Election Day Eclipse

The second of two total lunar eclipses this year visible from Tucson will occur early next Tuesday morning, November 8. Yes, this is Election Day in the U.S. Having a total lunar eclipse on Election Day is so rare that it has never happened before since the United States was founded in 1776. Whether or not our nation survives its current paroxysms, we can rest assured that lunar eclipses will continue to occur as they have for billions of years.

Here are the local circumstances for Tucson, Arizona.

Time (MST)EventAltitude
1:02 a.m.Penumbral Eclipse Begins69˚
~1:45 a.m.Penumbra First Visible?62˚
2:09 a.m.Partial Eclipse Begins57°
3:16 a.m.Total Eclipse Begins44°
3:59 a.m.Greatest Eclipse35°
4:42 a.m.Total Eclipse Ends26°
5:23 a.m.Astronomical Twilight Begins18°
5:49 a.m.Partial Eclipse Ends13°
5:52 a.m.Nautical Twilight Begins12°

There are few astronomical events as impressive as a total lunar eclipse, and we’ll have a front-row seat Election Day morning.

Every month, the full moon passes close to the Earth’s shadow, but because of the Moon’s tilted orbit it usually passes above or below the shadow cone of the Earth. This month is different!

Tuesday morning, the Moon orbits right through the Earth’s shadow. At 1:02 a.m., the Moon dips his proverbial toe into the Earth’s shadow, when the Moon is 69˚ above Tucson’s SW horizon. This is the undetectable beginning of the eclipse, when the leading edge of the eastward orbiting-Moon “sees” a partial solar eclipse. When no part of the Moon sees anything more than the Earth blocking some but not all of the Sun, we call that a penumbral eclipse. The very subtle penumbral shading may just begin to be detectable around 1:45 a.m.

When the partial eclipse begins at 2:09 a.m., the upper left edge becomes the first part of the Moon to “see” a total solar eclipse. In other words, from part of the Moon now, the Earth totally eclipses the Sun.

Totality begins at 3:16 a.m. when all of the Moon sees the Earth completely blocking the Sun. Mid-totality occurs at 3:59 a.m., when the center of the Moon is closest to the center of the Earth’s shadow. At that moment, the Moon’s coppery color should be darkest.

That color is caused by sunlight refracting (bending) through the Earth’s atmosphere and shining on the Moon even though from the Moon the Earth is completely blocking the disk of the Sun. The reddish or orangish color imparted to the Moon during totality is the combined light of all the world’s sunrises and sunsets. What a beautiful thought! Had the Earth no atmosphere, the Moon would utterly disappear from view during totality—the time it is completely within the Earth’s umbral shadow.

Totality ends at 4:42 a.m., and the partial eclipse ends at 5:49 a.m. during morning twilight. When the last vestiges of partial solar eclipse leave the Moon at 6:56 a.m., the (penumbral) eclipse ends at moonset as the Sun is rising in the ESE.

This leisurely event can be enjoyed with the unaided eye, binoculars, a telescope, or all three. Don’t let anyone in the family miss seeing it!

The next total eclipse will not grace our skies until March 13, 2025.

If you haven’t already done so, please be sure to vote! It is your responsibility that comes with the privileges of your living in these United States. And voting should only be the beginning of your civic involvement. The quality of our government and elected representatives is directly proportional to the sum total of our collective civic involvement. And that has been pretty poor in recent years. Unlike an eclipse, democracy is not a spectator sport!

Sagittarius Time Machine

The bright stars that outline our constellations beckon to us from a remarkably wide range of distances. Many of these stars are super-luminous giant stars and hot blue dwarf stars. More typical stars like our Sun—and the even more abundant red dwarf stars—are much too faint to see with our unaided eyes, unless they are only a few light years away. Thus many of the stars we see when we look up at the night sky are the intrinsically brightest ones, the “whales among the fishes.”

Trigonometric parallax directly provides us with the best estimate of the distance to each of these stars (provided they are not more than a few hundred light years away), and once you know the distance, it is easy to calculate when the light you are seeing tonight left each one of them. It is enjoyable to contemplate what was going on in Earth history when each star’s light began its long journey across interstellar space, the tiniest fraction of which is reaching your eyes as you look up on a clear night.

This article is the next in a series featuring the major stars of a prominent constellation. We turn now towards Sagittarius, which is currently crossing the celestial meridian at the end of evening twilight.

