APOD: Julius Caesar and Leap Days (2016 Feb 29)

[Nitpicker]

Dear neufer, the time it takes for the Earth to circle the Sun is commonly known as a year. The year has been crafted carefully by humans to keep the seasons well synchronized with our calendars, for our convenience. You can stick your sidereal year where the Sun don't shine, Sir!

(It isn't a circle either. Ye Gods!)

[Nitpicker]

Next you'll be insisting that a day is 23 hours, 56 minutes, and 4 seconds.

[geckzilla]

The Earth is a football in a football-shaped orbit!

[Nitpicker]

The Earth is a football in a football-shaped orbit!

And every four years, the Earth loses a few weeks to something called the Fédération Internationale de Football Association World Cup. It suddenly seems perfectly reasonable, now that you've described the Earth as a football (of ambiguous shape).

[neufer]

APOD specifically states:

• "the time it takes for the Earth to circle the Sun"
  
  and not: the time it takes for the Sun to appear to circle the Earth.

The fixed stars simply define the Mach inertial frame of reference in which the action takes place.

Dear neufer, the time it takes for the Earth to circle the Sun is commonly known as a year. The year has been crafted carefully by humans to keep the seasons well synchronized with our calendars, for our convenience. You can stick your sidereal year where the Sun don't shine, Sir!

A day IS defined as:

• the average time it takes for the Sun to appear to circle the Earth
  
  and not: the time it takes for the Earth to rotate on its axis.

The day and year were defined long before anyone even knew that the Earth rotated or went around the Sun.

Hence: In modern terms, the time it takes for the Earth to circle the Sun is slightly more than the time it takes for the Earth to rotate 366 times (with respect to the Sun -- actually we now know this takes about 366.2591 [~365.256363004/(1 - 1/365.256363] rotations).

[Chris Peterson]

A day IS defined as:

the average time it takes for the Sun to appear to circle the Earth

A day is defined as 86 400 seconds. Any other definition requires some kind of qualification (e.g. solar day, stellar day, etc). All of the different types of years you've been talking about are based on 86 400 second days.

[neufer]

A day IS defined as:

the average time it takes for the Sun to appear to circle the Earth

A day is defined as 86 400 seconds. Any other definition requires some kind of qualification (e.g. solar day, stellar day, etc). All of the different types of years you've been talking about are based on 86 400 second days.

• We are arguing about an APOD explanation that was both:
  very precise numerically and very ambiguous verbally.

[Chris Peterson]

A day is defined as 86 400 seconds. Any other definition requires some kind of qualification (e.g. solar day, stellar day, etc). All of the different types of years you've been talking about are based on 86 400 second days.

• We are arguing about an APOD explanation that was both:
  very precise numerically and very ambiguous verbally.

Which is why I'm being precise.

[Nitpicker]

My argument remains the same ... the time taken for the Earth to circle the Sun is the tropical (or solar) year with respect to the Sun, and the sidereal year with respect to the "fixed stars".

Sidereal time is great for tracking objects in the outer solar system and beyond, which is best done at night (i.e. where the Sun don't shine).

Solar time has historically been the time that matters most on Earth and our every-day modern standards for time measurement are adjusted to it, when practical.

In the context of the Julian and Gregorian calendars, I don't think the APOD explanation is mistaken (in any way) to refer to the tropical year. Furthermore, to argue that the explanation is "very ambiguous verbally", when the difference between the two years is only about 20 minutes ... well, we've spent far more time arguing about it.

[Nitpicker]

Hence: In modern terms, the time it takes for the Earth to circle the Sun is slightly more than the time it takes for the Earth to rotate 366 times (with respect to the Sun -- actually we now know this takes about 366.2591 [~365.256363004/(1 - 1/365.256363] rotations).

I sense from the above, that you also quibble with the APOD explanation's equivalence of "the time it takes for the Earth to rotate with respect to the Sun" and "a day of 86,400 seconds". But I would argue that your numbers are only correct with respect to the "fixed stars" (or the Mach thingy you called it) and where a rotation is defined as 360 degrees relative to the "fixed stars", which isn't terribly useful to regular people who just need to get to work on time.

