by the ever increasing lunar phase (as they also approach opposition). While Jupiter and Saturn increases less than 0.75 magnitude, Mars dramatically brightens more than 3.5 magnitudes. For plotting purposes, brightest magnitudes are positive (negative or a negative). At new moon, Jupiter is 3.4 magnitudes brighter than Mars. At full moon, planet magnitudes can vary as follows: Mars +/- 0.8; Jupiter +/- 0.2, Saturn +/- 0.7 from average.

Comparing planetary occultations during total lunar eclipses., the search yielded some unexpected results. Only about 5% of all occultations are easily visible (in dark skies) from a given location. The average duration of a full moon is about 30 hours, so one would expect a little more than 4% of planetary occultations to occur during this lunar phase. However, Mars with its 25-27 month period between oppositions, will encounter a full moon only 42% of the time as compared to Saturn.

Between the years 1-3000, about 5% of Mars', 10% Saturn's and 15% of Jupiter's full moon encounters occur within 15 hours of mid-totality. No same day events occurred for Mars during 1000-2000 or will for Jupiter during 2000-3000; although six minor partial eclipses with Jupiter occur (three between the years 2059-2093 and three between 2932-2990). Saturn will experience 22 same day partial eclipses while Mars will have only three during the third millennium. The 99% eclipse with Saturn in 2612 is the only significant partial eclipse conjunction in the "near" future. See supplemental Table 3.1S

On average, about one third of these full moon encounters occur within four hours of mid-totality. Distribution of these nearer time encounters vary greatly. The first millennium had 25 occurrences, six of which were occulted during totality, while this millennium had only ten (one during totality). The next 1,000 years will not include any events with Jupiter and will be limited to eight-four hours or less alignments (three during totality). Between 3000-3999, there will be no occultations during totality for Mars and Saturn (two of Saturn's encounters will occur within four hours of mid-totality). Jupiter on the other hand will have two-four hour or less alignments (both resulting in totality-occultation). See Table 3.4.

Conclusions

All planetary occultation during totality occur within two hours of occultation mid-point (minimum planet-moon separation) and mid-totality. The last worldwide event was visible on Dec 30, 1591 (Saturn) . Because Jupiter lies within the moon's ecliptic plane, a certain periodicity exists when the eclipsed moon (all types) can occult this planet. A 57.89 or 68.81 years series occurs then after about 781 years, the next series begins. Mars and Saturn are outside the critical 2 degs 35 min ecliptic latitude for a portion of its synodic orbital period and therefore does not follow a regular cycle series of events.

Although lunar totality is visible over more than half the Earth, the limitations of witnessing a bright planet occulted by an eclipsed moon include: (1) not all occultations go through the central axis of the moon where the maximum path width would be about 2,100 miles (the moon's diameter); and (2) although the worldwide duration of an occultation can last up to 4.5 hours (about one hour at a given location), examples in this study are solely dependent on the duration of totality which is considerably shorter (0 to 106 minutes).

While there are several dozen examples when a bright planet is near a total or partial eclipse over the millennia, the rarity of seeing a planet occulted during totality is one of astronomy's rarest predictable events unless see two planets disappear behind the moon at the same time is considered. The dual occultations in 1998 and 2038 will be our only opportunity for generations to come. For those who cannot wait, at least in today's world, we can imagine what these sights would look like through our virtual reality PC's.

