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Apparitions, Conjunctions & Elongations
2010 to 2015
by Martin J. Powell
"Venus usually gets a bad press in the descriptive literature. Regular devotees know it is otherwise.
A beautiful object that fascinates as it frustrates"
- Richard Baum and David Graham, BAA Mercury & Venus Section (1995)
Venus - the brightest of the naked-eye planets - has an alternating cycle of morning and evening apparitions (periods of naked-eye visibility) interspersed with short periods of non-visibility when it is too close to the Sun to observe. Venus appears to the naked-eye as a brilliant-white 'star' and is the third brightest object in the sky (after the Sun and Moon); it is so bright, in fact, that it can cast shadows at night around the time of its greatest brilliancy. When it is on view, Venus is usually the first 'star' to become visible after dusk, or it is the last to disappear from view at dawn.
Venus in the dawn sky, filmed with a video camera in July 2004 (click on image for a larger picture).
Venus can appear somewhat menacing when it appears to 'hover' in twilight just above rooftop-height in the evening or morning sky - which is why it is often reported as a UFO by the uninitiated. Most people have probably seen the planet at some point during their lifetime but many have assumed it was just 'a particularly bright star'. Venus is often involved in spectacular conjunctions (close passes) with other planets and it can even be glimpsed in daylight.
This article discusses some of the more visually challenging aspects of the planet's visibility in the sky, considered from the standpoint of the naked-eye planet observer.
We begin with a study of when Venus can be seen in the sky alongside one or more of her Solar System siblings - namely, when she is involved in planetary conjunctions.
Venus Conjunctions with Other Planets, 2010 to 2020
Viewed from the orbiting Earth, whenever two planets appear to pass each other in the night sky (a line-of-sight effect) the event is known as a conjunction or an appulse. Conjunctions are generally considered most noteworthy when they involve two bright planets, and no planetary conjunction is more spectacular than those involving Venus.
During the course of one Earth year, Venus is seen to complete over 1½ circuits of the zodiac, and in doing so it passes each of the planets in the sky - a few of them on more than one occasion. However, not all of these conjunctions will be visible from the Earth because many of them take place too close to the Sun. Furthermore, not all conjunctions will be seen from across the world; the observers' latitude will affect the altitude (angle above the horizon) at which the two planets are seen at the time of the event, and the local season will affect the sky brightness at that time. The observers' latitude affects the altitude of the planets in two ways:
(a) the rising and setting angles of celestial bodies in relation to the observer's local horizon varies by latitude; the closer an observer is positioned to the Equator (latitude = 0°) the steeper the celestial body will rise and set. At the Equator, celestial bodies are seen to rise and set at a 90° angle to the horizon. At mid-Northern and Southern latitudes the angle is more gentle (ca. 40-50°), reducing further as one approaches the Poles (latitudes 90° North and 90° South). At the Poles themselves, celestial bodies do not rise or set (rising and setting angle = 0°); instead, they move in paths which are parallel to the horizon, their altitude above the horizon remaining fixed throughout the day. Across the world, celestial bodies will always move across the sky in a path which is parallel with the celestial equator (i.e. where the declination of celestial bodies is 0°).
Venus and Jupiter (far left of picture) appear through a break in the clouds in a planetary conjunction photographed in the evening sky in September 2005. Venus is the brighter of the two planets (click on image to see the full-sized picture).
(b) the angle of the ecliptic (the path of the Sun, Moon and planets through the zodiac) to the local horizon varies according to latitude and the time of the day. The ecliptic is inclined at about 23½° to the celestial equator, the result being that the ecliptic can present either a steep, an intermediate or a shallow angle to the horizon at the point where the conjunction takes place (in the Eastern or Western sky). At mid-Northern latitudes, for example, a conjunction taking place on Spring evenings (i.e. in the Western sky after sunset) which is positioned 30° East of the Sun (solar elongation = 30°E) will appear higher in the sky than a 30° West conjunction which is seen on Spring mornings. This is because, seen from mid-Northern latitudes, the ecliptic presents a steeper angle to the horizon after sunset on Spring evenings than it does before sunrise on Spring mornings. Six months later in the mid-Northern hemisphere the opposite is true: Autumn evening conjunctions are less well seen than those in Autumn mornings.
Because Venus never appears more than 47° from the Sun, it follows that any planetary conjunction involving Venus will also never occur above this angular distance, i.e. its solar elongation will always be less than 47°. For an Earthbound observer, a superior planet (i.e. Mars and beyond) seen at such a small elongation poses something of a problem, since it will then be considerably more distant from the Earth (and therefore fainter) than when it is closest and brightest in the sky (namely, at opposition, when its elongation is 180° from the Sun). Mars suffers particularly in this respect; at opposition its apparent magnitude is typically around -2.0, however when it is in conjunction with Venus its brightness will always have dropped by two or three magnitudes to around +1.5 or so; Mars' distinct coloration is often much less evident as a result.
Jupiter is affected to a much lesser extent since it is always above magnitude -1.6 (brighter than Sirius, the brightest star in the sky). Conjunctions between Venus and Jupiter are arguably the most spectacular to view, the two planets rivalling each other in colour and brightness. In the brightness stakes, Venus always wins the contest.
Uranus and Neptune are rather more tricky objects to observe whenever they are involved in Venus conjunctions, because Uranus is only just visible to the naked eye and Neptune is never a naked-eye object. Twilight quickly renders these two planets invisible (even through binoculars), so conjunctions taking place less than about 20° from the Sun will be difficult or impossible to see.
Conjunctions between Venus and Mercury happen two or three times a year but many of them are too close to the Sun to observe; even when they are visible they will often be difficult to see because of their narrow solar elongation. The visible events are listed below, although observers may prefer to view these planets with greater ease over a period of time, when the two are much further apart but visible in the same morning or evening apparition (see the section 'Venus & Mercury Paired Apparitions' below).
Note that, because many of the following conjunctions occur in twilight, the planets involved may not appear as bright as their listed magnitude suggests.
Venus conjunctions with other planets from 2010 to 2015 The column headed 'UT' is the Universal Time (equivalent to GMT) of the conjunction (in hrs : mins). The separation (column 'Sep') is the angular distance between the two planets, measured relative to Venus, e.g. on 2015 Jul 1, Jupiter is positioned 0°.4 North of Venus at the time shown. The 'Fav. Hem' column shows the Hemisphere in which the conjunction will be best observed (Northern, Southern and/or Equatorial). The expression 'Not high N Lats' indicates that observers at latitudes further North than about 45°N will find the conjunction difficult or impossible to observe because of low altitude and/or bright twilight.