[neufer]

Hence: In modern terms, the time it takes for the Earth to circle the Sun is slightly more than the time it takes for the Earth to rotate 366 times (with respect to the Sun -- actually we now know this takes about 366.2591 [~365.256363004/(1 - 1/365.256363] rotations).

I sense from the above, that you also quibble with the APOD explanation's equivalence of "the time it takes for the Earth to rotate with respect to the Sun" and "a day of 86,400 seconds". But I would argue that your numbers are only correct with respect to the "fixed stars" (or the Mach thingy you called it) and where a rotation is defined as 360 degrees relative to the "fixed stars", which isn't terribly useful to regular people who just need to get to work on time.

• Astronomers aren't regular people

[Nitpicker]

Astronomers aren't regular people

Not in my experience, no. They can work strange hours, too.

[neufer]

My argument remains the same ... the time taken for the Earth to circle the Sun is the tropical (or solar) year with respect to the Sun,

My argument remains the same ... "the time taken for the Earth to circle the Sun with respect to the Sun," is a ridiculous definition for "the tropical year." If the Earth stood still in its orbit but the axis "precessed" it could not be considered to "circle the Sun" in any way.

[Nitpicker]

Well, okay, the tropical year can be relative to the northward equinox if you prefer. (Though the ancients probably measured it by comparing the sunrise/sunset with known easterly/westerly bearings.) The point is that it is not relative to the "fixed stars", because that would be a poor way to define a calendar tied to the seasons.

Indeed, the "with respect to the Sun" from the APOD explanation, is in reference to a day of 86,400 seconds (i.e. the time it takes for Earth to rotate), not in reference to the time it takes Earth to circle the Sun (which is what I suggested earlier -- my mistake). But in the context of this APOD, the tropical year is implied, as no other year makes sense.

[Nitpicker]

Just for fun, I've made an accurate scale drawing of the (slightly) elliptical orbit of the Earth-Moon system around the Sun. Note that relative to the "fixed stars", the equinoxes and solstices rotate (opposite to the direction of orbit) about the Sun every ~26,000 years, or about 50 arcsec per year. The equinoxes and solstices define the Earth's seasons and the direction of the Earth's axial tilt.

The perihelion-aphelion line, known as the line of apsides, also precesses (along with the minor axis of the ellipse) about the ellipse centre, but much more slowly, taking ~112,000 years for a complete revolution relative to the "fixed stars". But relative to the equinoxes and solstices, the line of apsides processes (i.e. rotates in the direction of orbit) every ~21,000 years.

I think I must be a bit wrong about the apsidal precession. It is in the orbital direction, both relative to the "fixed stars" and relative to the equinoxes. But it seems that precession, not procession, is the correct term in this context, regardless of direction.

[Chris Peterson]

Indeed, the "with respect to the Sun" from the APOD explanation, is in reference to a day of 86,400 seconds (i.e. the time it takes for Earth to rotate)...

The time it takes for the Earth to rotate with respect to the Sun? That's a solar day, and is approximately (but never exactly) 86 400 s.

[Nitpicker]

Indeed, the "with respect to the Sun" from the APOD explanation, is in reference to a day of 86,400 seconds (i.e. the time it takes for Earth to rotate)...

The time it takes for the Earth to rotate with respect to the Sun? That's a solar day, and is approximately (but never exactly) 86 400 s.

Ah, the dangers of quoting out of context ...

In the context of the APOD explanation text:

In modern terms, the time it takes for the Earth to circle the Sun is slightly more than the time it takes for the Earth to rotate 365 times (with respect to the Sun -- actually we now know this takes about 365.24219 rotations).

I interpret the "365.24219 rotations" to mean 365.24219 days, each of length 86,400 seconds. Yes, each solar day has a slightly different length. And the 365.24219 number is also averaged and rounded.

[Chris Peterson]

I interpret the "365.24219 rotations" to mean 365.24219 days, each of length 86,400 seconds. Yes, each solar day has a slightly different length. And the 365.24219 number is also averaged and rounded.