Table 3.4:  Bright Planetary Occultations During Totality (1-4000 A.D.)
Occultation  	Mid-Point	Totality 	Moon at Zenith
Year 	Date 	UT  	Lat/Long	UT	Lat/Long	Mag.	Planet	     Description

*400	Dec.	17	21h	-5/49E	19h	23/73E	          1.03  Jupiter (-2.7) SE Hemisphere
*412	Nov.	4	22	-44/44E	21	16/48E	          1.59   Mars (-1.9)	SE Hemi (next in 2076 yrs.) 
*502	Dec.	29	13	28/164E	15	23/135E	          1.63   Saturn(-0.5)	N Pacific (next in 1078 yrs.)
*524	May	3	20	-70/87W	19 	-17/81E	          1.63 	Jupiter(-2.6)	Conjunction (<15' east)
*755	Nov.	23	21	54/ 29E	19	21/75E	          1.38 	Jupiter(-2.8)	Arctic
*810	Jun.	20	21	-21/45E 20	-24/61E   	  1.82 	Jupiter(-2.8)	Antarctic
*879	Apr.	10	12	-72/65E 11	-9/168W	          1.34  Jupiter(-2.5)	Antarctic (next in 2705 yrs.)
*1580	Jul.	26	12	32/159E	11	-17/165W          1.24  Saturn(0.2)	Central Pacific (Uranus)
2076	Jun.	17  	2	-67/164E 3	20/146W           1.76  Saturn(-0.1)	Antarctic (3' north)
*2344	Jul.	26	12	17/166E	12	-19/175E          1.31	Saturn(0.1)	Southern US
2412	Nov.	18  	1	65/150W	0	19/3W             1.39  Saturn(-0.4)	Conjunction (2 Degs.)
*2488	Apr.	26 	8	-63/116E9	-14/138W          1.36	Mars(-1.6) 	Antarctic
2612	Sep.	2 	10	70/144E	10	8/144W            0.99  Saturn(0.5) 	15' from partial eclipse
2821	Jun.	7  	2	63/3E	1	23/10W            1.72  Mars(-2.1)  	Atlantic Ocean Rim (67' south)
2829	Jan.	11  	7	34/105W	4	22/51W            1.78  Saturn(-0.4)	N. America (just after totality)
*2977	Jan.	26 	8	17/115W	9	19/129W           1.17  Saturn(-0.3)	Central-S. America
3584	Jun. 	6	16	-69/ 99E14	-22/148W          1.14	Jupiter(-2.5)	SW Indian Ocean
3881	Jun.	25	10	-60/162W10 	-23/143W          1.79	Jupiter(-2.6)	SE Indian Ocean
Table 3.4 lists all occasions during 4000 years when Mars, Jupiter and Saturn are occulted by a total lunar eclipse. Several of the best conjunctions are included as well (italic). Dates prior to 1582 are on the Julian calendar; the latter are Gregorian. Each line gives the approximate Universal time of central occultation (minimum separation) and mid-totality. Magnitude phase of lunar eclipse shows total eclipses greater than 1.0. Magnitudes follow planets. Description highlight regional visibility or circumstance of events. During the 1580 eclipse, Uranus reappears 13 minutes before Saturn disappears, all during totality! Note that a close conjunction of planet and partial eclipsed moon will still be visible over more than half the Earth during most events. Jean Meeus' work on occultations of Bright Planets by the Eclipsed Moon for the period -100 to +3000 revealed additional umbral occultations during totality: 799 Jul 21 and 1418 Oct 14 for Jupiter; 195 Jul 10, and 1591 Dec 30 for Saturn. * denote similar findings, except for the 524 AD event which occurred during totality. Jean Meeus' list also includes several occultations before or after actual totality and during partial eclipses.

Table 3.5:  Uranus-Neptune Occultations During Totality (2000-4000 A.D.)
Occultation 	Mid-Point	Totality 	Moon at Zenith
Year 	Date 	        UT    Lat/Long   UT    Lat/Long Mag.	Planet 		Description