In the 'When Visible' column, a distinction is made between Dawn/Morning visibility and Dusk/Evening visibility; the terms Dawn/Dusk refer specifically to the twilight period before sunrise/after sunset, whilst the terms Evening/Morning refer to the period after darkness falls/before twilight begins (some conjunctions will take place in darkness, others will not, depending upon latitude). The 'Con' column shows the constellation in which the planets are positioned at the time of the conjunction.
To find the direction in which the conjunctions will be seen on any of the dates in the table, note down the constellation in which the planets are located ('Con' column) on the required date and find the constellation's rising direction (for Dawn/Morning apparitions) or setting direction (for Dusk/Evening apparitions) for your particular latitude in the Rise-Set direction table.
A table of planetary conjunctions involving Venus from 2016 to 2020 can be seen here.
Planetary conjunctions are interesting events to observe; some are more challenging than others, and one may have to wait long periods of time before any two planets come close together again. This is particularly so where they involve two superior planets, whose brightest and best conjunctions take place in the weeks around their opposition. The slow apparent motions of the superior planets often result in their conjunctions taking place many years apart - conjunctions between Jupiter and Saturn, for example, happen about 20 years apart, whilst those involving Uranus and Neptune happen about 172 years apart! Conjunctions involving Venus are, however much more frequent because of its faster apparent motion through the sky (about 1º.6 along the ecliptic per day).
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Venus and Mercury were involved in a paired apparition in the dawn sky from late December 2004 into early January 2005; in this picture, Venus is the lower and brighter of the two. Note how both planets are bright enough to cast reflections in still water (click on image to see the full-sized picture).
Venus-Mercury Paired Apparitions, 2010 to 2015
When can Venus and Mercury be seen together in the sky?
Whilst Venus is a relatively easy planet to find, fleeting Mercury is much more difficult because of its proximity to the Sun and the brevity of its appearances. In addition to this, Mercury's visibility is highly determined by the observer's latitude and local season. In general, Mercury is rather more easily observed from the Southern hemisphere than from the Northern. Seen through the telescope, Mercury is almost always a disappointment because of its small angular size and the low altitude at which it is normally observed.
Mercury - which typically appears orange-pink to the naked eye - is always seen against a twilit sky because its greatest solar elongation (angular distance from the Sun) is never more than 27°50'. The planet is best observed when it is at (or close to) its greatest elongation, but it can be a very challenging object to find when it is only just emerging from the Sun's glare, or just disappearing into it, i.e. when its solar elongation is less than about 20° or so.
Venus can prove useful in locating Mercury whenever the two planets appear close together in the sky - namely, when they are both undergoing morning or evening apparitions. These paired apparitions take place about two or three times a year, though only one or two of them will be easy to observe from any given location on Earth because of latitude and/or seasonal effects.
Between 2010 and 2015, there are twenty-four occasions when Venus and Mercury come close to each other in the sky. Eight of these occasions (a third of the total) can be eliminated because they are too close to the Sun to observe; of the remaining fifteen, six (40%) favour Northern hemisphere observers, five (33%) favour Southern hemisphere observers and the remaining four (27%) favour both hemispheres equally. A few of them are however difficult to observe from both hemispheres.
The following table lists the dates when our Solar System's two inferior planets can be seen together in the dawn or dusk sky from 2010 to 2015. Because the two planets come together over a period of time, a range of dates is given during which observations should take place. Mercury is more than 15° from the Sun throughout each period, which is usually centred around that planet's greatest elongation date. Searches for the planetary pair should commence shortly after sunset (for evening apparitions) or at the commencement of local morning twilight (for morning apparitions).
If spotting Mercury on these dates initially proves difficult with the unaided eye, panning the region of the sky around and below Venus with a pair of binoculars will help in locating it.
Observing Venus and Mercury together in the sky is a rewarding experience, but it also provides an opportunity to witness the motions of the planets over only a short period of time; in most cases, their relative positions will be seen to change in the course of just one day. Photographers may wish to take advantage of these pairings; a tripod-mounted camera will easily capture our two innermost planetary neighbours in the twilit sky using only a short exposure time. The addition of the crescent Moon to the scene adds further interest for the astro-photographer - to this end, the approximate dates when the Moon is near the two planets are also included in the table.
Paired Apparitions of Venus and Mercury from 2010 to 2015 In most cases the two planets come close together but do not reach conjunction (i.e. they do not attain the same Right Ascension); where they do reach conjunction, the Universal Time (UT) of the event is listed in the column headed 'Conj'. The Solar Elongation refers specifically to the date of closest approach.
The Approximate Period of Visibility is the period during which both Mercury and Venus are more than 15° from the Sun. The Constellation(s) column shows through which constellation(s) one or both of the planets move during the period. The 'Fav. Hem' column shows the Hemisphere in which the pairing will be best observed (Northern or Southern). Where the planet's greatest elongation occurs during the period, this is shown in the Greatest Elongation column; this happens on all occasions for Mercury but only on a handful of occasions for Venus.
To find the direction in which the two planets will be seen on any of the dates in the table, note down the constellation in which the planets are located on the required date and find the constellation's rising direction (for Dawn apparitions) or setting direction (for Dusk apparitions) for your particular latitude in the Rise-Set direction table.
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A Daylight Sighting of Venus
This photograph was taken by the author on June 18th 2007 at 1553 UT (4:53 pm BST) from the south-western United Kingdom. Venus can be seen as a bright point of light just to the right of the waxing crescent Moon, and it was easily seen with the naked eye. The planet's visibility was aided by the close proximity of the Moon, which provided a clear directional reference point and helped to focus the eye.
The photo was taken shortly after the Moon had passed in front of Venus, blocking it from view, in an event called an occultation.
Occultations of bright planets by the Moon are relatively frequent occurences, though any given event can only be seen across a specific region of the Earth. This particular occultation was visible from North-eastern North America, Europe and South-western Asia.
For details of forthcoming occultations, visit the IOTA website, find the 'Predictions' section for the current year then click on 'Worldwide Total Occultations of Major Planets'.
Venus was situated high in the sky and close to the author's local meridian (due South) when the photo was taken. Venus, then at magnitude -4.2, was technically a 'Evening Star', showing a Westward-facing half-phase through telescopes.
The easiest way to spot Venus in daylight is to observe it during a morning apparition, in the couple of weeks around greatest elongation, when the planet is positioned at a safe angular distance from the Sun. Easily spotted at dawn, Venus can then be observed through to sunrise and beyond.
Photo details: Taken using a tripod-mounted Canon EOS 300 Digital SLR camera.
A 250th-second exposure at f/8, ISO 100, with a 55-200mm lens set at 200mm.