Below you will find a chart showing the constellation Sagittarius and the bright stars that define its outline. The official IAU-approved star names are listed, where available, or the Bayer designation. There’s a printer-friendly PDF version of this chart at the bottom of this article. There’s room for you to write in the year when the light we are currently receiving left the photosphere of each star, using the provided table (which is updated automatically to today’s date).

The “Teapot” asterism of Sagittarius

The table below contains all the relevant information. There are three tabs: Parallax, Distance, and Time. The first three columns of each tab show the star name, the Bayer designation, and the spectral type and luminosity class listed in SIMBAD.

On the Parallax tab, the parallax in millarcseconds (mas) is listed in column D, along with the uncertainty in the parallax in column E, and the year the parallax was published in column F. All are from SIMBAD. I will update these values as new results become available, but please post a comment here if you find anything that is not current, or is incorrect.

On the Distance tab, the parallax and parallax uncertainty for each star is used to calculate the range of possible distances to the star (in light years) in columns D through F. The nominal value given in column E is our current “best guess” for the distance to the star.

On the Time tab, the range of distances from the Distance tab are used to determine the range of years when the light we are seeing at this point in time would have left the star. The earliest year (given the uncertainty in parallax) is shown in column D, the most likely year in column E, and the latest year (given the uncertainty in parallax) in column F.

Here’s a printer-friendly PDF version of the Sagittarius chart where after printing you can enter the nominal year from column E of the Time tab next to the name for each star. The year values on the Time tab will update automatically to reference the current date.

Peculiar Neutron Stars

There’s a lot we don’t know about neutron stars. Neutron stars are the densest objects we can directly observe, and we have little understanding of how matter behaves under such extreme conditions. Though there are a lot of neutrons in neutron stars, they are not entirely made of neutrons. Whether the interiors of neutron stars contain something other than the known elementary particles is an open question.

The nearest neutron star we know of is RX J1856.5-3754 in Corona Australis, just below Sagittarius. It regales us at a distance between 352 and 437 light years, with the most likely distance being 401 ly. Though most neutron stars we know of are pulsars (a good example of observational selection—we tend to discover what is easiest for us to discover), this one is not.

In addition to its intrinsic properties, how a neutron star looks to us also depends upon its orientation and the environs with which it interacts. These three factors have led to a variety of nomenclature that requires some explanation.

Pulsar – a highly-magnetized, fast-rotating neutron star whose magnetic poles emit beams of electromagnetic radiation. If either of the beams sweeps past the Earth, we observe periodic pulses of electromagnetic radiation coming from the neutron star.

Magnetar – an extremely-highly-magnetized, more-slowly-rotating neutron star that produces bursts of X-rays and gamma rays. Only some magnetars are pulsars. Anomalous X-ray pulsars (AXPs) are now thought to be magnetars.

Rotating Radio Transients (RRATs) – a neutron star that is a pulsar, but with the peculiar property that it emits a single short-lived and extremely bright radio burst quasi-periodically with long lulls in between. The radio bursts last only 2 to 30 milliseconds, with intervals ranging from 4 minutes to 3 hours between pulses.

Soft gamma repeaters (SGRs) – a neutron star—possibly a type of magnetar—that emits large bursts of gamma-rays and X-rays at irregular intervals. If not a magnetar, it may be a neutron star with a disk of material in orbit around it.

Compact Central Objects in Supernova remnants (CCOs in SNRs) – a radio-quiet X-ray-producing neutron star surrounded by a supernova remnant. These have thermal emission spectra, and a weaker magnetic field than most neutron stars.

X-ray Dim Isolated Neutron Stars (XDINS) – an isolated, nearby (otherwise, it would be too faint to see) young neutron star. Only seven of these have been discovered to date (see The Magnificent Seven).

And that’s not all. Clearly, we have a lot more to learn about neutron stars.

There are currently about 3,200 known neutron stars, almost all of them pulsars, and all of them in our Milky Way galaxy and the Magellanic Clouds. About 5% are members of a binary system.

I know of no comprehensive catalog of neutron stars, but here is a catalog of pulsars:

ATNF Pulsar Catalogue
https://www.atnf.csiro.au/research/pulsar/psrcat/

A new and exciting frontier for exploring neutron stars is gravitational wave astronomy. All gravitational-wave observations to date have come from merging binaries consisting of black holes and neutron stars. Events include black hole – black hole mergers, neutron star – neutron star mergers, and neutron star – black hole mergers.


