Mercury from the Arctic – how maps and horoscopes show the problem

Ever since the 2006 redefinition of “planet” and my first study of Pluto’s orbit before its discovery in 1930, I have known that the high eccentricity of Mercury’s orbit means Mercury’s maximum elongation (angular distance from the Sun) can vary from 18˚ (precisely 17.9˚) to 28˚ (precisely 27.8˚). The precise value depends on whether Mercury is closer to the northern hemisphere summer solstice than the Sun, or closer to the winter solstice:

• if Mercury is closer to the northern hemisphere summer solstice, its maximum elongation is only around 18˚ or 19˚
• it Mercury is closer to the northern hemisphere winter solstice, its maximum elongation is as much as 25˚ to almost 28˚
• the mean for all elongations is 22.6˚ for both western and eastern elongations, but western ones show a larger variation than eastern

Elongations of Mercury from 2000 to 2015 (“western” positive; “eastern” negative)

The fact that Mercury’s farthest elongations happen when it is closer to the northern hemisphere winter solstice than the Sun has long been known to cause problems observing it in high northern latitudes – for instance, it is generally believe that Copernicus working as far south as Poland never saw Mercury at all. In these areas, lengthy twilight means that at its farthest elongations on northern spring mornings and late-summer evenings Mercury may not set after the Sun at all, even at 27.4˚ East of the Sun on 15 August this year in Fairbanks, Alaska:

Sky map (drawn from ‘Your Sky’) for Fairbanks, Alaska, 21:50, 15 August 2016. Note the extremely narrow angle between horizon and ecliptic plane, and that Mercury, though at maximum eastern elongation, is setting with the Sun and is hence not visible

Horoscopes can represent this problem quite well if we use the space-based Campanus house system based around equally subdividing the prime vertical:

As can easily be seen, all the houses except the first, sixth, seventh and twelfth are exceedingly small: the four succedent houses are around 3˚ of longitude in size and the third, fourth, ninth and tenth are only around 1˚ of longitude in size each. This, nonetheless, is an accurate representation of the heavens as viewed from Fairbanks on a late-summer sunset, though the more purely astronomical picture shown above does add critical detail about how dark or bright the sky is. The critical point is that there is only a few degrees of elevation between the highest and lowest points on the ecliptic, and consequently the horizon can move extremely fast. Mercury actually sets from the purely two-dimensional astrological (ecliptic) perspective less than nine minutes after the Sun does so. At this time (6:04 UTC, 22:04 in Fairbanks itself) the Sun is only a second or so below the horizon so would still be very bright.

Consequently, at these farthest elongations, a skywatcher in Arctic or subarctic regions will never get Mercury at all visible: the Sun will completely block any attempt to see the planet.

The same principle applies to Mercury’s farthest western elongations, which occur with the Sun and Mercury are inverted in name, and their positions flipped by 180 degrees of ecliptic longitude. In astrological terms, one reverses the “planets”’ names and then places them in opposite signs. Be careful that doing one or the other would be impossible since Mercury would move from aphelion to perihelion and could never be at so large an angular distance from the Sun when viewed from Earth.

If we go beyond the polar circle the problem becomes even more extreme and interesting. Taking Dikson, Krasnoyarsk Krai – before virtually emptying the northernmost town over 10,000 in the world – we can see something quite interesting occur on 7 to 8 April (entirely 7 April 1993 UTC) from the perspective of a horoscope:

Horoscope for sunrise in Dikson, Krasnoyarsk Krai, on the day of a maximum western Mercury elongation of 27.8 degrees. Note how the horoscope is aligned in a clockwise direction, because what would ordinarily be the Midheaven at that sidereal time is actually below the horizon. 22˚♊︎, though the highest point on the chart, is at its lowest point attained in Dikson, whereas 22♐︎˚is the lowest point on the chart but at the highest point it can attain in Dikson

What’s notable is the here, more than seven degrees above the Arctic Circle,the sun has risen but Mercury, though still to its West, remains below the horizon because the horoscope is aligned clockwise and the signs are rising at this time of day in reverse order. This can be seen if we move to a later time in the morning:

Horoscope for Mercury’s rising in Dikson, Krasnoyarsk Krai, on the day of a maximum western Mercury elongation of 27.8 degrees. Note how the horoscope is aligned in a clockwise direction, and that mercury is never visible as owing to this clockwise alignment it rises after the Sun.

As you can see, when Mercury has risen, the Sun is already well above the horizon and fully bright. In contrast, when the Sun and Mercury are setting inside the Arctic Circle during this farthest western Mercury elongation (or conversely rising during a farthest-eastern elongation in late summer) the houses are conventionally aligned counterclockwise and Mercury, again, sets before the Sun or rises after it:

As you can see, Mercury is setting here with the ordinary MC in place at its highest culmination, above the horizon. From the chart below, we can see it takes four hours and fourteen minutes for the Sun to set after Mercury has done so:

This means that the “far” elongations cannot allow any view of Mercury in the Arctic, and this can be verified for this far western elongation with further sky charts for Dikson from the April 1993 western elongation:

As you can see, Mercury is in either picture never above the horizon at any point where the Sun is below. Indeed, as confirmed by the charts for 2300 and 2348 UTC earlier in this post, and from the royal blue picture that is used in ‘Your Sky’ to indicate that the sky is bright, Mercury is below the horizon of a fully brightened sky all along.

