APOD: Julius Caesar and Leap Days (2020 Feb 29)

[APOD Robot]

Julius Caesar and Leap Days

Explanation: In 46 BC Julius Caesar reformed the calendar system. Based on advice by astronomer Sosigenes of Alexandria, the Julian calendar included one leap day every four years to account for the fact that an Earth year is slightly more than 365 days long. In modern terms, the time it takes for the planet to orbit the Sun once is 365.24219 mean solar days. So if calendar years contained exactly 365 days they would drift from the Earth's year by about 1 day every 4 years and eventually July (named for Julius Caesar himself) would occur during the northern hemisphere winter. By adopting a leap year with an extra day every four years, the Julian calendar year would drift much less. In 1582 Pope Gregory XIII provided the further fine-tuning that leap days should not occur in years ending in 00, unless divisible by 400. This Gregorian Calendar system is the one in wide use today. Of course, tidal friction in the Earth-Moon system slows Earth's rotation and gradually lengthens the day by about 14 milliseconds per century. That means that leap days like today will not be necessary ... about 4 million years from now.

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[jks]

Nice choice for the APOD today! But I think that the Earth's rotation is currently slowing by about 1.4 milliseconds per century, as opposed to 14 milliseconds per century as stated in the caption.

The link at the end of the caption states that the Earth's rotation is currently slowing at 14 microseconds per year on average. Multiply that by 100 and the result is 1.4 ms / century. Use of this value (1.4 ms / century) is consistent with the Earth's day increasing by about 56 seconds, leading to no need for leap days in about 4 million years, as stated in the link.

[orin stepanek]

http://asterisk.apod.com/viewtopic.php?f=23&t=40323

I just posted this!

[ytliu0]

The average length of a Gregorian year is 365.2425 days, which is slightly longer than the topical year 365.24219 days. The Gregorian calendar accumulates one day of error in about 3000 years, which is much shorter than the timescale of the slowdown of Earth's rotation. So the leap year system in the Gregorian calendar still needs to be adjusted in the future for the calendar to be in sync with the seasons.

[neufer]

---

<<In Ireland and Britain, it is a tradition that women may propose marriage only in leap years. Supposedly, a 1288 law by Queen Margaret of Scotland (then age five and living in Norway), required that fines be levied if a marriage proposal was refused by the man; compensation was deemed to be a pair of leather gloves, a single rose, £1 and a kiss. In some places the tradition was tightened to restricting female proposals to the modern leap day, February 29, or to the medieval (bissextile) leap day, February 24. According to Felten: "A play from the turn of the 17th century, 'The Maydes Metamorphosis,' has it that 'this is leape year/women wear breeches.' A few hundred years later, breeches wouldn't do at all: Women looking to take advantage of their opportunity to pitch woo were expected to wear a scarlet petticoat — fair warning, if you will."

In Li'l Abner, Sadie Hawkins was the daughter of Hekzebiah Hawkins, one of Dogpatch's earliest settlers and the "homeliest gal in all them hills". She grew frantic waiting for suitors until she reached age 35 and was still a spinster, and her father was worried about her living at home for the rest of her life. In desperation, he called together all the unmarried men of Dogpatch and declared it "Sadie Hawkins Day". A foot race was decreed with Sadie pursuing the town's eligible bachelors. She was specifically interested in a handsome boy named Adam who was already in a courtship with Theresa, whose father was the area's largest potato farmer. Unlike Sadie, Theresa had a number of courtship offers. Matrimony as the consequence of losing the foot race, and the bachelors of the town were running for their freedom.>>

[neufer]

The link at the end of the caption states that the Earth's rotation is currently slowing at 14 microseconds per year on average. Multiply that by 100 and the result is 1.4 ms / century. Use of this value (1.4 ms / century) is consistent with the Earth's day increasing by about 56 seconds, leading to no need for leap days in about 4 million years, as stated in the link.

<<From the observed change in the Moon's orbit, the corresponding change in the length of the day can be computed:

+2.3 ms/century

However, from historical records over the past 2700 years the following average value is found:

+1.70 ± 0.05 ms/century

Opposing the tidal deceleration of Earth is a mechanism that is in fact accelerating the rotation. Earth is not a sphere, but rather an ellipsoid that is flattened at the poles. SLR has shown that this flattening is decreasing. The explanation is that during the ice age large masses of ice collected at the poles, and depressed the underlying rocks. The ice mass started disappearing over 10000 years ago, but Earth's crust is still not in hydrostatic equilibrium and is still rebounding (the relaxation time is estimated to be about 4000 years). As a consequence, the polar diameter of Earth increases, and the equatorial diameter decreases (Earth's volume must remain the same). This means that mass moves closer to the rotation axis of Earth, and that Earth's moment of inertia decreases. This process alone leads to an increase of the rotation rate (phenomenon of a spinning figure skater who spins ever faster as they retract their arms). From the observed change in the moment of inertia the acceleration of rotation can be computed: the average value over the historical period must have been about −0.6 ms/century. This largely explains the historical observations.>>

Tropical year= 365.24219 (24 hr) days = 365 (24 hr 57.33 sec) days.