Three Pulsars of Note

The Fastest – PSR J1748-2446ad in the constellation Sagittarius is the fastest-spinning pulsar known, rotating once every 1.40 milliseconds, or 716 times per second (716 Hz). An educated guess at the neutron star’s radius (16 km) tells us that the equatorial surface is spinning at about 24% of the speed of light! PSR J1748-2446ad is located at a distance of about 18,000 ly in the globular cluster Terzan 5. Fortuitously, PSR J1748-2446ad is an eclipsing binary system with a bloated and distorted low-mass main-sequence-star companion.

The Slowest – PSR J0901-4046 in the southern constellation Vela is the slowest-spinning pulsar known*, rotating once every 75.886 seconds. It is located at a distance of approximately 1,300 ly.

The Most Massive – PSR J0952–0607 in the constellation Sextans is the most massive neutron star (2.35±0.17 M) known, and the second-fastest-spinning pulsar known (1.41 ms, 707 Hz). PSR J0952–0607 is located in a binary system with a (now) substellar-mass companion that has been largely consumed by the neutron star. The distance to this system is highly uncertain.

* The white dwarf in the red-dwarf – white-dwarf binary system AR Scorpii rotates once every 117 seconds, and is thought to be the only known example of a white-dwarf pulsar.

References

Liz Kruesi (2022, July 2). Slowpoke pulsar stuns scientists. Science News, 202(1), 8.
https://www.sciencenews.org/article/pulsar-radio-waves-neutron-star-astronomy

Govert Schilling (2022, July 28). Black widow pulsar sets mass record.
https://skyandtelescope.org/astronomy-news/black-widow-pulsar-sets-mass-record/

Scorpius Time Machine

The bright stars that outline our constellations beckon to us from a remarkably wide range of distances. Many of these stars are super-luminous giant stars and hot blue dwarf stars. More typical stars like our Sun—and the even more abundant red dwarf stars—are much too faint to see with our unaided eyes, unless they are only a few light years away. Thus many of the stars we see when we look up at the night sky are the intrinsically brightest ones, the “whales among the fishes.”

Trigonometric parallax directly provides us with the best estimate of the distance to each of these stars (provided they are not more than a few hundred light years away), and once you know the distance, it is easy to calculate when the light you are seeing tonight left each one of them. It is enjoyable to contemplate what was going on in Earth history when each star’s light began its long journey across interstellar space, the tiniest fraction of which is reaching your eyes as you look up on a clear night.

This article is the first in a series featuring the major stars of a prominent constellation. We turn now towards Scorpius, which is currently crossing the celestial meridian at the end of evening twilight.

Below you will find a chart showing the constellation Scorpius and the bright stars that define its outline. The official IAU-approved star names are listed, where available, or the Bayer designation. There’s a printer-friendly PDF version of this chart at the bottom of this article. There’s room for you to write in the year when the light we are currently receiving left the photosphere of each star, using the provided table (which is updated automatically to today’s date).

Scorpius

The table below contains all the relevant information. There are three tabs: Parallax, Distance, and Time. The first three columns of each tab show the star name, the Bayer designation, and the spectral type and luminosity class listed in SIMBAD.

On the Parallax tab, the parallax in millarcseconds (mas) is listed in column D, along with the uncertainty in the parallax in column E, and the year the parallax was published in column F. All are from SIMBAD. I will update these values as new results become available, but please post a comment here if you find anything that is not current, or is incorrect.

On the Distance tab, the parallax and parallax uncertainty for each star is used to calculate the range of possible distances to the star (in light years) in columns D through F. The nominal value given in column E is our current “best guess” for the distance to the star.

On the Time tab, the range of distances from the Distance tab are used to determine the range of years when the light we are seeing at this point in time would have left the star. The earliest year (given the uncertainty in parallax) is shown in column D, the most likely year in column E, and the latest year (given the uncertainty in parallax) in column F.

Here’s a printer-friendly PDF version of the Scorpius chart where after printing you can enter the nominal year from column E of the Time tab next to the name for each star. The year values on the Time tab will update automatically to reference the current date.

Constellations Old and New

The celestial sphere is a jigsaw puzzle with 88 pieces. The oldest piece is arguably the constellation Ursa Major, The Great Bear. Based on historical writings, prehistoric art, and the knowledge that this group of stars represented a bear in many cultures scattered throughout the world leads scholars to believe that this constellation was first described around 11,000 B.C., perhaps earlier.

The newest constellations are the 17 listed in the table below. Thirteen of these were invented by French astronomer Nicolas-Louis de Lacaille (1713-1762) during his stay at the Cape of Good Hope in 1751 and 1752, and the other four (Puppis, Pyxis, Vela, and Carina) are portions of the ancient enormous constellation Argo Navis, described by Ptolemy (c. 100 – c. 170). Though all of these constellations reside completely in the southern hemisphere of the sky (and thus can be best observed in the southern hemisphere), all but two of them (Mensa and Octans) have a portion that rises above the southern horizon as seen from Tucson, however scant and brief.

