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http://www.fys.ruu.nl/~strous/AA/en/samenstand.html

AstronomyAnswersConjunctions

Once in a while there are rumors about upcoming conjunctionsof "all"planets, which

some people expect to hae great conse!uences onarth. #or example, there wassome $unwarranted% panic about theconjunctionof someplanetsin &ay '(((. )his

essay explains about conjunctionsofplanetsand other celestial bodies, and that those

hae no measurable influence on arth, except for the tidesthat the *unand &oon

raise.

*ome !uestions that are answered here are:

+hat is a conjunction of celestial bodies

+hat is the meaning of a conjunction

-ow can you measure the closeness of a conjunction

+hat conjunctions hae been and are coming -ow close together can the planets get in the sy

+here are the planets now in the sy

What is a conjunctionof celestial bodies?

http://www.fys.ruu.nl/~strous/AA/en/samenstand.htmlhttp://www.fys.ruu.nl/~strous/AA/en/antwoorden/astronomen.htmlhttp://www.fys.ruu.nl/~strous/AA/en/samenstand.htmlhttp://www.fys.ruu.nl/~strous/AA/en/samenstand.htmlhttp://www.fys.ruu.nl/~strous/AA/en/samenstand.htmlhttp://www.fys.ruu.nl/~strous/AA/en/boom/planeet.htmlhttp://www.fys.ruu.nl/~strous/AA/en/antwoorden/planeten.html#earthhttp://www.fys.ruu.nl/~strous/AA/en/antwoorden/planeten.html#earthhttp://www.fys.ruu.nl/~strous/AA/en/samenstand.htmlhttp://www.fys.ruu.nl/~strous/AA/en/samenstand.htmlhttp://www.fys.ruu.nl/~strous/AA/en/samenstand.htmlhttp://www.fys.ruu.nl/~strous/AA/en/antwoorden/planeten.htmlhttp://www.fys.ruu.nl/~strous/AA/en/antwoorden/planeten.htmlhttp://www.fys.ruu.nl/~strous/cgi-bin/glossary.cgi?l=en&o=conjunctionshttp://www.fys.ruu.nl/~strous/cgi-bin/glossary.cgi?l=en&o=planetshttp://www.fys.ruu.nl/~strous/cgi-bin/glossary.cgi?l=en&o=earthhttp://www.fys.ruu.nl/~strous/AA/en/samenstand.html#tideshttp://www.fys.ruu.nl/~strous/AA/en/antwoorden/zon.htmlhttp://www.fys.ruu.nl/~strous/AA/en/boom/maan.htmlhttp://www.fys.ruu.nl/~strous/AA/en/#whathttp://www.fys.ruu.nl/~strous/AA/en/#meaninghttp://www.fys.ruu.nl/~strous/AA/en/#meaninghttp://www.fys.ruu.nl/~strous/AA/en/#measurehttp://www.fys.ruu.nl/~strous/AA/en/#measurehttp://www.fys.ruu.nl/~strous/AA/en/#mshttp://www.fys.ruu.nl/~strous/AA/en/#closehttp://www.fys.ruu.nl/~strous/AA/en/#closehttp://www.fys.ruu.nl/~strous/AA/en/#nowhttp://www.fys.ruu.nl/~strous/AA/en/samenstand.htmlhttp://www.fys.ruu.nl/~strous/AA/en/colofon.htmlhttp://www.fys.ruu.nl/~strous/AA/en/reken.htmlhttp://www.fys.ruu.nl/~strous/AA/en/sterrenhemel/index.htmlhttp://www.fys.ruu.nl/~strous/AA/en/wetenschap.htmlhttp://www.fys.ruu.nl/~strous/AA/en/boom/index.htmlhttp://www.fys.ruu.nl/~strous/AA/en/antwoorden/vraag.htmlhttp://www.fys.ruu.nl/~strous/AA/en/antwoorden/index.htmlhttp://www.fys.ruu.nl/~strous/AA/en/woordenboek_frame.htmlhttp://www.fys.ruu.nl/~strous/AA/en/index.htmlhttp://www.fys.ruu.nl/~strous/AA/en/samenstand.htmlhttp://www.fys.ruu.nl/~strous/AA/en/antwoorden/astronomen.htmlhttp://www.fys.ruu.nl/~strous/AA/en/samenstand.htmlhttp://www.fys.ruu.nl/~strous/AA/en/samenstand.htmlhttp://www.fys.ruu.nl/~strous/AA/en/boom/planeet.htmlhttp://www.fys.ruu.nl/~strous/AA/en/antwoorden/planeten.html#earthhttp://www.fys.ruu.nl/~strous/AA/en/samenstand.htmlhttp://www.fys.ruu.nl/~strous/AA/en/antwoorden/planeten.htmlhttp://www.fys.ruu.nl/~strous/cgi-bin/glossary.cgi?l=en&o=conjunctionshttp://www.fys.ruu.nl/~strous/cgi-bin/glossary.cgi?l=en&o=planetshttp://www.fys.ruu.nl/~strous/cgi-bin/glossary.cgi?l=en&o=earthhttp://www.fys.ruu.nl/~strous/AA/en/samenstand.html#tideshttp://www.fys.ruu.nl/~strous/AA/en/antwoorden/zon.htmlhttp://www.fys.ruu.nl/~strous/AA/en/boom/maan.htmlhttp://www.fys.ruu.nl/~strous/AA/en/#whathttp://www.fys.ruu.nl/~strous/AA/en/#meaninghttp://www.fys.ruu.nl/~strous/AA/en/#measurehttp://www.fys.ruu.nl/~strous/AA/en/#mshttp://www.fys.ruu.nl/~strous/AA/en/#closehttp://www.fys.ruu.nl/~strous/AA/en/#nowhttp://www.fys.ruu.nl/~strous/AA/en/samenstand.html