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Venus in Transit
While Venus can be seen in the daytime, there is another, very rare event involving the planet that requires daytime viewing. It is known as a transit of Venus, and whenever they are seen they are spectacular to watch and - in recent times - have caused considerable media attention across the world. During a transit, Venus is seen as a small, black dot moving slowly in an East-to-West direction across the face of the Sun. The event lasts about 5-6 hours, depending upon the planet's relative speed and which part of the Sun's disk the planet is transiting. Venus transits can only occur whenever the planet is close to its ascending node or descending node (the points in its orbit where the planet crosses the ecliptic heading Northwards or Southwards, respectively). For a transit of Venus to take place, the planet must be within a few days of inferior conjunction (directly between the Earth and the Sun) and be crossing one of these nodes at the same time. Because of the positioning of the nodes in relation to the Earth's orbit, transits can only take place around June 7th (descending node) or December 8th (ascending node) although the node positions and the event dates slowly change over time. The ascending and descending nodes of the planets are positioned exactly 180° apart - hence the six-month difference between these two dates.
Transits of Venus take place at intervals of 113½ years ± 8 years. In other words, they occur in pairs (one 8-year Venus cycle apart) after an interval of just over a century. The pattern runs as follows: 121½ years, 8 years, 105½ years, 8 years, 121½ years, etc. There were no Venus transits in the 20th century (prior to that, they took place in December 1874 and December 1882). The first transit of the 21st century took place on June 8th 2004 and the next (8 years later) was on June 5th-6th 2012; the 2004 event transited the Southern hemisphere of the Sun and that in 2012 transited the Northern hemisphere of the Sun.
Transit of Venus
The first of only two Venus transits in the 21st century took place on June 8th 2004. The silhouette of Venus appeared as a small, circular black dot on the Sun's disk when projected through a telescope on to a piece of card.
The safest way to observe Venus transits is to project the image of the Sun through a refracting telescope on to a piece of white card (i.e. the image of the Sun is projected backward through the telescope, from the main object glass through to the eyepiece and on to the card). In practice, a second piece of card is normally attached to the telescope, positioned just behind the eyepiece and perpendicular to the telescope's axis, in order to create a shadow around the projected image and thereby improving its contrast. The solar image on the card appears pale white, the silhouette of Venus looking like a small black dot (rather like a large sunspot). Transits can also be observed safely through a telescope by attaching an aluminised mylar solar filter to the front of the telescope, ahead of the object glass (always ensuring beforehand that the filter has not been damaged in any way!!). If a Mylar filter is used the solar disk appears pale blue. Filters can also be purchased which can be attached to conventional cameras for photographing the event.
Similar filters for observing transits are commercially available which allow direct observing of the Sun using a pair of cardboard 'spectacles' (referred to as solar viewers or eclipse shades); these are commonly sold to the general public in advance of a total eclipse of the Sun. Again, extreme caution must be taken when using them.
When wearing eye protection, can Venus be seen against the Sun using just the naked-eye? The human eye is capable of resolving objects down to about 1' (1 arcminute, or 1/60th of a degree). At inferior conjunction, Venus can attain an apparent diameter of up to 65" (65 arcseconds, or just over 1 arcminute) so it is therefore possible to see the planet's disk against the Sun with the naked-eye, assuming of course that one is wearing eye protection and has good eyesight. During the June 2004 transit, the author was fortunate enough to have clear skies for the event from his observing location in the south-western United Kingdom (albeit a little cloudy at the start!). Looking through solar viewer 'glasses', Venus could be discerned as a tiny dot - at the threshold of visibility - against the solar disk.
The 2004 event was seen from much of the inhabited world, with the exception of the Western USA, Mexico, New Zealand and Southern Chile/Argentina. The 2012 event was seen in its entirity from eastern Asia, the South-east Pacific Ocean (New Zealand and central/Eastern Australia), the North-western USA (Alaska) and North-western Canada (the Sun being above the horizon throughout). For much of the inhabited world, however, the transit was already in progress at sunrise or sunset so it was not seen in its entirity. Observers in Portugal, South-western Spain, Western and South-western Africa and the Southern and Eastern regions of South America did not see the event at all because the Sun was below the horizon. More details of the 2012 transit (with an animation showing its progress and visibility across the world) can be found on the 'Venus Transit 2012' page.
Mercury is also involved in solar transits, since it also passes directly between the Earth and the Sun. Mercury, however, appears much smaller than Venus so a telescope is always required to view the event. Transits of Mercury are much more common than Venus transits; again they can only take place when the planet's node crossing coincides with its inferior conjunction (for Mercury, this is around November 9th and May 7th). November transits of Mercury repeat at intervals of 7, 13 and 46 years whilst those in May repeat at intervals of 13 and 46 years (hence November transits are more common than May transits). May transits are slower than November transits because Mercury is then close to the aphelion point in its orbit (i.e. its furthest point from the Sun); likewise November transits are swifter because the planet is then near perihelion (its closest point to the Sun). The last transit of Mercury took place on November 8th 2006 and the next will be on May 9th-10th 2016.
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Viewing Venus before Sunrise/after Sunset, 2010 to 2020
When is the best time to see Venus with the naked-eye?
This question is frequently asked by newcomers to astronomy, however the answer is not quite as straightforward as it might first seem. Essentially, there are four ways in which the 'best' time to see the planet can be defined: by maximum altitude, by maximum brightness, by maximum elongation and by maximum visibility duration. These will now be discussed in turn.
(a) By Maximum Altitude
Telescopic observers of Venus often prefer to observe the planet in bright twilight or daylight (see above) because the planet's brilliance causes an uncomfortable glare when seen through the eyepiece against a dark sky. The planet's altitude (angle above the horizon) is then high up, where atmospheric turbulence is less of a problem than when the planet is positioned low down above the horizon (where it is normally positioned after sunset or before sunrise).
A planet reaches its highest point in the sky when it crosses the observer's meridian (the theoretical line passing directly above the observer's head from North to South - see diagram). However in the case of the inferior planets (Mercury and Venus) this always happens in daylight because these planets are never far away from the Sun. Whilst Venus can be glimpsed with the naked-eye in daylight when it is far away from the Sun (the Sun being carefully shielded from view), it is highly dangerous to attempt observing the planet when it is close to the Sun!!
Having ruled out (on practical grounds) daylight observations of Venus by the naked-eye, it follows that the optimum time to catch the planet is when it is highest in the sky, either before sunrise (for morning apparitions) or after sunset (for evening apparitions).
In the tables which follow, the direction and altitude of Venus are listed for a variety of latitudes at a point in time thirty minutes before sunrise/after sunset. While this might seem an arbitrary time to adopt, it is useful in that the planet is almost always visible by this time (though the sky itself will not normally be dark enough for stars to be seen). The planet will also be about as high in the sky as it can possibly be whilst still being clearly visible to the naked-eye (thus allowing a telescope to be pointed at it safely, under twilit conditions). For evening apparitions, thirty minutes after sunset is also the time at which observers hunting for Mercury will often begin their search for that planet (if it is also undergoing an evening apparition).