Newest Constellations

Constellation Description Declination
Puppis The Stern (of Argo Navis) -51˚ to -11˚
Pyxis The Compass (of Argo Navis) -37˚ to -17˚
Fornax The Laboratory Furnace -40˚ to -24˚
Antlia The Air Pump -40˚ to -25˚
Sculptor The Sculptor's Workshop -39˚ to -25˚
Caelum The Sculptor's Chisel -49˚ to -27˚
Microscopium The Microscope -45˚ to -27˚
Vela The Sail (of Argo Navis) -57˚ to -37˚
Horologium The Pendulum Clock -67˚ to -40˚
Norma The Carpenter's Square -60˚ to -42˚
Pictor The Painter's Easel -64˚ to -43˚
Telescopium The Telescope -57˚ to -45˚
Carina The Keel (of Argo Navis) -76˚ to -51˚
Reticulum The Net -67˚ to -53˚
Circinus The Compasses -71˚ to -55˚
Mensa The Table Mountain -85˚ to -70˚
Octans The Octant -90˚ to -74˚

Which (mostly) northern constellations were added last? Around 70 years prior to Lacaille, Johannes Hevelius (1611-1687) described the seven constellations in the table below. These constellations were first published posthumously in 1690.

Newest More Northerly Constellations

Constellation Description Declination
Lynx The Lynx +33˚ to +62˚
Lacerta The Lizard +35˚ to +57˚
Canes Venatici The Hunting Dogs +28˚ to +52˚
Leo Minor The Lion Cub +23˚ to +41˚
Vulpecula The Fox +19˚ to +29˚
Sextans The Sextant -12˚ to +6˚
Scutum The Shield -16˚ to -4˚

Let us now return to the oldest constellation, Ursa Major. The earliest extant literary work describing the constellations, including Ursa Major, is Phainómena by the Greek didactic poet Aratus (c. 315 BC – 240 BC). Phainómena is based on an earlier work by the Greek astronomer and mathematician Eudoxus of Cnidus (c. 408 BC – c. 355 BC), now lost. Earlier, the Greek poets Homer and Hesiod (~700 BC) mentioned the constellations, and we know that the Babylonians had a well-developed system of constellations (~2000 BC), as did the Sumerians even earlier (~4000 BC), later assimilated by the Greeks.

Here is what Aratus says in Phainómena about Ursa Major, in context.

The numerous stars, scattered in different directions, sweep all alike across the sky every day continuously for ever. The axis, however, does not move even slightly from its place, but just stays for ever fixed, holds the earth in the centre evenly balanced, and rotates the sky itself. Two poles terminate it at the two ends; but one is not visible, while the opposite one in the north is high above the horizon. On either side of it two Bears wheel in unison, and so they are called the Wagons. They keep their heads for ever pointing to each other's loins, and for ever they move with shoulders leading, aligned towards the shoulders, but in opposite directions. If the tale is true, these Bears ascended to the sky from Crete by the will of great Zeus, because when he was a child then in fragrant Lyctus near Mount Ida, they deposited him in a cave and tended him for the year, while the Curetes of Dicte kept Cronus deceived. Now one of the Bears men call Cynosura by name, the other Helice. Helice is the one by which Greek men at sea judge the course to steer their ships, while Phoenicians cross the sea relying on the other. Now the one is clear and easy to identify, Helice, being visible in all its grandeur as soon as night begins; the other is slight, yet a better guide to sailors, for it revolves entirely in a smaller circle: so by it the Sidonians sail the straightest course.

Between the two Bears, in the likeness of a river, winds a great wonder, the Dragon, writhing around and about at enormous length; on either side of its coil the Bears move, keeping clear of the dark-blue ocean. It reaches over one of them with the tip of its tail, and intercepts the other with its coil. The tip of its tail ends level with the head of the Bear Helice, and Cynosura keeps her head within its coil. The coil winds past her very head, goes as far as her foot, then turns back again and runs upward. In the Dragon's head there is not just a single star shining by itself, but two on the temples and two on the eyes, while one below them occupies the jaw-point of the awesome monster. Its head is slanted and looks altogether as if it is inclined towards the tip of Helice's tail: the mouth and the right temple are in a very straight line with the tip of the tail. The head of the Dragon passes through the point where the end of settings and the start of risings blend with each other.

