Selenelion

Selenelion

also selenehelion; horizontal eclipse

Both bodies are within half a degree of the water, and neither is where it is drawn. The figure is on the headland for the ordinary reason: height lowers both horizons at once, and the observer is paid for the climb twice.

Type	Simultaneous observation
Requires	A total lunar eclipse at moonrise or moonset
Bodies visible	Two
Bodies actually above the horizon	Nought
The margin
Refraction at the horizon	About 34′, each body[1]
Semidiameter, Sun	About 16′
Semidiameter, Moon	About 15′
Lunar parallax, against	Up to about 57′[2]
Observer's height	Helps, and is why it is hunted from hills
In practice
Window	About four minutes; ten from a headland
Best horizons	Sea, or a summit
Cited as evidence against	The round Earth
Evidence against it	No

A selenelion, also selenehelion or horizontal eclipse, is the sight of the Sun and the totally eclipsed Moon at the same moment, one on each horizon.^[3] It occurs when a total lunar eclipse falls at moonrise or moonset, and it is prized by observers because the geometry that produces the eclipse also, on the face of it, forbids the sight of it.

A lunar eclipse requires the Moon to be in the Earth's shadow, which lies opposite the Sun. The two bodies are therefore about 180° apart, and an observer who has one of them on the horizon should have the other exactly as far below. That the pair are seen together is not an error of report: it is seen, it is photographed, and it is predicted in advance for particular coastlines. The extra sky is furnished by the air.

The geometry that forbids it

At mid-eclipse the Moon sits near the axis of the Earth's shadow, and that axis points away from the Sun. Reckoned from the centre of the Earth, the two bodies are separated by very nearly half a turn.

For an observer this is a hard constraint. Altitude on the celestial sphere is measured from the horizon plane, and two points 180° apart must sit at altitudes that sum to zero: if the Sun stands one degree up, the antisolar point stands one degree down. There is no arrangement of a spherical Earth, and none of a flat one, in which two diametrically opposite points are both above the same plane. The prohibition is not a fact about the shape of the world. It is a fact about opposite directions, and it would hold on any world whatever.

This is worth stating plainly, because the argument built on the selenelion supposes the difficulty to be peculiar to the globe. It is not. The prohibition follows from the two bodies standing opposite, not from the world being curved, and what the observation therefore tests is whether the air bends light. That is a question about the atmosphere, and not about the shape of anything.

The atmosphere that permits it

Air is denser at the bottom than at the top, and a ray entering it obliquely bends downward towards the denser medium. The eye, which reads a ray as a straight line, therefore places the source higher than it is. At the horizon the displacement is at its largest, running to about 34′ of arc, better than half a degree.^[1]

Three further quantities enter, and it is worth setting them out, because the sum is closer than the popular account suggests.

The first term is the one always quoted. The second is quieter: sunrise is reckoned from the upper limb, not the centre, so each body is granted its own semidiameter, about 16′ for the Sun and 15′ for the Moon.^[4] The third is the observer's own height, which lowers the visible horizon by the dip and can reach a degree or two from a summit over water.^[5]

The last term is subtracted, and it is the one the popular account omits. The Moon is near enough for its direction to depend on where the observer stands: at the horizon it appears up to about 57′ lower than it would from the centre of the Earth, and the shadow it must be inside is defined from that centre.^[2] Roughly half of what refraction concedes is spent before the observation has begun.

What is left is about forty minutes of arc, and the observer's hill is paid twice over, the dip lowering both horizons at once. Near the horizon the Sun changes altitude by roughly ten minutes of arc for every minute of time, so at sea level the pair stand together for some four minutes, and a thousand feet of headland turns that into ten.^[6] That is the whole of the margin. It is why a selenelion is hunted from cliffs, and why two towns a short way apart will differ on whether there was one.

Which side the shadow is on

A second objection is made of the same photographs. The Earth is under the observer's feet, so its shadow ought to reach the Moon from below; and in the photographs the umbra lies across the upper part of the disc instead, as though it had come down out of the open sky.

Nothing is falling on the Moon. The Moon is sliding into the shadow, sideways, and it goes in leading limb first.

The shadow keeps station with the Sun and works round the sky once a year. The Moon goes round once a month and so laps it, gaining half a degree an hour, which is enough to carry it clean across in three and a half hours. The limb that darkens first is simply the one in front.