Table 1 shows the highest altitude attained by the planet (30 minutes before sunrise/after sunset) for a variety of latitudes. Because Venus apparitions repeat in an 8-year cycle (see 'The Venus 8-year Cycle' below) the table is arranged such that the maximum altitude of the planet can be looked up within each apparition. For example, in 2010 (year designator A under the author's 8-year cycle sequence) observers situated at latitude 40º North found Venus highest in the sky (30 minutes after sunset, since it was an evening apparition) in early June, when it was seen at an altitude of 21º above the West-North-Western horizon. The table also tells us which latitudes will benefit most during any particular Venus apparition; in 2010, observers situated in low Southern latitudes (25º to 35º South) saw the planet at a higher altitude than anywhere else, though this did not occur until mid- to late August.
Table 1: Maximum altitudes attained by Venus (30 mins before sunrise/after sunset) during the 8-year cycle for a variety of latitudes from 2010 to 2020. For example, in 2013 from latitude 30° North, the maximum altitude at which Venus will be seen (30 minutes after sunset, since it is an Evening apparition) will be 24° in early December of that year, at which time it will be seen in the South-west; the planet will be positioned in Sagittarius at the time. Note that in some years (e.g. 2012 and 2015) there are two Greatest Elongations in the same year (an Evening and a Morning elongation); the Evening elongation always takes place first. There are no greatest elongations in 2016.
The Approximate Apparition Period is the period during which Venus is positioned more than 10° in longitude from the Sun; these are the earliest and latest dates at which Venus is likely to be seen. These dates apply primarily to Equatorial latitudes; from other latitudes, the planet is likely to become visible some time after the first date listed, and to become lost from view some time before the second date listed.
The Venus Elongation Cycle Year Designator (column VEC YD) is the author's attempt to simplify the Venus 8-year cycle into a memorable format - see the section entitled 'The Venus 8-year Cycle' below for a full explanation. In the above table the Venus Cycle begins to repeat from 2018, when the Greatest Elongation (46°E) takes place in mid-August, as it had done 8 years earlier in 2010.
The range of visible altitudes of the planet through the various apparitions is not solely a consequence of the observers' latitude; Venus is continually moving along the ecliptic (the path of the Sun, Moon and planets through the zodiac) which carries the planet further North or South during the course of any given apparition. The planet's movement is predominantly Eastward (known as prograde motion) but it is occasionally Westward (retrograde). In general, planets situated at a Northern declination (i.e. at angles North of the celestial equator, e.g. +9º, +22º, etc) are better seen from the Northern hemisphere, and planets positioned at a Southern declination (e.g. -12º, -20º) are better seen from the Southern hemisphere. Hence if the planet heads Northwards along the ecliptic during any particular apparition, its visibility from the Northern hemisphere will generally begin to improve, and if it heads Southwards its visibility from the Southern hemisphere will improve. In the case of the inferior planets, this will only apply if the planet's solar elongation (its angular distance from the Sun) is sufficiently wide for the planet to remain well seen.
Note that, because the rising and setting angles of celestial bodies around the Equator (latitude 0º) are very steep, the continual Northward-Southward motion of Venus along the ecliptic often has little overall effect on its altitude when seen from these latitudes.
One might think that Venus' maximum altitude in the evening or morning sky would be reached when the planet attained its highest declination during an apparition. Whilst this holds true for the superior planets, for the inferior planets it is not always the case because their visibility is restricted to the region of sky which is only a short angular distance above the Eastern or Western horizon. Superior planets can easily be seen whenever they cross the meridian (this happens in darkness for much of the year) however when Venus crosses the meridian (i.e. when it is highest) it is always daylight. Consequently, only telescopic observers benefit from Venus' high declination values. When the planet is low above the Eastern/Western horizon before sunrise/after sunset, a high declination value has little effect on its altitude; in fact its solar elongation is the greater factor. For the inferior planets the main result of high declination values is to carry the planets' rising or setting points further North or South along the horizon. A high Northerly declination will cause the planet to rise/set further North along the horizon, whilst a high Southerly declination will cause it to rise/set further South along the horizon.
Also included in the table is the constellation in which the planet is positioned at the date indicated. Hence in 2010 in early June, Venus is positioned in the constellation of Gemini; it then heads Southward, through Cancer, Leo and into Virgo, where it is situated when it is seen at its highest altitude (at latitude 35º South) in late August of that year.
Note how the maximum altitude of the planet during any particular apparition drifts across the various latitudes over time, the lag time being from two to four months. During such a prolonged period, Venus' distance, apparent size (angular diameter), phase and brightness will have changed somewhat. Staying with the 2010 apparition, an observer situated at latitude 40º North viewing the planet when it is highest in the sky after sunset (in early June) will see it as a small object showing a gibbous phase through a telescope, shining at an apparent magnitude of -4.0. An observer situated at latitude 45º South, however, will see the planet at twice the apparent size and showing a half-phase by the time it is highest in their sky in late August of that year; the planet will also have brightened to magnitude -4.3. It is also worth pointing out that, because of seasonal variations, a planet may be highest in an observer's sky at a time which coincides with local high summer, so that the planet is seen mostly against a twilit sky. Whilst this would normally be a major obstacle to observing most other planets, in the case of Venus it is much less of a concern because of its sheer brilliance.
Table 1 allows us to follow the motion of Venus through the zodiac constellations during each of the planet's ten apparitions. Depending upon the apparition in question, the dates will read either right-to-left across the table, or left-to-right. Hence in the 2010 apparition (year designator A) the dates move from left-to-right across the table, the planet moving from Taurus through to Virgo, whilst in the 2013/14 apparition (year designator D) the dates move from right-to-left, the planet moving from Scorpius through to Sagittarius during that time. The changing date directions are a consequence of the planet's motion through the zodiac, coupled with the particular arrangement of latitudes across the table.
Looking at the table in general, Venus' altitude is seen to be rather higher when viewed from Southern hemisphere latitudes than from Northern. Whilst this is partly due to Solar System mechanics, it is mostly caused by the fact that the majority of the Southern hemisphere population resides in low Southern latitudes (i.e. North of 45º South) whereas the population in the Northern hemisphere extends to much higher latitudes (50º North and higher) where Venus' altitude is typically much lower.
(b) By Maximum Brightness
Whilst Venus is always very bright (it is always brighter than apparent magnitude -3.8) there is an argument to be made that the best time to view the planet is when it reaches its maximum brightness. In practice, the brightness variations shown by Venus around its peak brightness are rather small and most observers will notice little difference with the naked-eye. Also, Venus is often viewed in twilight, which confuses the picture somewhat since a fair brightness comparison cannot be made when seeing the planet against a dark sky as opposed to a twilit sky.