Total Lunar Eclipse 2022 #1

The first of two total lunar eclipses this year visible from Tucson will occur conveniently this Sunday evening, May 15 (16 May 2022 UT).

Here are the local circumstances for Tucson, Arizona.

Time (MST)EventAltitude
7:06 p.m.Moonrise
7:28 p.m.Partial Eclipse Begins
8:29 p.m.Total Eclipse Begins14°
9:12 p.m.Greatest Eclipse21°
9:54 p.m.Total Eclipse Ends26°
10:56 p.m.Partial Eclipse Ends33°
11:30 p.m.Penumbra last visible?35°
11:51 p.m.Penumbral Eclipse Ends36°

There are few astronomical events as impressive as a total lunar eclipse, and we’ll have a front-row seat Sunday evening.

Every month, the full moon passes close to the Earth’s shadow, but because of the Moon’s tilted orbit it usually passes above or below the shadow cone of the Earth. This month is different!

Sunday evening, the Moon orbits right through the Earth’s shadow. At 6:32 p.m., the Moon dips his proverbial toe into the Earth’s shadow, when the Moon is still 7˚ below Tucson’s ESE horizon. This is the undetectable beginning of the eclipse, when the leading edge of the eastward orbiting-Moon “sees” a partial solar eclipse. When no part of the Moon sees anything more than the Earth blocking some but not all of the Sun, we call that a penumbral eclipse. The very subtle penumbral shading may just begin to be detectable around 7:00 p.m., but here in Tucson the Moon won’t even rise until six minutes after that.

When the partial eclipse begins at 7:28 p.m., the lower left edge becomes the first part of the Moon to “see” a total solar eclipse. In other words, from part of the Moon now, the Earth totally eclipses the Sun.

Totality begins at 8:29 p.m. when all of the Moon sees the Earth completely blocking the Sun. Mid-totality occurs at 9:12 p.m., when the center of the Moon is closest to the center of the Earth’s shadow. At that moment, the Moon’s color should be darkest.

That color is caused by sunlight refracting (bending) through the Earth’s atmosphere and shining on the Moon even though from the Moon the Earth is completely blocking the disk of the Sun. The reddish or orangish color imparted to the Moon during totality is the combined light of all the world’s sunrises and sunsets. What a beautiful thought! Had the Earth no atmosphere, the Moon would utterly disappear from view during totality—the time it is completely within the Earth’s umbral shadow.

Totality ends at 9:54 p.m., and the partial eclipse ends at 10:56 p.m. As the last vestiges of partial solar eclipse leave the Moon, the (penumbral) eclipse ends at 11:51 p.m.

This leisurely event can be enjoyed with the unaided eye, binoculars, a telescope, or all three. Don’t let anyone in the family miss seeing it!

Emergence

Physics is the fundamental science in that it describes the workings of the universe at all scales.  No other science is so comprehensive.

Will our knowledge of physics finally lead us to a “Theory of Everything”?  Perhaps, but the Theory of Everything alone will not be able to describe, predict, or explain its full expression upon/within the universe—no more so than our musical notation system can explain how a Brahms symphony was composed, nor its effect upon the listener.

Reductionism states that the whole is the sum of its parts, but emergence states that the whole is more than the sum of its parts.

There are many examples of emergent properties in the natural world, what one might call radical novelty.  Some examples:  crystal structure (e.g. a salt crystal or a snowflake), ripples in a sand dune, clouds, life itself.  Social organization (e.g. a school of fish or a city), consciousness.

John Archibald Wheeler (1911-2008) created a diagram that nicely illustrates an emergent property of the universe that is important to us.

The universe viewed as a self-excited circuit. Starting simply (thin U at right), the universe grows in complexity with time (thick U at left), eventually giving rise to observer-participancy, which in turn imparts “tangible reality” to even the earliest days of the universe.

Richard Wolfson writes,

At some level of complexity, emergent properties become so interesting that, although we understand that they come from particles that are held together by the laws of physics, we can’t understand or appreciate them through physics alone.

I like to think of emergence as an expression of creativity. Our universe is inherently creative, just as we humans express ourselves creatively through music, art, literature, architecture, and in so many other ways.

Creativity is the most natural process in the universe. It’s in our DNA.

But DNA alone can’t explain it.

References

Richard Wolfson, The Great Courses, Course No. 1280, “Physics and Our Universe: How It All Works”, Lecture 1: “The Fundamental Science”, 2011.