2014	Oct.  	8	10h	72/101E	11h	6/167W	1.15	Uranus(5.7)	North Pole (5 Degs. abv hor)
2022	Nov.  	8	13	58/134E	11	17/169W	1.34	Uranus(5.6)	Far East
2568	Jan.	15	23	65/165E	0	21/5E	1.30	Neptune(7.8)	Eastern Russia
2676	Sep.	14	5	17/92W	7	-4/103W	1.01	Neptune(7.8)	Mid-North Atlantic Ocean
2745	Jul.	6	0	6/13E	0	-23/2E	1.48	Uranus(5.5)	Middle East
2919	Mar. 	7	19	-30/52E	20	5/62E	1.70	Neptune(7.9)	South Indian Ocean
3263	Sep.	10	1	19/17W	0	-5/13E	1.28	Uranus(5.7)	Mid-Atlantic Ocean
3487	Aug.	26	15	-5/134E	16	-10/116E1.53	Neptune(7.8)	India, SE Asia
3613	Nov.	10	18	64/68E	16	18/112E	1.22	Uranus(5.7)	Europe, Scandinavia
3697	Nov.	11	21	574E	21	18/33E	1.35	Uranus(5.7)	Europe, Scandinavia
Table 3.5 lists all occasions, during the next 2000 years when Uranus and Neptune are occulted by a total lunar eclipse. Each line gives the approximate Universal time of central occultation (minimum separation) and mid-totality. Magnitudes follow planets. Description highlight regional visibility. Note that a close conjunction of planet and partial eclipsed moon will still be visible over more than half the Earth during most events. All events were simulated with Dance of the Planets software.

3. BRIGHT PLANET CONJUNCTIONS DURING SOLAR TOTALITY

Bright planets are occulted by the sun more often than most people realize because these events are impossible to observe. However, occasionally, a planet may be very near the sun during a total solar eclipse. This section explores this type of event.

Table 3.6:  Bright Planet Occultations by the Sun (2000-2099 A.D.)
MERCURY           	MARS   VENUS 	          JUPITER	SATURN
2000,  2046,  2092 	2023	2000	          2007		2004
2002,  2048,  2094 	2038	2008	          2013		2020
2006			2045    2016		  2019		2034
2007,  2053,  2099 	2070	2024	          2025		2050
2009,  2055  		2077	2032		  2032		2063
2013,  2059                     2040	          2037		2079
2015,  2061 		        2048	          2044		2093
2020,  2066 		                          2049
2022,  2068 		        2081	          2056
2026,  2072 		        2089	          2061
2033,  2079 		        2097	          2068
2035,  2081 		                          2073
2039,  2085 
2040,  2086 		                          2090
                                                  2096
Table 3.6 list the occasions when the brightest planets are occulted by the sun. Note the periodicity of: Mercury=46 years (occurring in May or Nov.), Venus=8 years (mid May-mid Jun.. & mid Nov. - mid Dec.), Jupiter=5.5 years (mid JUN-mid Jul. & mid Dec.-mid Jan.), and Saturn=14 years (Jan. or Jul.) on average. Each series eventually ends only to resume again years later. Mars had nine events in the 20th century without an obvious return cycle (May or Nov). The inferior planets exhibit repeated positions in the sky (similar to the sun-moon Saros cycle) while the superior planets' occultations occur by their repeated crossing of the sun's orbital plane (twice during the planet's orbital "year" around the sun).

Mercury and Venus occultation by the sun is sometimes known as an anti-transit. Just how rare is a transit or occultation of a planet during solar totality? For Mercury, a transit occurs just two days after an total eclipse in 2450 and 2496 while Venus will be occulted by the sun three days after an eclipse in 2291 (table 3.7). The solar conjunctions of Mercury in 2013 and 2059 (46 calendar years apart) will also include Saturn (nearby). The last event (involving Venus) occurred in 1966 and was popularized in a High Altitude Observatory/NCAR radial density filter photograph of the solar corona

Table 3.7: Bright Planet Conjunctions During Solar Totality

	          LOCATION                                TOTALITY 	     MAXIMUM
DATE	SUN	                    PLANET	                         MAG.	       ECLIPSE	   REMARKS