Yes, I agree. As previously noted, a "day" is defined as exactly 86 400 seconds, and doesn't correspond exactly to any physical day. It is very close to the mean solar day, of which there are approximately the count you gave in a tropical year (the time it takes to make one full circuit of the seasons- that is, from any solstice or equinox to the same one the following year).

[Nitpicker]

By my calculations -- unchecked -- the length of the solar day (from solar noon to solar noon) varies throughout the year, from about 22 seconds shorter, to about 28 seconds longer than a standard day of 86,400 seconds.

[neufer]

A day is defined as 86,400 seconds. Any other definition requires some kind of qualification (e.g. solar day, stellar day, etc). All of the different types of years you've been talking about are based on 86,400 second days.

[c]_From Thou Art That_ By Joseph Campbell[/c]
<<To give a sense of the real meaning of this agricultural mythology, one must examine the actual number of years it takes for the spring equinox to pass through all the signs of the zodiac. Called "the procession of the equinoxes," it takes 25920 years to complete a cycle of the zodiac. Divide that by 60 and you get 432. This number, as we shall see, provides the link between the agricultural mythology and the actual cycles of time.

Some years ago a friend of mine gave me a book, Cooper's Aerobics, that told how many laps a man would have to swim every day in order to stay healthy. A footnote read: "A man in perfect physical shape, at rest, has a heartbeat of about one beat per second." At sixty seconds to a minute and sixty minutes to an hour, in one day of twenty-four hours, the heart beats 86,400 times (half of which is 43200). The heartbeat matches the beat of the universe; They are the same. That coincidence of rhythm was the point of the old cosmic mythologies. The latter envisioned this microcosm, or little cosmos, and the macrocosm, or big cosmos, as resonating to the same beat. When a person tells the doctor "I've got a fever," the doctor takes his pulse to see if it registers in harmony with the 43200 beats--that is, to find out if the patient is in tune with nature.

These numbers, anchored in the sumerian discovery that the order of the universe can be discovered mathematically, are found almost everywhere. In the Hindu sacred epics, the number of years calculated to the present cycle of time, the Kali Yuga as it is known, is 432000, the number of the "great cycle" (mahayuga) being 4,320,000. In the Icelandic Eddas, one reads of the 540 doors in Othin's (Wotan's) Hall through which, at the end of the cycle of time, 800 divine warriors would pass to battle the antigods in that "Day of the Wolf" to mutual annihilation. Multiplying 540 by 800 equals 432000.

An early babylonian account translated into greek by a babylonian priest named berossos in 280 B.C., tells us that 432000 years passed between the time of the rise of the city Kish and the coming of the mythological flood (the biblical story derives from this earlier source). In a famous paper on "Dates in Genesis," the Jewish Assyriologist Julius Oppert, in 1877, showed that in the 1656 years from creation to the flood, 86,400 weeks (i.e. the span of creation in the first chapter of genesis) had passed. Again, half of which produces 43200.

That's a hint, buried in Genesis, that two notions of God are to be found in its pages. The first was the willful, personal creator who grieved at the wickedness of his creatures and vowed to wipe them out. The other God, in complete contrast, is found hidden in that disguised number 86,400, a veiled reference to the gentile, sumero-babylonian, mathematical cosmology of cycles, ever recurring, of impersonal time. During this cycle, kingdoms and peoples arise and recede in seasons of the multiple of 43200. We recall that the jewish people were exiles in babylon for half a century and could, indeed, have absorbed these notions that, exquisitely hidden, provide a subtext of recurring cycles of time in their scriptures.

The mysterious procession of the night sky, then, with the soundless movement of planetary lights through fixed stars, had provided the fundamental revelation, when mathematically charted, of a cosmic order. The universe as living being in the image of a great mother, within whose womb all the worlds, both of life and death, had their existence. The human body is a duplicate, in miniature, of that macrocosmic form.

Throughout the whole a secret harmony holds sway. It is the function of mythology and relevant rites to make this macro-microcosmic insight known to us just as it is the function of medicine (recall the 43200 beats of the heart every 12 hours) to keep us in harmony with the natural order.