“And the end of all our exploring will be to arrive where we started and know the place for the first time.” – T. S. Eliot

Ending Spring Forward, Fall Back

On March 15, the U.S. Senate voted unanimously to end the twice annual switch between Standard Time and Daylight Saving Time. So far so good. That leaves us now with two choices: standard time year round or daylight saving time year round. Unfortunately, they have chosen the latter. The fact that there was no debate on this point suggests the esteemed senators collectively have little understanding of science—or, at least, biology and astronomy.

Most astronomers (those that actually observe) and astronomy educators don’t like daylight saving time because it delays the onset of darkness by an hour: most of us observe in the evening and not right before dawn. Cruelly, daylight saving time prevents many young people from experiencing the wonders of the night sky because it gets dark around or after their bedtime during the warmer months of the year.

Non-astronomers (which, let’s face it, includes most of us) that rise early in the morning will spend even more of their year getting up while it is still dark out. In the northern U.S. at least that means that during the winter months, many school children will be going to school in the dark when it is still bitterly cold.

I have written previously on this topic.

As for biology, unless all of us also start our work days and school days an hour later, year-round daylight saving time will further mess with our already-damaged circadian rhythms—and most of us don’t get enough sleep as it is. As many studies have shown, this leads to a number of negative consequences affecting our health and well being.

The answer is, of course, to adopt standard time year-round as Arizona currently does. Even that is now in jeopardy as Arizona is likely to join the bandwagon and go to permanent daylight saving time, if this legislation is enacted.

This legislation now goes to the U.S. House of Representatives and, if it passes there, on to President Biden’s desk to sign into law. If that happens, most/all? of the U.S. will be going to permanent daylight saving time beginning officially November 5, 2023 (actually, March 12, 2023).

Is anyone pushing for year-round standard time instead? You bet.

I encourage you to support this organization, Save Standard Time, a registered 501(c)(4) nonprofit organization.

February is Short, the Moon Makes Haste…

Each night for the next several nights, the Moon sets much later than it did the previous night. This happens for two reasons.

First, this week the plane of the Moon’s orbit is nearly perpendicular to our horizon, so much of the Moon’s orbital motion eastward relative to the background stars (if we could see them) during the day takes it directly away from the western horizon, thus slowing as much as possible its inexorable march towards the west caused by the Earth’s rotation.

Second, this week the Moon is moving north in declination, and this, too, increases the amount of time the Moon stays above the horizon. The closer to the north celestial pole an object is, the longer it stays above our horizon, the further north along the western horizon it sets, and the later it sets. The Moon’s motion during the day northward relative to the celestial equator causes the Moon to set further north than it would have otherwise. The combination of these two factors makes moonset much later each night, as shown in the table below.

But, why doesn’t moonrise also occur much later each morning? As you can see by inspecting the table above, the Moon rises only a little later each day, in marked contrast to the leaps and bounds moonset is later each night. The factors are the same, but the effect is different. Because the Moon is moving north and is thus rising further north every morning, it rises earlier than it would have otherwise. Although the Moon is rising later each day due to its eastward orbital motion, moonrise is only a little later due to the countereffect of an earlier rise time stemming from the Moon’s more northerly declination.

It is no wonder humans have always been fascinated by the Moon’s complex motion. Throughout history, a number of mathematicians have taken up the challenge of trying to understand and predict the Moon’s motion, leading to several important advancements in mathematics.

Zodiacal Light 2022

In 2022, the best dates and times for observing the zodiacal light are listed in the calendar below. The sky must be very clear with little or no light pollution. The specific times listed are for Dodgeville, Wisconsin (42° 58′ N, 90° 08′ W).

Here’s a nicely-formatted printable PDF file of the zodiacal light calendar:

January 2022
SUN MON TUE WED THU FRI SAT
            1
2 3 4 5 6 7 8
9 10 11 12 13 14 15
16 17 18 19
Zodiacal Light 6:36 – 6:38 p.m. West
20
Zodiacal Light 6:37 – 7:37 p.m. West
21
Zodiacal Light 6:38 – 7:38 p.m. West
22
Zodiacal Light 6:39 – 7:39 p.m. West
23
Zodiacal Light 6:40 – 7:40 p.m. West
24
Zodiacal Light 6:41 – 7:41 p.m. West
25
Zodiacal Light 6:42 – 7:42 p.m. West
26
Zodiacal Light 6:43 – 7:43 p.m. West
27
Zodiacal Light 6:44 – 7:44 p.m. West
28
Zodiacal Light 6:46 – 7:46 p.m. West
29
Zodiacal Light 6:47 – 7:47 p.m. West
30
Zodiacal Light 6:48 – 7:48 p.m. West
31
Zodiacal Light 6:49 – 7:49 p.m. West
         