If days continue to lengthen at +1.70 ms/century
leap years will be unnecessary in ~3.4 million years.

[Chris Peterson]

If days continue to lengthen at +1.70 ms/century
leap years will be unnecessary in ~3.4 million years.[/c]

And then, after that, they'll start becoming necessary again.

[neufer]

The average length of a Gregorian year is 365.2425 days, which is slightly longer than the topical year 365.24219 days. The Gregorian calendar accumulates one day of error in about 3000 years, which is much shorter than the timescale of the slowdown of Earth's rotation. So the leap year system in the Gregorian calendar still needs to be adjusted in the future for the calendar to be in sync with the seasons.

A simplified Gregorian calendar
(i.e., every year divisible by four is a leap year, except for years divisible by 100)
would have years of 365.24 days.

Tropical year= 365.24219 (24 hr) days = 365.24 (24 hr 0.518 sec) days.

If days continue to lengthen at +1.70 ms/century
a simplified Gregorian calendar could be used in ~30,000 years.

[Chris Peterson]

The average length of a Gregorian year is 365.2425 days, which is slightly longer than the topical year 365.24219 days. The Gregorian calendar accumulates one day of error in about 3000 years, which is much shorter than the timescale of the slowdown of Earth's rotation. So the leap year system in the Gregorian calendar still needs to be adjusted in the future for the calendar to be in sync with the seasons.

A simplified Gregorian calendar
(i.e., every year divisible by four is a leap year, except for years divisible by 100)
would have years of 365.24 days.

Tropical year= 365.24219 (24 hr) days = 365.24 (24 hr 0.518 sec) days.

If days continue to lengthen at +1.70 ms/century
a simplified Gregorian calendar could be used in ~30,000 years.

Of course, the basis of all our civil time measurements lies on a continuous count using atomic clocks. No adjustments are made to allow for either the irregular rotation rate of the Earth, the slowing of the Earth, or the non-integral relationship between Earth's rotation rate and year length.

[neufer]

Of course, the basis of all our civil time measurements lies on a continuous count using atomic clocks. No adjustments are made to allow for either the irregular rotation rate of the Earth, the slowing of the Earth, or the non-integral relationship between Earth's rotation rate and year length.

The basis of all our scientific time measurements lies on a continuous count using atomic clocks.

(The basis of all our civil time measurements lies on a discontinuous count using atomic clocks.)

<<A leap second is a one-second adjustment that is occasionally applied to Coordinated Universal Time (UTC), to accommodate the difference between precise time (as measured by atomic clocks) and imprecise observed solar time (known as UT1 and which varies due to irregularities and long-term slowdown in the Earth's rotation). The UTC time standard, which is widely used for international timekeeping and as the reference for civil time in most countries, uses precise "atomic time" and consequently would run ahead of observed solar time unless it is reset to UT1 as needed. The leap second facility exists to provide this adjustment.

Doomsday Clock graph, 1947–2020. The lower points on the graph represent a higher probability of technologically or environmentally-induced catastrophe, and the higher points represent a lower probability.

---

Because the Earth's rotation speed varies in response to climatic and geological events, UTC leap seconds are irregularly spaced and unpredictable. Insertion of each UTC leap second is usually decided about six months in advance by the International Earth Rotation and Reference Systems Service (IERS), to ensure that the difference between the UTC and UT1 readings will never exceed 0.9 seconds.

This practice has proved disruptive, particularly in the twenty-first century and especially in services that depend on precise time stamping or time-critical process control. The relevant international standards body has been debating whether or not to continue the practice, with an increasing number of nations supporting its abolition.>>

[Chris Peterson]

Of course, the basis of all our civil time measurements lies on a continuous count using atomic clocks. No adjustments are made to allow for either the irregular rotation rate of the Earth, the slowing of the Earth, or the non-integral relationship between Earth's rotation rate and year length.

The basis of all our scientific time measurements lies on a continuous count using atomic clocks.

(The basis of all our civil time measurements lies on a discontinuous count using atomic clocks.)