Which limb that is depends on where the Moon is going, and near the horizon that is not where it looks. The gain on the shadow is eastward, and east, at the western horizon, is neither sideways nor down: it is the slope the Moon has just come down, and it points back up into the sky. A Moon setting in the west enters the shadow by its upper limb, and the dark spreads downward across the disc. A Moon rising in the east, at an evening selenelion, does the reverse and is eclipsed from below. Away from the horizon the same motion lies nearly level, which is why a midnight eclipse arrives from the side and is never complained of.

At New York on the morning of 8 November 2022 the Moon's gain on the shadow stood 20° from straight up.

The rest is the chord. The umbra is a disc 1°21′ wide, better than two and a half times the Moon,^[7] and the Moon does not cross its middle: it passes north of the centre at one eclipse and south of it at another, which throws first contact a little to one side of the leading point. That morning the miss was 0.2404°, almost all of it northward, and it moved the contact 15° round the limb.^[8] Twenty degrees and fifteen: the shadow arrived 35° from straight up, which in a photograph is the top of the Moon.^[9]

Two other forms of the objection travel with it. That the shadow ought to come from the west every time has the traffic running the wrong way, since it is the Moon that overtakes the shadow and the eastern limb that goes first, at every lunar eclipse there has ever been.^[10] And that it ought to come from below forgets that the Moon is not falling anywhere. It is going past.

The use made of it

The selenelion is a favourite of the flat cosmographies, where it is presented as an observation the round Earth cannot survive: the Sun and Moon are opposite, both are seen, and the globe is therefore in error.^[11]

The difficulty is that the argument needs the observation to be unexplained, and it is not. What resolves it is a correction of about half a degree, tabulated since antiquity and applied by every navigator taking a sight: it is printed in the same almanac one must open to learn that the eclipse is coming at all. An objection answered on the page facing the prediction is a thin objection.

The argument does sometimes state its own allowance, and the allowance is handsome. Refraction at the horizon, it is conceded, may run to a degree, or two degrees at the very most; and the sight is then pronounced to require more than that. It requires 34′, once for each body, which is a little over one degree for the pair, against a ceiling of two freely given. The concession is made in the sentence before the conclusion it destroys, and the subtraction is not carried out.

Worse for the argument, the same literature has already conceded that the air is strong. It is refraction that is called upon when a hull, having gone, comes back; refraction that carries a city sixty miles across a lake and stands it on the horizon.^[12] Having made the atmosphere powerful enough to return a ship, one cannot then be astonished at it lifting a disc through half a degree. It is the same quantity, and it was granted first.

What is left is a preference about which consequences of the air are counted. Refraction restores the hull and is admitted; refraction raises the Moon and the raising is not mentioned. It is the manoeuvre this encyclopedia records, in its filing form, under Grimble's razor: the inconvenient half of an entailment is not answered, it is not minuted.

None of which touches the phenomenon, which is real, handsome, and worth rising for.

Observed

Selenelions are computed in advance, since everything they require is tabulated. The eclipse of 8 November 2022 produced one along the eastern seaboard of North America, the totally eclipsed Moon setting in the west while the Sun came up in the east, and was reported from New York, Boston and the Maritimes.^[13] The eclipse of 3 March 2026 produced another across the eastern half of the United States and Canada.^[14]

The advice given to observers on both occasions was the same, and is the article in miniature: find height, find a clean horizon, and look early.

See also

• Moon – the body whose parallax nearly forbids this, and supplies the 57 arcminutes to be paid back
• Celestial refraction – the half-degree that does the work, measured honestly and filed otherwise
• Dip of the horizon – why the observer climbs a hill before disputing the shape of the world
• Looming – refraction handing back a thing the curve had taken
• Eight inches per mile squared – the figure that is correct, and the inference from it that is not
• Celestial theodolite – the instrument that measures this same half-degree and files it as a missing curve
• Grimble's razor – the method by which the awkward half of an entailment stops being minuted
• The Bedford Level experiment – six miles of water, measured repeatedly, to opposite conclusions