1966	Nov.	12	15h09m	-17d41m	V	15h14m -17d21m	-3.9 sup-36.2/47.4W	Venus 77' separation
2013	Nov.	1	14h35m	-15d13m	M	14h20m -13d56m	4.9 inf	-40.3/160.1W	Saturn 14h48m -13d59m
2059	May 	13	3h15m	+18d21m	M  	3h09m +17d30m 	-2.1 sup-11.6/101.3W	Saturn   3h23m +16d32m
2139	Jan. 	30	20h50m	-17d41m	S 	20h45m -18d35m	0.6	-40.2/21.9E	Saturn 32' conj Jan 28
2150	Jun. 	25	6h15m	+23d22m	S	6h07m +22d31m 	-0.1	18.2/177.5E	Saturn 54' conj Jun 22
2179	Nov.	28	16h18m	-21d22m	M	16h21m -22d11m 	-1.3 sup-16.4/105.5W	Mercury 33' conj Nov 27
2218	Apr.	25	2h12m	+13d17m	M  	2h10m +12d30m 	-2.2 sup49.9/171.3E	Mars 2h04m +12d12m
2240	Aug.	18	9h53m	+12d52m	J	9h50m +13d54m 	-1.7	-13.5/30.9W	Jupiter 43' conj Aug 17
2263	Jun.	6	4h59m	+22d40m	V	4h58m +23d06m 	-3.7 inf53.6/175.7W	Venus 28' conj Jun.  6
2273	May	17	3h39m	+19d27m	J	3h43m +18d52m 	-2.0 	22.6/29.0W	Jupiter 46' conj May 18
2291	May	28	4h23m	+21d32m	V	4h20m +21d04m 	-3.9 sup28.3/143.8W	Venus 13'* occult Jun.  1
2292	May	17	3h40m	+19d32m	M  	3h33m +18d18m	5.6 inf	-18.7/29.6W	Mercury 26' conj May 16
2306	Feb. 	14	21h48m	-13d16m	J 	21h47m -14d07m  -2.0	-11.3/60.9E	Jupiter 42' conj Feb 13
2374	Dec.	4	16h42m	-22d11m	J	16h46m -21d45m  -1.7	-13.9/42.6W	Jupiter 33' conj Dec.  5
2377	Apr.	9	1h11m	+7d32m	M  	1h13m  +6d47m  	-2.1 sup-37.8/159.9E	Mercury 59' conj Apr.  8
2382	Jul.  	12	7h26m	+21d56m	V	7h23m +22d41m 	-3.9 sup5.8/128.9E	Venus 45' conj Jul 14
2429	Dec.	26	18h21m	-23d18m	S 	18h11m -22d24m	0.4	-53.8/47.4E	Saturn 57' conj Dec 23
2450	May	12	3h18m	+18d11m	M  	3h34m +19d54m 	5.0 inf	6.0/152.7E	Mercury 5'* transit May 14.
2459	Jun. 	1	4h39m	+22d04m	M	4h22m+21d28m  	-1.9 sup-67.6/45.0E	Mercury 34' conj Jun.   4
2496	May	13	3h26m	+18d42m	M	3h37m +19d41m	5.4 inf	81.8/73.1W	Mercury 8'* transit May 15
2587	Dec.	20	17h55m	-23d21m	V	17h49m -22d10m  -3.9 inf-45.7/111.3W	Venus 57' conj Dec 19
Table 3.7 list all occurrences when a bright planet Mercury=M, Venus=V, Jupiter=J, and Saturn=S, are within three days of <=60' conjunction with a total solar eclipse. Inf and sup for Mercury and Venus indicate inferior and superior type of conjunctions. For the period 2000-2500 A.D., Mercury has 826 solar conjunctions <=60', Venus 212 events, Jupiter: 350 events, and Saturn 149 events. During this period, no events occur for Mars. Note the transits in 2450 and 2496 (46 years) just miss being eclipsed as well. In 1966 denotes event was not a true conjunction.



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