February 2022
SUN MON TUE WED THU FRI SAT
    1
Zodiacal Light 6:50 – 7:50 p.m. West
2
Zodiacal Light 7:04 – 7:51 p.m. West
3 4 5
6 7 8 9 10 11 12
13 14 15 16 17 18
Zodiacal Light 7:10 – 7:51 p.m. West
19
Zodiacal Light 7:12 – 8:12 p.m. West
20
Zodiacal Light 7:13 – 8:13 p.m. West
21
Zodiacal Light 7:14 – 8:14 p.m. West
22
Zodiacal Light 7:15 – 8:15 p.m. West
23
Zodiacal Light 7:16 – 8:16 p.m. West
24
Zodiacal Light 7:18 – 8:18 p.m. West
25
Zodiacal Light 7:19 – 8:19 p.m. West
26
Zodiacal Light 7:20 – 8:20 p.m. West
27
Zodiacal Light 7:21 – 8:21 p.m. West
28
Zodiacal Light 7:22 – 8:22 p.m. West
         

March 2022
SUN MON TUE WED THU FRI SAT
    1
Zodiacal Light 7:24 – 8:24 p.m. West
2
Zodiacal Light 7:25 – 8:25 p.m. West
3
Zodiacal Light 7:26 – 8:26 p.m. West
4
Zodiacal Light 8:14 – 8:27 p.m. West
5
6 7 8 9 10 11 12
13 14 15 16 17 18 19
Zodiacal Light 8:47 – 8:59 p.m. West
20
Zodiacal Light 8:48 – 9:48 p.m. West
21
Zodiacal Light 8:49 – 9:49 p.m. West
22
Zodiacal Light 8:51 – 9:51 p.m. West
23
Zodiacal Light 8:52 – 9:52 p.m. West
24
Zodiacal Light 8:53 – 9:53 p.m. West
25
Zodiacal Light 8:55 – 9:55 p.m. West
26
Zodiacal Light 8:56 – 9:56 p.m. West
27
Zodiacal Light 8:57 – 9:57 p.m. West
28
Zodiacal Light 8:59 – 9:59 p.m. West
29
Zodiacal Light 9:00 – 10:00 p.m. West
30
Zodiacal Light 9:02 – 10:02 p.m. West
31
Zodiacal Light 9:03 – 10:03 p.m. West
   

April 2022
SUN MON TUE WED THU FRI SAT
          1
Zodiacal Light 9:05 – 10:05 p.m. West
2
Zodiacal Light 9:11 – 10:06 p.m. West
3 4 5 6 7 8 9
10 11 12 13 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30

May 2022
SUN MON TUE WED THU FRI SAT
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31        

June 2022
SUN MON TUE WED THU FRI SAT
      1 2 3 4
5 6 7 8 9 10 11
12 13 14 15 16 17 18
19 20 21 22 23 24 25
26 27 28 29 30    

July 2022
SUN MON TUE WED THU FRI SAT
          1 2
3 4 5 6 7 8 9
10 11 12 13 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30
31            

August 2022
SUN MON TUE WED THU FRI SAT
  1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25
Zodiacal Light 3:33 – 4:11 a.m. East
26
Zodiacal Light 3:35 – 4:35 a.m. East
27
Zodiacal Light 3:36 – 4:36 a.m. East
28
Zodiacal Light 3:38 – 4:38 a.m. East
29
Zodiacal Light 3:39 – 4:39 a.m. East
30
Zodiacal Light 3:41 – 4:41 a.m. East
31
Zodiacal Light 3:42 – 4:42 a.m. East
     

September 2022
SUN MON TUE WED THU FRI SAT
        1
Zodiacal Light 3:44 – 4:44 a.m. East
2
Zodiacal Light 3:45 – 4:45 a.m. East
3
Zodiacal Light 3:47 – 4:47 a.m. East
4
Zodiacal Light 3:48 – 4:48 a.m. East
5
Zodiacal Light 3:49 – 4:49 a.m. East
6
Zodiacal Light 3:51 – 4:51 a.m. East
7
Zodiacal Light 3:52 – 4:52 a.m. East
8
Zodiacal Light 3:57 – 4:54 a.m. East
9 10
11 12 13 14 15 16 17
18 19 20 21 22 23 24
Zodiacal Light 4:14 – 5:14 a.m. East
25
Zodiacal Light 4:16 – 5:16 a.m. East
26
Zodiacal Light 4:17 – 5:17 a.m. East
27
Zodiacal Light 4:18 – 5:18 a.m. East
28
Zodiacal Light 4:19 – 5:19 a.m. East
29
Zodiacal Light 4:21 – 5:21 a.m. East
30
Zodiacal Light 4:22 – 5:22 a.m. East
 