Not so. Civil time is derived from a continuous time system. The master clock for civil time is continuous. That is, civil time is a derived measurement. We look at what the Earth is doing with respect to the master clock, and use that to calculate a correction which then defines UTC.

[donbo]

Is that the constellation Cassiopeia on the 'heads' side of the coin, just above the crescent moon?

[neufer]

Is that the constellation Cassiopeia on the 'heads' side of the coin, just above the crescent moon?

• Cassiopeia, the crescent moon & Caesar's Comet:

<<Caesar's Comet (also Sidus Iulium ("Julian Star") was a seven-day cometary outburst seen in July 44 BC. It was interpreted by Romans as a sign of the deification of recently assassinated dictator, Julius Caesar (100–44 BC). It was perhaps the most famous comet of antiquity.

Based on two sketchy reports from China (May 30) and Rome (July 23), an infinite number of orbit determinations can fit the observations, but a retrograde orbit is inferred based on available notes. The comet approached Earth both inbound in mid-May and outbound in early August. It came to perihelion on May 25, −43 at a solar distance of about 0.22 AU. At perihelion the comet had a solar elongation of 11 degrees and is hypothesized to have had an apparent magnitude of around −3 as the Chinese report is not consistent with daytime visibility during May. Between June 10 and July 20 the comet would have dimmed from magnitude +1 to around magnitude +5. Around July 20, −43, the comet underwent an estimated 9 magnitude outburst in apparent magnitude and had a solar elongation of 88 degrees in the morning sky. At magnitude −4 it would have been as impressive as Venus.

Caesar's Comet was known to ancient writers as the Sidus Iulium ("Julian Star") or Caesaris astrum ("Star of Julius Caesar|Caesar"). The bright, daylight-visible comet appeared suddenly during the festival known as the Ludi Victoriae Caesaris – for which the 44 BC iteration was long considered to have been held in the month of September (a conclusion drawn by Edmund Halley). The dating has recently been revised to a July occurrence in the same year, some four months after the assassination of Julius Caesar, as well as Caesar's own birth month. According to Suetonius, as celebrations were getting underway, "a comet shone for seven successive days, rising about the eleventh hour, and was believed to be the soul of Caesar."

The Comet became a powerful symbol in the political propaganda that launched the career of Caesar's great-nephew (and adoptive son) Augustus. The Temple of Divus Iulius (Temple of the Deified Julius) was built (42 BC) and dedicated (29 BC) by Augustus for purposes of fostering a "cult of the comet". (It was also known as the "Temple of the Comet Star".) At the back of the temple a huge image of Caesar was erected and, according to Ovid, a flaming comet was affixed to its forehead:

To make that soul a star that burns forever
Above the Forum and the gates of Rome.

Tracing the coinage from 44 BC through the developing rule of Augustus reveals the changing relationship of Julius Caesar to the Sidus Iulium. Robert Gurval notes that the shifting status of Caesar's comet in the coinage follows a definite pattern. Representations of the deified Julius Caesar as a star appeared relatively quickly, occurring within several years of his death. About twenty years passed, however, before the star completed its transformation into a comet. Starting in 44 BC, a money maker named P. Sepullius Macer created coins with the front displaying Julius Caesar crowned with a wreath and a star behind his head. On the back, Venus, the patron goddess of the Julian family, holds a starred scepter. Gurval maintains that this coin was minted about the time of Caesar's assassination and thus probably would not have originally referred to his deification. As it circulated, however, it would have brought that idea to mind because of Caesar's new cult. Kenneth Scott's older work The Sidus Iulium and the Apotheosis of Caesar contests this by assuming that the comet did indeed spark this series because of similarity to other coins he produced. A series of Roman aurei and denarii minted after this cult began show Mark Antony and a star, which most likely represents his position as Caesar's priest. In later coins likely originating near the end of Octavian's war with Sextus Pompey, the star supplants Caesar's name and face entirely, clearly representing his divinity.

One of the clearest and earliest correlations of Caesar to a comet occurred during the Secular Games of 17 BC when money maker M. Sanquinius fashioned coins whose reverse sports a comet over the head of a wreathed man whom classicists and numismatists speculate is either a youthful Caesar, the Genius of the Secular Games, the Julian family, or Aeneas’ son Iulus. These coins strengthened the link between Julius Caesar and Augustus since Augustus associated himself with the Julians. Another set of Spanish coins displays an eight-rayed comet with the words DIVVS IVLIVS, meaning Divine Julius.