Nonetheless Venus does have two positions within its orbit when it is reaches its brightest magnitude as seen from the Earth, and they take place in the same relative positions in each apparition. They are referred to as the greatest brilliance (or greatest brilliancy) points and they occur when the planet is 40º East or West of the Sun and it displays a 28% illuminated crescent phase. Venus will typically attain a magnitude somewhere between -3.9 and -4.5 around these times, the brightness variation being due to the changing distances between Venus and the Earth on each occasion. Venus' greatest brilliance occurs about 35 days (5 weeks) after its greatest elongation East (in evening apparitions) and 35 days (5 weeks) before its greatest elongation West (in morning apparitions).
The brightest magnitude Venus can attain is around -4.6 (some sources say -4.7) and this occurs when the planet is not only at its greatest brilliancy point but also close to its perihelion (i.e. the point in its orbit which brings it closest to the Sun). During a Venus apparition cycle of 8 years, there are four occasions where the planet reaches its greatest brilliancy point within a month or two of the planet's perihelion; referring to Table 1, these are in mid-December 2010 (a morning apparition, year designator B under the author's Venus cycle sequence), early December 2013 (an evening apparition, year designator D), mid-February 2014 (a morning apparition, year designator E) and mid-February 2017 (an evening apparition, year designator H1).
Note that Venus' greatest brilliance is sometimes referred to by its more technically-correct term greatest illuminated extent. In other words, it is the time at which the planet shows the greatest illuminated area on the sky, taking account of the fact that the planet's apparent diameter (angular size) changes considerably during the course of any given apparition. For example, when the planet is approaching inferior conjunction and displaying a large crescent phase, the planet's apparent diameter is considerably larger than it displays at its greatest brilliance point. However the crescent is also much thinner as it approaches inferior conjunction, thereby reducing the overall area which is illuminated.
(c) By Maximum Elongation
It is commonly thought that the best time to observe Venus is when it reaches its maximum elongation (greatest elongation) from the Sun. The planet is then at its greatest angular distance from the Sun, theoretically allowing an extensive period of observation. However the situation is complicated because Venus is subject to the same visibility problems as its partner inferior planet, Mercury. The angle of the ecliptic to the local horizon before sunrise/after sunset varies according to latitude and season, so that the planet appears high above the horizon on some occasions, but low down on other occasions. At equatorial latitudes and up to mid-Northern and mid-Southern latitudes, the effect is minimal because of the steeper rising and setting angles of celestial bodies, however the closer to the Polar regions an observer is situated, the more significant this effect becomes. Hence observers situated at high-Northern latitudes (about 45º North and higher) and high-Southern latitudes (about 45º South and higher) will experience this effect the most.
At high-Northern latitudes, for example, greatest elongations taking place on Spring evenings are better seen than those on Spring mornings, whilst greatest elongations taking place on Autumn mornings are better seen than those on Autumn evenings.
If one adopts the Southern hemisphere definition of the seasons (i.e. the local seasons, where Spring begins at the September Equinox, summer begins at the December Solstice, etc.) then high-Southern latitudes will experience the same effect as high-Northern latitudes: greatest elongations taking place on Spring evenings are better seen than those on Spring mornings, whilst greatest elongations taking place on Autumn mornings are better seen than those on Autumn evenings. However, as has previously been mentioned, the impact of this is not too severe since the majority of the Southern hemisphere population resides to the North of latitude 45º South.
The visibility of the inferior planets as seen from high-Northern and high-Southern latitudes is summarised in Table 2.
Table 2: Visibility of Mercury & Venus from high Latitudes according to Local Season
Visibility is graded as Good/Fair/Poor, indicating a steep/medium/shallow ecliptic angle to the local horizon, respectively.
Hence greatest elongations taking place in late October mornings (Autumn/Fall in the Northern hemisphere, Spring in the Southern hemisphere) will be well seen from high-Northern latitudes but poorly seen from high-Southern latitudes.
Likewise, greatest elongations taking place in late March evenings (Spring in the Northern hemisphere, Autumn in the Southern hemisphere) will be well seen from high-Northern latitudes but poorly seen from high-Southern latitudes.
At times of the year other than the ideal dates, the angular distance of Venus at greatest elongation (45º, 46º or 47º from the Sun) can cause problems because the planet may then occupy a part of the ecliptic which places it low above the horizon before sunrise or after sunset (these times of the year are listed under 'Poor' visibility in Table 2). A good example of this occurs when Venus' greatest elongation East takes place in Autumn evenings at high-Northern latitudes. At this time the Sun occupies a position along the ecliptic on the Virgo/Libra border, whilst Venus is positioned in Ophiuchus, about 47º South-east of the Sun. Venus is then close to its most Southerly position in the zodiac, occupying a part of the ecliptic which presents a shallow angle to the local horizon just after sunset - consequently placing the planet low down in the sky. At the same time, in high-Southern latitudes (where it is then Spring) the ecliptic presents a steep angle to the local horizon, providing excellent views of the planet.
Indeed, it is often the case that when visibility is good in one hemisphere, it is poor in the other. In the Northern hemisphere, for example, when Venus reaches greatest elongation East on Spring evenings the Sun is positioned in Pisces and Venus is positioned in Aries, some 46º North-east of the Sun. Seen from the Northern hemisphere, the ecliptic then presents a steep angle to the local horizon, the planet appearing high in the sky after sunset, giving the best possible view of the planet from that hemisphere. However, in the Southern hemisphere (where it is Autumn) the view is poor, the ecliptic presenting a shallow angle to the local horizon after sunset.
The situation on the planet's greatest elongation day is demonstrated in Table 3, which lists each of the Venus apparitions in the 8-year cycle (see below for details) showing the planet's altitude and direction in the sky (30 minutes before sunrise/after sunset). It is interesting to compare the altitudes attained by the planet on its greatest elongation day with the highest altitude attained by the planet at other times during the same apparition (listed in Table 1); this will be discussed in greater detail in the following section.
Table 3: Altitude & Direction (30 mins before sunrise/after sunset) & Visibility Duration of Venus on the day of Greatest Elongation for a variety of latitudes during the 8-year cycle from 2010 to 2018. The Visibility Duration of the planet (in hrs:mins) is the length of time during which Venus is above the horizon before sunrise (for Morning apparitions) or after sunset (for Evening apparitions). An italicised duration means that Venus is seen under twilight conditions through to its setting, i.e. it is not seen against a truly dark sky (twilight in this case refers to nautical twilight, which ends when the Sun is more than 12° below the horizon).