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)here is a conjunctionof celestial bodies if those bodies are $temporarily% close

together in the sy.)he picture $taen by the author on ' 0anuary '(( with a digital

camera% shows a conjunction of0upiterand*aturn. 0upiter is the brightest "star" just

right of center, and *aturn is in the lower right1hand corner. )he small group of stars

to the upper right of 0upiter are the 2leiades, and the brightest starat the left1hand side

is Aldebaran. )he twoplanetsare about 3 degreesapart.

-ow close together must the celestial bodies be to be in conjunction )hat depends on

who you as. 4f you thin it is only a "real" conjunction if twoplanetsare less than

(5 apart, but your friend is satisfied already with '(5, then your friend will see more

and longer lasting conjunctionsthan you will.

4f there are more than two celestial bodies inoled, then you must decide when all of

them are in conjunction. 4s that when they all fit within a circle of a certain diameter

Or when the distance between each pair of successieplanets$from left to right% is

less than a limit alue Or do you use still another measure

4t is clear that the meaning of the word "conjunction" is not ery precise. 6y adjusting

your definition you can find few, or instead manyconjunctions.

What does a conjunctionmean?

Only one conjunctionin the sy has noticeable influence onarth, and that is the

conjunction of the *unand the &oon. *uch a conjunction happens wheneer it is7ew

&oon, and then the tidal forcesof the*unand &oonadd up and we haespringtide

with on aerage a larger difference between high and low tidethan usual.

)he distances and masses of theplanetsare such that they hae no measurable tidal

influence on arth. )his is clear from the following table, which lists the maximum

tidesdue to theplanetsand the *un, compared to the tidesdue to the &oon. )he

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strength of the tide due to aplanetor other body increases when the mass of the body

increases, but decreases rapidly $as the third power% when the distance of the body

increases. )he tides due to the &oon are more important than the tides due to the *un

because the much smaller distance of the *un outweighs the much greater mass of the

*un.

7ame &ass 8istance )ides

&oon (.('9 (.(('3

*un 99';

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How can you measure the closeness of a conjunction?

)here is no clear border between haing aconjunctionand not haing a conjunction,

so it is more useful to use a measure that indicates how close the conjunction is at any

moment. +ith such a measure, you can also effectiely compare different

conjunctions.

An obious measure for the closeness of a conjunction ofplanetsis the diameter of

the smallest circle that encloses all of theplanets, but that circle can usually only be

found after a tedious search, and does not depend on the distribution of theplanets

within the circle.

A better measure for calculating is what 4 call the conjunction spread. )he calculation

of the conjunction spreadis fairly easy and re!uires no searching, and this measure

changes wheneer any oneplanetCs location changes.

Dou calculate the conjunction spreadas follows: 8etermine for eachplanetthat is

included the ector of length that points fromarthto thatplanet.Eall the length of

the aerage of all of those ectors r. )he conjunction spread win degreesis then e!ual

to

$!. % w= sqrt(-26262.45 log( r))

with "s!rt" the s!uare root, and "log" the natural logarithm. #or planets distributed

randomly across the ecliptic, with standard deiation sin theeclipticallongitude, w

e!uals twice s.

What conjunctionshave been and are coming?

Mercury- Saturn

4Ce calculated the conjunction spread$as seen fromarth% for theplanets&ercury

through *aturn, which can be seen with the unaided eye, for a period of three million

days between *O2 model of 6retagnon and #rancou, as shortened by &eeus. )heconjunction

spreadduring this period shows periodic behaior with main periods of 9;;, 93?, and

3? days, corresponding to the synodicalperiods of the arthwith 0upiter, *aturn,and &ars.