The poet Virgil writes in his ninth eclogue that the star of Caesar has appeared to gladden the fields. Virgil later writes of the period following Julius Caesar’s assassination, "Never did fearsome comets so often blaze." Gurval points out that this passage in no way links a comet to Caesar's divine status, but rather links comets to his death.

It is Ovid, however, who makes the final assertion of the comet's role in Julius Caesar's deification. Ovid describes the deification of Caesar in Metamorphoses (8 AD):

• Then Jupiter, the Father, spoke..."Take up Caesar’s spirit from his murdered corpse, and change it into a star, so that the deified Julius may always look down from his high temple on our Capitol and forum." He had barely finished, when gentle Venus stood in the midst of the Senate, seen by no one, and took up the newly freed spirit of her Caesar from his body, and preventing it from vanishing into the air, carried it towards the glorious stars. As she carried it, she felt it glow and take fire, and loosed it from her breast: it climbed higher than the moon, and drawing behind it a fiery tail, shone as a star.

In Shakespeare’s Julius Caesar (1599), Caesar's wife remarks on the fateful morning of her husband's murder: "When beggars die there are no comets seen. The heavens themselves blaze forth the death of princes."

• A few scholars, such as Robert Gurval of UCLA and Brian G. Marsden of the Harvard-Smithsonian Center for Astrophysics, leave the comet's very existence as an open question. Marsden notes in his foreword to Ramsey and Licht's book, "Given the circumstance of a single reporter two decades after the event, I should be remiss if I were not to consider this [i.e., the comet's non-existence] as a serious possibility."

>>

[neufer]

Of course, the basis of all our civil time measurements lies on a continuous count using atomic clocks. No adjustments are made to allow for either the irregular rotation rate of the Earth, the slowing of the Earth, or the non-integral relationship between Earth's rotation rate and year length.

The basis of all our scientific time measurements lies on a continuous count using atomic clocks.

(The basis of all our civil time measurements lies on a discontinuous count using atomic clocks.)

Not so. Civil time is derived from a continuous time system. The master clock for civil time is continuous. That is, civil time is a derived measurement. We look at what the Earth is doing with respect to the master clock, and use that to calculate a correction which then defines UTC.

continuous (adj.) "characterized by continuity, not affected by disconnection or interruption," 1640s, from French continueus or directly from Latin continuus "joining, connecting with something; following one after another," from continere (intransitive) "to be uninterrupted," literally "to hang together."

<<When it is mandated, a positive leap second is inserted between second 23:59:59 of a chosen UTC calendar date and second 00:00:00 of the following date. The definition of UTC states that the last day of December and June are preferred, with the last day of March or September as second preference, and the last day of any other month as third preference. All leap seconds (as of 2019) have been scheduled for either June 30 or December 31. The extra second is displayed on UTC clocks as 23:59:60. On clocks that display local time tied to UTC, the leap second may be inserted at the end of some other hour (or half-hour or quarter-hour), depending on the local time zone.

A negative leap second would suppress second 23:59:59 of the last day of a chosen month, so that second 23:59:58 of that date would be followed immediately by second 00:00:00 of the following date. Since the introduction of leap seconds, the mean solar day has outpaced atomic time only for very brief periods, and has not triggered a negative leap second.>>

[Chris Peterson]

The basis of all our scientific time measurements lies on a continuous count using atomic clocks.

(The basis of all our civil time measurements lies on a discontinuous count using atomic clocks.)

Not so. Civil time is derived from a continuous time system. The master clock for civil time is continuous. That is, civil time is a derived measurement. We look at what the Earth is doing with respect to the master clock, and use that to calculate a correction which then defines UTC.

continuous (adj.) "characterized by continuity, not affected by disconnection or interruption," 1640s, from French continueus or directly from Latin continuus "joining, connecting with something; following one after another," from continere (intransitive) "to be uninterrupted," literally "to hang together."

<<When it is mandated, a positive leap second is inserted between second 23:59:59 of a chosen UTC calendar date and second 00:00:00 of the following date. The definition of UTC states that the last day of December and June are preferred, with the last day of March or September as second preference, and the last day of any other month as third preference. All leap seconds (as of 2019) have been scheduled for either June 30 or December 31. The extra second is displayed on UTC clocks as 23:59:60. On clocks that display local time tied to UTC, the leap second may be inserted at the end of some other hour (or half-hour or quarter-hour), depending on the local time zone.

A negative leap second would suppress second 23:59:59 of the last day of a chosen month, so that second 23:59:58 of that date would be followed immediately by second 00:00:00 of the following date. Since the introduction of leap seconds, the mean solar day has outpaced atomic time only for very brief periods, and has not triggered a negative leap second.>>

Civil time is discontinuous. But the basis of civil time is not. Civil time is derived from TAI, which underlies all our time systems.