For example, in 2014 from latitude 40° North at thirty minutes before sunrise (since it is a Morning apparition) Venus will be seen at an altitude of 18° in the South-east; the planet will be visible for approximately 2 hrs and 3 mins before sunrise. Note that in some years (e.g. 2012 and 2015) there are two Greatest Elongations in the same year (an Evening and a Morning elongation); the Evening elongation always taking place first. There are no greatest elongations in 2016.
The Declination (Dec) is the angle of the planet measured North (+) or South (-) of the celestial equator on greatest elongation day. On the greatest elongation date, Venus' apparent magnitude is typically around -4.2 to -4.3.
The Venus Elongation Cycle Year Designator (column VEC YD) is the author's attempt to simplify the Venus 8-year cycle into a memorable format - see the section entitled 'The Venus 8-year Cycle' below for a full explanation.
(d) By Maximum Visibility Duration
During which part of Venus' apparition is the planet visible for the longest period of time before sunrise/after sunset?
The answer is commonly thought to be on its greatest elongation date (either East or West of the Sun), since the maximum angle of the planet from the Sun, when converted into Earth rotation time, theoretically equates to a maximum visibility duration on this date. If one assumes that a typical Venus greatest elongation angle is 45º from the Sun, and the Earth rotates at a rate of 15º per hour (i.e. the stars and planets appear to move Westwards at 15º per hour in the night sky) then Venus will be visible for (45º / 15º) = 3 hours before sunrise/after sunset on its greatest elongation date. In reality, the duration for which the planet is visible on greatest elongation day varies considerably according to the planet's position along the ecliptic, the observer's latitude and whether it is a morning or evening apparition.
Apart from its altitude and direction, Table 3 also includes the duration for which Venus is visible before sunrise (for morning elongations) or after sunset (for evening elongations). The variation is considerable indeed: from a mere 27 minutes to almost 5½ hours! Such extremes are seen to occur at high latitudes (in this case 60º North), far away from the Equator, where the visibility duration on greatest elongation day varies only slightly from the expected 3 hours. The most consistent duration in the 8-year cycle occurs in 2015 (year designator F1) where each latitude in the table sees Venus in the sky for just over 3 hours after sunset; the variation across latitudes in this case being only 9 minutes.
The average visibility duration of Venus on greatest elongation day, taken across all latitudes in the table and all apparitions in the 8-year cycle, is found to be 3 hours 2 minutes. The visibility duration for each individual latitude across the ten apparitions also averages out at about 3 hours. The visibility duration of Venus on greatest elongation day in any single apparition, however, does vary considerably according to the observer's latitude. Equatorial latitudes show little variation from the expected 3 hours (within 30 minutes or so) but the further one is situated from the Equator, the more significantly the duration is affected. This will largely depend upon Venus' declination on greatest elongation day; if it is positioned far above the celestial equator, (e.g. declination = +22º) its visibility will generally be better from the Northern hemisphere, but if it is far South of the celestial equator (e.g. declination = -22º) Southern latitudes will generally see it for longer.
Maximum visibility duration is directly related to maximum altitude, because the higher a planet is positioned in the night sky, the longer it will be visible for. If Venus reaches a high altitude in the sky before sunrise (on morning apparitions) it will have risen a long time beforehand. Likewise if the planet is high in the sky as it gets dark (e.g. 30 minutes after sunset during an evening apparition) it will remain visible for a long period of time before it sets. In this respect, it is worth comparing the altitude values in Table 3 with those listed in Table 1, which shows the maximum altitude attained by Venus thirty minutes before sunrise/after sunset during each of its ten apparitions. There is a rather surprising finding: the majority of the altitudes (61%) are not highest at the time of greatest elongation, but they are higher at another time of the year - despite the fact that the planet's solar elongation is then narrower. For example, at latitude 50º North in 2017 (year designator H2), the altitude of Venus on greatest elongation day (June 3rd) is 11º, when the planet is seen above the Eastern horizon at dawn. However, Table 1 shows us that in 2017, the maximum altitude attained by the planet during the apparition is 23º (12º higher than on greatest elongation day) which occurs in mid-August of that year, i.e. some 2½ months after greatest elongation day. Because of the higher altitude, the planet's visibility duration before sunrise in mid-August will also be substantially longer than 1 hr 42 minutes (the visibility duration on greatest elongation day). The altitude difference at this relatively high latitude can amount to several degrees, however as one gets closer to the Equator it becomes much less (1º or 2º). Nonetheless this does demonstrate that the highest altitude at which Venus will be seen during any given apparition - and hence its longest visibility duration - will not necessarily take place on greatest elongation day, as is commonly believed (Mercury, on the other hand, is best seen when at greatest elongation, since its narrow solar elongation affords us little opportunity to view it at other times).
To conclude, there is no 'best' time to see Venus with the naked-eye - in fact it is a trade-off between altitude, brightness, elongation distance and visibility duration. Venus is interesting to view at all times during its apparition, its constantly varying dynamics providing a real challenge to the dedicated naked-eye planet observer.
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The Venus 8-Year Cycle: Greatest Elongation & Conjunction Date Ranges, 2010 to 2041
Venus completes one orbit of the Sun in 224.7 Earth days (i.e. 0.61521 tropical years, or about 8 months). Viewed from the orbiting Earth, Venus takes 583.9 days (1.5986 tropical years, just over 19 months) to move from one inferior conjunction to the next; this is known as the synodic period, which is defined as a planets' orbital period as seen from the Earth. It is the time taken for a planet to return to a particular orbital configuration, e.g. a conjunction or (for superior planets) an opposition (for further details on Venus' varying configurations, see the 'Planet Movements' page).
Venus and the Earth have, over many millions of years, reached an orbital near-resonance such that 8 Earth orbits are very nearly equal to 13 Venus orbits (i.e. 13 orbits x 0.61521 years = 7.9977 Earth orbits). Essentially this means that every 8 years, as seen from the Earth, Venus returns to very nearly the same part of the sky with respect to the background stars (usually within about 2º of its previous position). Hence if we see Venus in the constellation of Gemini in early June of 2010, we can expect to see it at nearly the same position in Gemini in early June of 2018. This is commonly referred to as the Venus 8-Year Cycle and its existence has been known since ancient times.
However, since thirteen Venus orbits do not equal eight Earth orbits exactly (they are a little short of it) the cycle is not a precise one. Consequently, after each cycle, Venus drifts westwards along the zodiac by about 2º.3, its associated orbital configurations taking place 2-3 days earlier. In 2011 for example, Venus reaches its greatest Western elongation on January 8th; eight years later (2019) its greatest Western elongation takes place on January 6th (i.e. two days earlier). Venus' orbital configuration dates drift backwards through the calendar by about 2.34 days per 8-year cycle, completing a full year in about 1,247 Earth years (about 156 Venus cycles). The 2-3 day backward drift is only partly caused by the inexact resonance between the two planets. After a full cycle, Venus arrives at the same point in the sky only about 22 hours 'early'; the majority of the drift is caused by the addition of the Leap Day every four years (two days of which will occur in an 8-year period).