)he next table shows for a few alues of the conjunctionspread during which fraction

of timethe conjunctionspread of &ercury through *aturn $as seen from arth% is less

than or e!ual to that alue.

spread $5% (. ;. 9

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#or example, the conjunction spread is smaller than (.5 during only one ten

thousandth of the time, and the conjunction spread is less than '.?5 during half of

the time $and greater than that during the other half of the time%.

)he next diagram also shows during which fraction of the time the conjunction spread

of &ercury 1 *aturn is less than certain alues.

)he conjunction spread wis shown along the horiFontalaxis, measured indegrees.

)he ertical axis measures the chance $ G eerything% that the conjunction spread at a

randomly selected moment is not more than the alue displayed along the horiFontal

axis. #or example, if you go up straight from the ( on the horiFontal 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 (.(((, which means that the part of the time during which the conjunction

spread is (5 or less is e!ual to about (.((( or (.(H or one part in ten thousand.

)his diagram is a so1called double logarithmic plot. *hort and longer dashes are

indicated Along the horiFontal and ertical axes. ach next longer dash represents a

alue that is ten times $an order of magnitude% greater than the preious one, as theassociated numbersshow. )o get the alues of the short dashes you should multiply

the alue of the next left or lower longer dash with ', 9, < through ;. )hen comes

another longer dash which represents ( times as much as the preious longer dash.

)he first couple of alues associated with the longer and short dashes starting at the

in the lower left1hand corner of the diagram are: $long%, ' $short%, 9 through ;

$short%, then ( $long%, '( $short%, 9( through ;( $in steps of (%, then (( $long%, '((

$short%, and so on.

)he dashes line shows the results of an approximation formula, e!ual to

$!. '% P(

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)he aboe diagram shows the conjunction spread for the years;;; through '((

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4n the aboe figure you can see how much time there is, on aerage, between two

successie conjunctions $local minimums in the conjunction spread% that are closer

than a selected alue. #or example, a conjunction with a conjunction spread of at most

(5 occurs on aerage once per 93 years, and a conjunction spread of at most 9(5

happens on aerage once eery years. )he correspondence between the

conjunction spread wand the aerage time interal tis reasonably approximatd by

$!. 9% w= 75 ( t- 0.35)(-0.34)

6elow is a table with information about the top 9( of closest conjunctions $with the

smallest conjunction spreads% of &ercury through *aturn during the period

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'

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08 a m d w r c

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'(?;(?? ((3 ? 9

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conjunction, the wider most of them are. +ith these seen planets the closest

conjunction has a spread of =.95, whereas with the four planets mentioned before the

smallest spread is only '.

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)he planets follow fixed orbits around the *un, and cannot appear just anywhere in

the sy. )he aboe diagram shows the orbits of all planets on 0anuary $inecliptical

coordinates% in the sy. )he location of the *unis indicated by the small s!uare. )he

planets cannot appear in other places in the sy on that date.

6y shifting the planets freely along their orbits we can find the closest conjunction

that is possible in principle at any gien day of the year. )he aboe diagram shows the

results of a search for the closest possible conjunctions.)he numbersalong thehoriFontalaxis show the beginning of the corresponding months for example, ' G the

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beginning of #ebruary. )he ertical axis shows the smallest conjunction spreadthat 4

found, measured in degrees. #or eachplanet, the orbit was taen from the orbital

period that started on 0anuary '(((. $)he results for planetary orbits from 0anuary

9((( are irtually the same: the standard deiation of the difference is only (.((', and

probably mostly due to the search algorithm.%

)he smallest possible conjunction spreads$of &ercury 1 *aturn% is neer greater than

.'5 $as is approached on '9 &ay and '= 7oember%, and is neer smaller than (.9(5

$as is approached on 9 &arch near ecliptical coordinates 9'5, I5 and elongation

';5 east, and on 9 *eptember near ecliptical coordinates

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together during all of '(((, and are in opposition towards the end of '(((. Around

&ay '((( $near '(((.< on the horiFontal axis% &ercury and *aturn are all reasonably

close together $in conjunction%, but @ranusand 7eptune do not participate. &idway

through '((, &ars, @ranusand 7eptune are in opposition, 0upiter and *aturn are in

conjunction with the *un, and >enusis the morning star. )he conjunctionsof &ercury

through *aturn around &ay '((' and around *eptember '(

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languages: LenMLnlM

http://www.astro.uu.nl/~strous/AA/en/samenstand.html;

Last updated: 2!"2"#

)his web space courtesy of the Astronomical 4nstitute / @trecht @niersity.

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