[MarkBour]

...
Opposing the tidal deceleration of Earth is a mechanism that is in fact accelerating the rotation. Earth is not a sphere, but rather an ellipsoid that is flattened at the poles. SLR has shown that this flattening is decreasing. The explanation is that during the ice age large masses of ice collected at the poles, and depressed the underlying rocks. The ice mass started disappearing over 10000 years ago, but Earth's crust is still not in hydrostatic equilibrium and is still rebounding (the relaxation time is estimated to be about 4000 years). As a consequence, the polar diameter of Earth increases, and the equatorial diameter decreases (Earth's volume must remain the same). This means that mass moves closer to the rotation axis of Earth, and that Earth's moment of inertia decreases. This process alone leads to an increase of the rotation rate (phenomenon of a spinning figure skater who spins ever faster as they retract their arms). From the observed change in the moment of inertia the acceleration of rotation can be computed: the average value over the historical period must have been about −0.6 ms/century. This largely explains the historical observations.>>

This doesn't make sense to me. I'm tempted to say that the reasoning doesn't hold water.
(No offense, Art, I'm taking issue with Wikipedia, not you directly.)

The article is claiming that because of the loss of ice at the poles, the earth is rebounding there and being lifted up, so that more mass is closer to the axis of rotation than before.

The article is implying that the ground is rebounding because of the loss of mass on top of it. And, if this is the reason, it will only rebound to counter the loss of weight on top of it. Meanwhile, that great mass of ice has migrated from the poles, and is now causing an increase in sea level at lower latitudes.

If anything, then, the warming climate and melting of polar glaciers should increase the amount of mass near the equator and increase the moment of inertia for the Earth.

It's possible I'm misunderstanding what exactly the article is claiming. They may be talking about a temporary situation that would only cover part of the time of the melting. But so far, their claim makes little sense to me.

Meanwhile, there are lots of other effects of a warming atmosphere, so the reality of Earth's moment of inertia and tidal deceleration will be quite complex. (But if one can determine the actual distribution of mass, and how it has actually changed, then the venerable equations are not that complex.

[neufer]

...
Opposing the tidal deceleration of Earth is a mechanism that is in fact accelerating the rotation. Earth is not a sphere, but rather an ellipsoid that is flattened at the poles. SLR has shown that this flattening is decreasing. The explanation is that during the ice age large masses of ice collected at the poles, and depressed the underlying rocks. The ice mass started disappearing over 10000 years ago, but Earth's crust is still not in hydrostatic equilibrium and is still rebounding (the relaxation time is estimated to be about 4000 years). As a consequence, the polar diameter of Earth increases, and the equatorial diameter decreases (Earth's volume must remain the same). This means that mass moves closer to the rotation axis of Earth, and that Earth's moment of inertia decreases. This process alone leads to an increase of the rotation rate (phenomenon of a spinning figure skater who spins ever faster as they retract their arms). From the observed change in the moment of inertia the acceleration of rotation can be computed: the average value over the historical period must have been about −0.6 ms/century. This largely explains the historical observations.>>

This doesn't make sense to me. I'm tempted to say that the reasoning doesn't hold water.
(No offense, Art, I'm taking issue with Wikipedia, not you directly.)

The article is claiming that because of the loss of ice at the poles, the earth is rebounding there and being lifted up, so that more mass is closer to the axis of rotation than before.

The article is implying that the ground is rebounding because of the loss of mass on top of it. And, if this is the reason, it will only rebound to counter the loss of weight on top of it. Meanwhile, that great mass of ice has migrated from the poles, and is now causing an increase in sea level at lower latitudes.

If anything, then, the warming climate and melting of polar glaciers should increase the amount of mass near the equator and increase the moment of inertia for the Earth.

It's possible I'm misunderstanding what exactly the article is claiming. They may be talking about a temporary situation that would only cover part of the time of the melting. But so far, their claim makes little sense to me.

1) "The ice mass started disappearing over 10000 years ago,
2) but Earth's crust is still not in hydrostatic equilibrium and is still rebounding."

Ergo...

• 1) the water mass transfer from pole to equator was basically over
  2) long before the crust rebound mass transfer from equator to pole.

From historical records over the past 2700 years we have been in a spin up situation due to crustal rebound.

Global warming could produce enough Greenland & Antarctic melting that we go back to a spin down situation (followed by a delayed spin up again) but this is all short term stuff compared to the millions of years required to lose the need for leap days.