An apparition is defined as the period of time during which a planet can be seen from the Earth; it excludes the time when planet is too close to the Sun to be visible. In the case of Venus, this will typically be when it is more than about 10º from the Sun (for most planets it is 15º or more, however Venus is bright enough to be seen in bright twilight or even daylight). Venus will typically be caught in the glare of the Sun for a total of around 90 days in any synodic period; the non-visibility period is much shorter when it passes through inferior conjunction (on the near side of the Sun to the Earth) than when it passes through superior conjunction (on the far side of the Sun) because the planet's apparent motion is much faster when it passes between the Earth and the Sun.
In the course of an 8-year cycle, Venus will be seen to complete ten apparitions (five in the morning and five in the evening), each apparition lasting about 35 weeks (9 months). With each successive apparition, the planet is positioned further Eastwards along the ecliptic by about 215º (roughly seven zodiac constellations further along). Because each apparition is about 9 months long (plus a period in between apparitions where the planet is too near the Sun to observe) it follows that in some years the apparition will extend into the following year.
In Tables 1, 3 and 4 the author has assigned a letter or a letter/number combination (A, C1, etc.) to each apparition in the Venus cycle (the letters refer to a specific calendar year, based upon when the planet's greatest elongation takes place - this is explained more fully below). The five evening apparitions are A, C1, D, F1 and H1 and the five morning apparitions are B, C2, E, F2 and H2. If we were to plot the position of Venus above the horizon at 30 minutes after sunset on each day during a particular evening apparition, we would see the planet trace out an intriguing but beautiful path across the Western sky. The appearance of this path will depend upon the observer's latitude and the position of Venus in the zodiac during the particular apparition. In the diagrams below, the path of Venus for each of the five evening apparitions are shown for an observer situated at a high-Northern latitude of 55º North.
The Path of Venus in the Evening Sky (30 mins after sunset) for an observer at latitude 55° North during Apparition A (e.g. 2002, 2010 and 2018).
The Path of Venus in the Evening Sky (30 mins after sunset) for an observer at latitude 55° North during Apparition C1 (e.g. 2003/2004, 2011/2012 and 2019/2020).
The Path of Venus in the Evening Sky (30 mins after sunset) for an observer at latitude 55° North during Apparition D (e.g. 2005/2006, 2013/2014 and 2021/2022).
A composite photograph of the 2005/2006 apparition was taken from Istanbul (latitude 41° North) by Turkish amateur astronomer Tunc Tezel.
The Path of Venus in the Evening Sky (30 mins after sunset) for an observer at latitude 55° North during Apparition F1 (e.g. 2006/2007, 2014/2015 and 2022/2023).
The Path of Venus in the Evening Sky (30 mins after sunset) for an observer at latitude 55° North during Apparition H1 (e.g. 2008/2009, 2016/2017 and 2024/2025).
A composite photograph of the 2000/2001 apparition (also apparition H1) was taken from Istanbul (latitude 41° North) by Turkish amateur astronomer Tunc Tezel.
Paths of Venus in the Evening Sky (30 mins after sunset) for each of the five evening apparitions in the Venus cycle, as seen by an observer at latitude 55° North. Move your pointing device over each image (or click on the picture) to see the approximate dates when the planet attains each part of the track (the dates are approximate because the diagrams do not refer to specific years). The dates are colour-coded such that the year in which greatest elongation takes place is green; where an apparition begins in the previous year, the dates are shown in pink and where the apparition continues into the following year the dates are shown in yellow. The letters GE refer to the planet's greatest elongation (followed in brackets by its angular distance from the Sun) and the letters GB refer to the planet's greatest brilliance point (followed in brackets by its apparent magnitude).
The azimuth (Az, along the bottom of each diagram) is the bearing measured clockwise from True North (where 0° = North, 90° = East, 180° = South, etc.). The altitude (Alt) is the angle measured vertically from the local horizon (the horizon itself is 0°); to see how altitude is measured, see the diagram here. Azimuth and altitude are co-ordinates which are used for high-accuracy tracking of objects across the sky; in astronomy it is mainly used for setting telescopes which are fitted with altazimuth mounts.
The five Venus paths show interesting variations in their height (altitude) and width (azimuthal range). The discerning naked-eye observer will be looking to see when the planet's maximum altitude (highest point of the curve) nearly coincides with its greatest elongation, because this will be the optimum time to observe it. At latitude 55° North this occurs in apparition C1 (calendar years 2004, 2012, 2020..). Apparition H1 is also favourable (although a little less so, the planet being positioned lower down in the sky) and perhaps also apparition F1. Apparitions A and D are poor, the planet being low down virtually throughout. These observations are of course specific to latitude 55° North, although they hold well for high-Northern latitudes in general. For latitudes which are closer to the Equator the paths traced out by Venus will generally be more open and higher, reaching the maximum altitudes shown in Table 1 above.
Note that apparitions C1 and H1 are rather similar in form because during these apparitions the planet's position in the zodiac differs by just one or two constellations. One evident difference between the two apparitions is the planet's setting position towards the end of the period. In apparition H1 the planet sets in the West-North-West at the end of the apparition in late March, when it is positioned in the constellation of Pisces. In apparition C1, however, the planet sets further Northwards at the end of the apparition (in late May) because it is then positioned at a more Northerly declination in Taurus (the effect of declination on a planet's rising/setting positions is discussed in the section 'Maximum Altitude' above).
In all cases where Venus is seen as an 'Evening Star', the planet enters the evening sky slowly, gaining altitude only gradually over time and reaching greatest elongation (East) several months later, but it exits the evening sky swiftly, losing altitude rapidly as it races towards inferior conjunction (when it passes directly between the Earth and the Sun). When the planet becomes a 'Morning Star' the opposite is true; it enters the morning sky swiftly, gaining altitude rapidly and taking only a couple of months to reach greatest elongation (West). There then follows a prolonged period of altitude loss, the planet exiting the sky slowly as it crawls towards superior conjunction (when it passes directly behind the Sun as seen from the Earth).
The 'Venus Elongation Cycle Sequence'
For the naked-eye observer, the Venus cycle provides a convenient mechanism with which to determine when a particular apparition will repeat, and to estimate the date(s) on which future orbital configurations will occur. The author will now attempt to simplify the Venus cycle into a memorable format, based upon the planet's greatest elongation date, one of which occurs in every apparition (an Eastern elongation in evening apparitions and a Western elongation in morning apparitions). It takes the form of an eight-letter sequence which the author has dubbed the 'Venus Elongation Cycle Sequence'.