(For the curious and for those who would want to examine ‘Your Sky’ further, dark blue indicates astronomical twilight, dark red civil twilight, and black is completely dark night).

If we look at the near elongations that occur when Mercury is closer to the northern hemisphere summer solstice than is the Sun, we of course have the problem that Mercury cannot be as far from the Sun as it could potentially be at other elongations, including those where at polar latitudes both planets are necessarily above or necessarily below the horizon. However, it is in Arctic latitudes that one might expect the possibility that a near elongation could provide a reasonable view of Mercury. Thus, we will look at the near elongation following the August 2016 far elongation. For Dikson, this occurs on 27 September 2016 at 23:09 UTC (05:09 28 September 2016 local time):

Sky view for a “favourable” Mercury elongation on 28 September 2016 at Dikson

As we can see, even here the viewing of Mercury is not very favourable – and such near elongations which allow even this good a view of Mercury from the Arctic are very rare because they must occur on a late September or early October morning. We can note Mercury just above the horizon at its maximum elongation of 17.9 degrees, but the planet does not get more than 12 degrees above the horizon at sunset during any period of 28 September. More than that, in the ‘Your Sky’ diagrams for Dikson on this day, there are substantial periods when Mercury is no shown even with the Sun below the horizon and the planet above.

Unless the guides are inaccurate, this does suggest that Mercury is almost impossible to view in Arctic skies. The horoscope diagram shows that from the point of view of the Prime Vertical, the angles even at sidereal times when the period of the “Midnight Sun” is on the Midheaven are not sharp enough for easy viewing:

Thus, we can see diagrammatically on two levels why Mercury is essentially an invisible planet to the Arctic and subarctic skywatcher:

1. the angle at far elongations is extremely low or even negative so Mercury is only above the horizon of a bright sky
2. at solstitial elongations the Sun and Mercury will never (or barely at subarctic latitudes) cross the horizon
3. at steeper-angled elongations on autumn mornings (or spring evenings, not shown) Mercury is only about 18 degrees from the Sun and can never get more than 6˚ above the horizon of a sky before civil dawn or after civil dusk

As a last word, because the steeper-angled elongations are the farther, from Antarctica Mercury remains easily visible, as can be seen from these views of the 1993 and 2016 far elongations from Vostok Station:

Sky at Vostok, Antarctica for the 27.8-degree western Mercury elongation of April 1993

One can see just how steep this far elongation is and that Mercury is visible on a fairly dark sky from Vostok.

Sky at Vostok, Antarctica, for the 27.4 degree eastern elongation of Mercury in August 2016

Although I may not have picked the best time, that the horizon is not shallow and Mercury easily visible can still be detected for this coming elongation as it would be viewed from Vostok.

A list that stands plain wrong

Tonight, I discovered that two years (almost) ago, Rugby League Week had written a list of “Nine Greatest Finals Chokes of All Time”:

#9. South Sydney v Manly, 2013 preliminary final
#8. South Sydney v Balmain, 1969 grand final
#7. St. George v Canterbury, 1985 grand final
#6. Parramatta v North Queensland, 2005 preliminary final
#5. Manly v Sydney Bulldogs, 1995 grand final
#4. Parramatta v Newcastle, 2001 grand final
#3. Parramatta v Canterbury, 1998 preliminary final
#2. Balmain v Canberra, 1989 grand final
#1. St. George Illawarra v Melbourne, 1999 grand final

To me, RLW’s list is as bad as any I have seen in my history of reading “lists”. For a first thing, as far as I am aware and have watched rugby league, I could not say that most of those listed were so much as especially bad. Balmain in 1969 were an often-overlooked group that had nearly won the second semi final an had beaten the Rabbitohs on the SCG 16—7 on opening day.

The Bulldogs in 1995 were rivalling their display in the 1985 Preliminary Final – the best I have seen by a team in rugby league – and Parramatta in 2001 had the excuse of Andrew Johns – widely regarded today as the greatest halfback ever, although I would nonetheless still keep the 2001 Eels in this list because they were truly outstanding during the home-and-away season. Balmain in 1989 had the most potent attack in the NSWRL to face and were very lucky to lead 12—2 at halftime as Canberra had had most of the territorial advantage.

Parramatta v Canterbury in the 1998 preliminary final is the one which I have fewest qualms about – the Eels were favoured and had stopped a free-scoring Bronco team earlier in the finals

Some that are badly missing:

• Cronulla in 1979 – they had the best defence with only 41 tries against but completely collapsed in the finals when viewed the chief rival to St. George.
• Eastern Suburbs in 1980 and 1981 – this constitutes the worst omission as the Roosters choked twice – most obviously with their lifeless performance as favorites in the 1980 decider.
• the 1982 Roosters who lost 0—33 on the wettest rugby day since the 1950s in the preliminary would also not be out of place
• Balmain in 1985 would have been that club’s best choice: they were clear second to St. George (with best home-and-away record after the 1940s), then without excuse via injuries or suspensions were thrashed in the wet by Parramatta
• Canterbury in 1993 and 1994 choked awfully twice due to their woeful fullback weakness – if they had possessed a fullback like the Eadie of 1978 I often imagine Canterbury could have got close to 48—0 for those two seasons
• Cronulla in 1999 is another one that seems to possess less logic than those listed by RLW – they were more clearly the best team in the home-and-away rounds than in 1988 and beat the Broncos 42—20, and in my recollection the Sharks’ 8—24 loss to the Dragons felt like a shock