References

1. ^ Standard horizontal refraction is taken as 34′ (about 0.57°) at the apparent horizon, and falls away rapidly with altitude; it is tabulated in every nautical almanac and is applied, unremarked, by every navigator taking a sight. The figure varies a few minutes of arc with temperature and pressure, which is why a selenelion is a matter of the morning as well as of the geometry.
2. ^ The Moon's equatorial horizontal parallax runs from about 54′ to 61′ over the month, its distance not being constant. The Sun's is about 9″ and may be neglected here. Parallax depresses a nearby body towards the horizon, and is therefore subtracted where refraction is added: the two are of the same order, and the popular account of the selenelion quotes only the one that helps.
3. ^ From the Greek selēnē, moon, and hēlios, sun. The compound is modern and the phenomenon is not; the alternative horizontal eclipse is the plainer term and describes the circumstance rather than the pair.
4. ^ The Sun's apparent diameter is about 0.53° and the Moon's about 0.52°, a coincidence which is also the reason there are total solar eclipses at all, and which is doing no work in this article beyond supplying two semidiameters.
5. ^ See dip of the horizon: the dip in arcminutes is very nearly the square root of the height of eye in feet, so a hundred feet buys ten minutes of arc and a high coastal summit rather more than a degree.
6. ^ The rate varies with latitude and season; ten minutes of arc to the minute of time is a fair figure for the middle latitudes near the horizon. The dip in arcminutes being close to the square root of the height of eye in feet, a thousand feet yields about 32′, and it is credited at both horizons at once, so the window is the plain margin plus twice the dip. Observers planning these expeditions quote a gain of about ten minutes from height, which is the same arithmetic approached from the other end.
7. ^ Earth's radius 6,371 km; the cone narrows by about 1,805 km over the 384,400 to the Moon; 4,566 km of umbral radius remain, against the Moon's 1,737, which is 2.63 to 1. Espenak's tables for 8 November 2022 give the umbral radius as 40.7′ and the Moon's as 15.3′, arrived at from the other end and agreeing.
8. ^ By the sky's reckoning, in which east is the direction of increasing right ascension. By the Moon's own reckoning it is the western limb: selenographic east faces Mare Crisium, which sits on the opposite side of the disc from celestial east, and the two conventions have run contrary since 1961. A good deal of the disagreement about which side a shadow arrived on is this, and is not a disagreement about the shadow.
9. ^ Espenak's sheet gives γ = 0.2570, the miss expressed in Earth radii as they appear from the Moon, and the same quantity in degrees as 0.2404. The two agree: the Earth's horizontal parallax that night was 0°56′08″, and 0.2570 of it is 0.2404°. It is recoverable a third way from the published coordinates, the Moon standing 13′20″ north of the antisolar point and 23 seconds of right ascension west of it, which comes again to 0.240°.
10. ^ Derived here from the published elements rather than quoted from them. The Moon's motion relative to the shadow lies at position angle 67°, reckoned from celestial north through east; the observer's zenith, for that declination setting at latitude 40°42′ north, lies at 47°; the difference is the 20°. The chord adds arcsin(0.2404 ÷ 0.9332) = 15°, the divisor being the separation of the two centres at first contact. The 35° is obtainable a second way, from the contact position angles themselves – 82° at first contact, 158° at the deepest shadow, 233° at the last – and the two routes agree. The angle between celestial north and the vertical runs to nothing on the meridian, reaches about 52° with the Moon a third of the way down, and is back to 47° at the horizon: it is not greatest at the horizon, which is the natural assumption and is wrong.
11. ^ The claim is made in the form that the Sun and Moon "are 180° apart" during the eclipse and that seeing both is therefore incompatible with a spherical Earth. The premise is correct and the inference does not follow, the same prohibition applying to a plane.
12. ^ The sinking-ship effect, and the Chicago skyline photographed across some sixty miles of Lake Michigan, are both offered in that literature as evidence against curvature, and both are superior mirages: refraction over a temperature inversion. The air is conceded to be strong in those cases, which is precisely what makes half a degree here unremarkable.
13. ^ Reported from the whole of the eastern seaboard as far south as the Outer Banks. The window at New York was a matter of minutes between sunrise and moonset.
14. ^ Visible across the eastern half of the United States and Canada, the Moon setting in totality as the Sun rose.

External links

• Novaya Zemlya effect and horizon refraction – Atmospheric Optics – the extreme case of the same bending
• Total lunar eclipse of 8 November 2022 – NASA Scientific Visualization Studio
• Total lunar eclipse of 3 March 2026: visibility map – NASA Scientific Visualization Studio
• Selenelion – general reference