October 2022
SUN MON TUE WED THU FRI SAT
            1
Zodiacal Light 4:23 – 5:23 a.m. East
2
Zodiacal Light 4:24 – 5:24 a.m. East
3
Zodiacal Light 4:25 – 5:25 a.m. East
4
Zodiacal Light 4:27 – 5:27 a.m. East
5
Zodiacal Light 4:28 – 5:28 a.m. East
6
Zodiacal Light 4:29 – 5:29 a.m. East
7
Zodiacal Light 4:30 – 5:30 a.m. East
8
Zodiacal Light 5:28 – 5:31 a.m. East
9 10 11 12 13 14 15
16 17 18 19 20 21 22
23
Zodiacal Light 4:48 – 5:12 a.m. East
24
Zodiacal Light 4:50 – 5:50 a.m. East
25
Zodiacal Light 4:51 – 5:51 a.m. East
26
Zodiacal Light 4:52 – 5:52 a.m. East
27
Zodiacal Light 4:53 – 5:53 a.m. East
28
Zodiacal Light 4:54 – 5:54 a.m. East
29
Zodiacal Light 4:55 – 5:55 a.m. East
30
Zodiacal Light 4:56 – 5:56 a.m. East
31
Zodiacal Light 4:57 – 5:57 a.m. East
         

November 2022
SUN MON TUE WED THU FRI SAT
    1
Zodiacal Light 4:59 – 5:59 a.m. East
2
Zodiacal Light 5:00 – 6:00 a.m. East
3
Zodiacal Light 5:01 – 6:01 a.m. East
4
Zodiacal Light 5:02 – 6:02 a.m. East
5
Zodiacal Light 5:03 – 6:03 a.m. East
6
Zodiacal Light 4:35 – 5:04 a.m. East
7 8 9 10 11 12
13 14 15 16 17 18 19
20 21 22
Zodiacal Light 4:21 – 5:21 a.m. East
23
Zodiacal Light 4:22 – 5:22 a.m. East
24
Zodiacal Light 4:23 – 5:23 a.m. East
25
Zodiacal Light 4:24 – 5:24 a.m. East
26
Zodiacal Light 4:25 – 5:25 a.m. East
27
Zodiacal Light 4:26 – 5:26 a.m. East
28
Zodiacal Light 4:27 – 5:27 a.m. East
29
Zodiacal Light 4:28 – 5:28 a.m. East
30
Zodiacal Light 4:29 – 5:29 a.m. East
     

December 2022
SUN MON TUE WED THU FRI SAT
        1
Zodiacal Light 4:30 – 5:30 a.m. East
2
Zodiacal Light 4:31 – 5:31 a.m. East
3
Zodiacal Light 4:32 – 5:32 a.m. East
4
Zodiacal Light 4:33 – 5:33 a.m. East
5
Zodiacal Light 4:41 – 5:34 a.m. East
6 7 8 9 10
11 12 13 14 15 16 17
18 19 20 21 22 23 24
25 26 27 28 29 30 31

The best nights to observe the zodiacal light at mid-northern latitudes occur when the ecliptic plane intersects the horizon at an angle of 60° or steeper. The dates above were chosen on that basis, with the Sun at least 18° below the horizon and the Moon below the horizon being used to calculate the times. An interval of time of one hour either before morning twilight or after evening twilight was chosen arbitrarily because it is the “best one hour” for observing the zodiacal light. The zodiacal light cone will be brightest and will reach highest above the horizon when the Sun is 18° below the horizon (astronomical twilight), but no less.

If you are interested in calculating the angle the ecliptic makes with your horizon for any date and time, you can use the following formula:

\cos I = \cos \varepsilon \sin \phi-\sin \varepsilon \cos \phi \sin \theta

where I is the angle between the ecliptic and the horizon, ε is  the obliquity of the ecliptic, φ is the latitude of the observer, and θ is the local sidereal time (the right ascension of objects on the observer's meridian at the time of observation).

Here’s a SAS program I wrote to do these calculations:

References
Meeus, J. Astronomical Algorithms. 2nd ed., Willmann-Bell, 1998, p. 99.