These old mythologies, then, put the society in accord with nature. Their festivals were correlated with the cycles of the seasons. That also put the individual in accord with the society and through that in harmony with nature. There is no sense of tension between individual and society in such a mythological world. The rules as well as the rituals of such a society put persons in accord not only with their social world, the world of nature without, but also with their own human nature within.>>

[Nitpicker]

Damn. I thought the answer was 42 ... hang on ... if you subtract 12 from 432 and divide by 10, you get 42. Oooooh.

[neufer]

Damn. I thought the answer was 42 ... hang on ...
if you subtract 12 from 432 and divide by 10, you get 42. Oooooh.

• 42 is the atomic number of molybdenum.

<<Devotees of The Hitch Hiker's Guide to the Galaxy will know that
"the Answer to the Ultimate Question of Life, the Universe, and Everything"
was determined by the computer 'Deep Thought' to be Forty-two.

Readers of an older generation were unsurprised by these revelations, since they were well aware of the importance of 42 in the paradoxical world of Lewis Carroll. For a start, the original title page of Alice's Adventures in Wonderland boasted it contained 42 illustrations. And at the trial of the Knave of Hearts when Alice started to grow larger again the King invoked: "Rule Forty-two. All persons more than a mile high to leave the court", and later claimed: "It's the oldest rule in the book".

Another Carrollian Rule 42, that of the Naval Code, according to the Preface to The Hunting of the SNARK, states: "No-one shall speak to the Man at the Helm, and the Man at the Helm shall speak to no-one". The first Fit of that poem mentions that the Baker, destined to be victim of the Boojum, "had Forty-two boxes all carefully packed, with his name painted clearly on each ... all left behind on the beach", and "he had seven coats on when he came, with three pairs of boots but had wholly forgotten his name" in other words he was clearly "all at sixes and sevens".>>

<<In the 2nd part of Carroll's later work Sylvie and Bruno, the German professor describes a railway system in which the trains move under gravity: "Each railway is in a long tunnel, perfectly straight: so of course the middle of it is nearer the centre of the globe than the two ends: so every train runs halfway downhill, and that gives it force enough to run the other half uphill" (what is this if not an example of Science Fiction worthy of Verne?). I am informed (reliably?) that such a grav(it)y train would make all its trips in 42 minutes, the same time it would take an object to fall through the centre of the earth, the time constant regardless of the tunnel's length.>>

<<The number 42 held a special meaning for Carroll. The first Alice book had 42 illustrations (though a last minute change raised the number to 50). An important nautical rule, Rule 42, is cited in Carroll's preface to _The Hunting of the Snark_ and the Baker comes aboard the ship with 42 carefully packed boxex. In _Phantasmagoria_ Carroll gives his age as 42 (although he was 5 years younger). The White King sends 4207 horses and men to restore Humpy Dumpty. Alice's age is seven years and six months, 7 x 6 = 42.>>

[Nitpicker]

I just knew you would mention atomic number 42.

Carroll was probably the original source of Adams' 42, viz:
https://en.wikipedia.org/wiki/42_%28num ... ar_culture

The number 42 is, in The Hitchhiker's Guide to the Galaxy by Douglas Adams, "[the] Answer to the Ultimate Question of Life, the Universe, and Everything", calculated by an enormous supercomputer named Deep Thought over a period of 7.5 million years. Unfortunately, no one knows what the question is. Thus, to calculate the Ultimate Question, a special computer the size of a small planet was built from organic components and named "Earth". This appeared first in the radio play and later in the novelization of The Hitchhiker's Guide to the Galaxy. The fact that Adams named the episodes of the radio play "fits", the same archaic title for a chapter or section used by Lewis Carroll in "The Hunting of the Snark", suggests that Adams was influenced by Carroll's fascination with and frequent use of the number. The fourth book in the series, the novel So Long, and Thanks for All the Fish, contains 42 chapters. According to the novel Mostly Harmless, 42 is the street address of Stavromula Beta. In 1994 Adams created the 42 Puzzle, a game based on the number 42.

[neufer]

• Arthur Dent: Beaver
  Ford Prefect: Butcher
  Zaphod Beeblebrox: Baker
  Snark/Boojum: The Total Perspective Vortex of Fit the Eighth