In Tables 1, 3 and 4 the author has assigned a letter (A to H) to a specific calendar year in the Venus cycle (in this case A = 2010, B = 2011, etc.). Hence the period A to H covers eight years, i.e. the Venus cycle. Since Venus has ten apparitions during this period (i.e. ten greatest elongations) a few of these years will contain more than one greatest elongation. The years in the sequence which contain two greatest elongations are suffixed with the number 1 (for an evening elongation) and 2 (for a morning elongation); these are C, F and H (in this case 2012, 2015 and 2017). Hence the year 2012 (year C) has both an evening greatest elongation (C1) and a morning greatest elongation (C2). Evening greatest elongations will always be found to precede morning greatest elongations in any given calendar year.
The sequence commences with a greatest elongation in the evening (A = 2010) then alternates (B = morning, C1 = evening, C2 = morning, etc) until the full cycle plays out and returns back to greatest elongation A (= 2018) eight years after the first.
Year G is the exception, since it contains no greatest elongations; it only contains an inferior conjunction (currently in early June). Year G contains the last part of a morning apparition (its greatest elongation taking place in the previous year) and the first part of an evening apparition (its greatest elongation taking place in the following year).
Therefore, we only need to remember the sequence:
A, B, C1-C2, D, E, F1-F2, (G), H1-H2
.. which begins with 2010 (year A, an evening elongation) and we have an entire Venus cycle stored in memory (year G is in brackets since it contains no greatest elongations). Future greatest elongation years (through to about 2041) can be determined using this sequence. Beyond 2017, starting years can be determined by adding multiples of 8 to the year 2010, and this will be the starting year (A) of another 8-year cycle. For example, two Venus cycles into the future gives us 2010 + (2 cycles x 8) = 2026 which is our new starting year (A) and evidently an evening greatest elongation.
We can now determine whether a specific year in the future will contain a morning or an evening greatest elongation. Simply subtract multiples of 8 from the year in question to bring it into the range 2010 (A) to 2017 (H1-H2). Say we wish to determine whether the year 2028 will contain a greatest elongation in the morning or the evening. We proceed as follows:
(2028 - 8) = 2020 (not within required range),
then (2020 - 8) = 2012 (within required range)
Therefore, the year 2028 will have the same greatest elongation(s) as that of 2012. We know from the memorized sequence that the start year (A) is 2010, so 2012 is the third year in the sequence, i.e. it is the third letter of the alphabet (= C). Now, we know that C has two greatest elongations within the same year (C1 and C2), the first (suffix 1) being an evening one. So in answer to our question, the year 2028 will contain two elongations, the first being an evening one and the second being a morning one.
Note that the sequence is based specifically upon Venus' greatest elongation dates and not on its apparitions; an apparition often begins in the year prior to a greatest elongation, or it ends in the year following a greatest elongation. In fact, in only three years of the 8-year cycle does an apparition begin and end within the same calendar year. Approximate start and end dates of the ten apparitions of the Venus cycle (for the years 2010 to 2020) are listed in the 'Maximum Altitude & Direction Table' above and the evening apparitions are illustrated in the above horizon diagrams (for latitude 55° North). The sequence does however help to establish whether an evening apparition, a morning apparition or both will take place (or have taken place) in any particular year.
The Venus cycle is summarised in Table 4, which gives the date ranges of the various orbital configurations within each of the apparition years. In this instance, Venus' inferior and superior conjunction dates are included which, like the other orbital configuration dates, drift backwards through the calendar over time.
Table 4: Venus Greatest Elongation & Conjunction Date Ranges & the 8-year Apparition Cycle for the period from 2010 to 2041, covering four Venus cycles. The years are grouped according to their Venus Elongation Cycle Year Designator and the events taking place in each apparition are listed, along with their date ranges.
For example, in the years 2011, 2019, 2027 and 2035 (Elongation Cycle Year 'B') Venus will be a Morning object, reaching its Greatest Western Elongation (47°W) in early January and reaching Superior Conjunction (passing directly behind the Sun as seen from the Earth) around mid-August. Some years include an Evening and a Morning elongation, e.g. the years 2012, 2020, 2028 and 2036 (Years 'C1' and 'C2' ); the Evening elongation appears under apparition'C1' and the Morning elongation appears under apparition'C2'.
Because successive dates in the 8-year cycle drift backwards in time by 2-3 days per cycle, the dates are listed with their associated year in brackets. Hence in Year 'A', the Greatest Elongation East date drifts backwards in time from Aug 20 (in 2010) to Aug 12 (in 2034). To determine an event date for a specific year through to 2041 (accurate to about 1 day), use the following method:
Say we wish to find the date of Venus' Greatest Elongation East in the year 2028. Look up the year in question (in the Years column; in this case it is under Year 'C1') then find the first date listed under the required event column (in this case Greatest Elongation East). The first date listed is March 27th (for 2012). Deduct the required year from the first year listed (hence 2028 - 2012 = 16 years) then multiply this by 0.2925 (i.e. 16 years x 0.2925 = 4.68 days, or about 5 days). This is the approximate number of days that the event date has drifted backward in time since the first event date listed. Now deduct the number of days' drift from the first date; the result will be the date of the event for the required year (in this case, March 27th minus 5 days = March 22nd). Therefore, in 2028 Venus' Greatest Elongation East will take place on March 22nd ± 1 day.
Future Amendments to the Sequence
It was mentioned a little earlier that the sequence works for dates through to 2041. Because the dates of greatest elongation drift backward through the calendar at 2-3 days per 8-year cycle, they will inevitably drift back into the previous year, at which time the sequence will require revision. This will first occur in 2042, by which time Venus' greatest elongation West will have drifted from early January (where it will be positioned through to 2035) into late December of 2042. At this point, year B will lose a greatest elongation West and year A will gain a greatest elongation West. Year A will then contain both an Eastern and a Western elongation, so it will split into A1 and A2 (again, the earliest apparition will be an evening one). The next revision will be required in 2056, when Venus' greatest elongation East will have drifted from early January (where it will be positioned through to 2049) into late December of 2056. Year H1 will then lose its greatest elongation East and year G will gain a greatest elongation East, so H1 and H2 will simply become H (since it will only have one greatest elongation in the year). Thereafter, no further changes to the sequence will be required for another 237 years.
If we include Venus' inferior and superior conjunction dates (i.e. if we include this data in table form, as in Table 4 above) changes will be required at more regular intervals. By 2049, for example, Venus' superior conjunction will have drifted back from early January (where it will be in 2042) into late December of 2049; year A will then lose a superior conjunction and year H will gain a superior conjunction. However the sequence itself will only require an amendment whenever a greatest elongation date drifts back into a previous year.
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Current Position of the Sun and the Brighter Naked-Eye Planets ('Live' Star Map)
Copyright © Martin J Powell March 2010 with minor amendments June 2012