Heliacal Rising of Sirius

[Robert Tulip]

Heliacal Rising of Sirius
Robert Tulip
The day each year that Sirius is first visible in the pre-dawn sky, known as its heliacal rising, was used in ancient Egypt to mark the annual cycle of the heavens. In historical times, the heliacal rising is near the summer solstice. Sirius is invisible below the Egyptian horizon for about 70 days each year since its setting with the sun after the spring equinox. But these dates change, and the period of invisibility used to be much longer. This paper examines the change in the location and date of the heliacal rising of Sirius caused by precession of the equinox. The diagrams were produced using astronomy software SkyGazer 4.5. They show the approximate moment of dawn, with the sun at the left on the horizon, on the approximate day on which Sirius is first visible again on the south-eastern horizon. There is some variance between the diagrams which could be made more precise by using the exact moment when both the sun and Sirius are on the horizon, but this small error does not affect the overall result, which is to show how the heliacal rising point of Sirius, as viewed from Cairo, oscillates between the south and south-east horizon.

The Egyptians used the heliacal rising of Sirius as a marker for the annual rising of the Nile. Due to their use of a 365 day calendar, comprising twelve months, each with three x ten day weeks, plus five epagomenal days, the heliacal rise of Sirius drifted around their year over a 1461 year period known as the Sothic Cycle. Egyptian knowledge of this Sothic Cycle shows that they understood the period of the tropical year as 365.25 days.

Sirius 12000BC Heliacal Rising Cairo.gif 51.11 KiB

In the year 12,000 BC, a date well before historical records, this diagram shows the southeast horizon from Cairo, and all locations at the same latitude of 30° north, at just before dawn on 25 June. Here we see that Sirius, the brightest star in the diagram, crossed the meridian (the vertical green line), the most northerly point for all stars in their daily cycle, just below the horizon (the curved green line), and so was then never visible at that latitude over the course of the year. This diagram also shows the spring equinox point of the sun, marked by the meeting point of the celestial equator (white) and the ecliptic, the path of the sun along the zodiac (yellow). The equinoctial point was then in the constellation of Virgo, opposite its current position in Pisces. This diagram also shows the bright star Canopus, half way between the South Celestial Pole (the axis of the earth) and the South Ecliptic Pole (the axis of the sun). Over the slow 25,765 year period of precession of the equinox, Canopus and Sirius inscribe a circle around the South Ecliptic Pole. Apart from proper motion, the relative movement of stars in the galaxy, these stars have inscribed the same path for millions, even billions, of years. Each day all the stars appear to rotate around the celestial poles. In circling the pole, Sirius never rose above the horizon at Cairo in 12,000 BC. Over the slow sweep of the succeeding millennia, first Sirius, and then its southern bright companion Canopus, gradually moved into view from Egypt.


Sirius 11000BC Heliacal Rising Cairo.gif 24.07 KiB

In 11,000 BC, the date of the highest northerly position of Sirius at dawn had moved back several weeks to 17 July. We see that Sirius was slightly closer to the horizon, but was still invisible at Cairo. The spring point, where the ecliptic crosses the equator, has precessed through the constellation of Virgo.

Sirius 10000BC Heliacal Rising Cairo.gif [ 25.02 KiB
In 10,000 BC, Sirius reached the horizon from Cairo just east of due south on 25 July, so barely came into view. The path of each star across the sky forms a circle around the South Celestial Pole, so in this picture, Sirius rose just above the horizon for a few days each year. Interestingly, this epoch of the first visibility of Sirius from Cairo is sometimes coincidentally referred to as ‘the first time’ or Zep Tepi, in Egyptian myth, and is generally marked by the fact that the spring point was in the constellation of Leo. I am not aware of previous study of the movement of Sirius in this way though that would associate it with the Zep Tepi myth.


By 9000 BC, the heliacal rising point of Sirius had moved to 165° east of north, still at about 25 July, and the spring point was in Leo. The millennial movement of the heliacal rising point now starts to accelerate eastward.

Sirius 9000BC Heliacal Rising Cairo.gif 25.35 KiB


By 8000 BC, Sirius rose at about 155° east on 12 July, while the equinox point had moved to between Leo and Cancer. Here, and above, we can also see Sirius’s neighbour, Orion, in its northward climb towards its current position on the celestial equator. The movement east of the Sirius heliacal rising point is also a move towards the celestial equator, which always crosses the horizon at 90° from north.

Sirius 8000BC Heliacal Rising Cairo.gif 26.85 KiB


In 7000 BC, Sirius rose on 10 July at 145° east, while the equinox point was in Cancer.

Sirius 7000BC Heliacal Rising Cairo.gif 26.45 KiB

Continuing, we see that by 7000BC the heliacal rising point of Sirius had moved nearly halfway along the horizon from due south, where it first only appeared on one day of the year, to its present position close to southeast, where it is visible from Cairo for all the year except for 70 days.


In 6000 BC, the rising point had moved to southeast on 12 July, making Sirius readily visible for several months low in the southern sky. The equinox had reached Gemini.

Sirius 6000BC Heliacal Rising Cairo.gif 27.23 KiB


In 5000 BC, Sirius rises closer to east than south on about 8 July, and its companion Orion is about half way between the horizon and the equator. The equinox point is in Gemini.

Sirius 5000BC Heliacal Rising Cairo.gif 24.77 KiB


In 4000 BC, approaching historical times, Sirius is now rising at 125° east on 6 July, as the equinox occurs in Taurus.

Sirius 4000BC Heliacal Rising Cairo.gif 28.52 KiB


3000 BC marks the approximate beginning of the dynastic age in Egypt. The position of the heliacal rising of Sirius has shifted only 5° in the last thousand years, compared to about a 15° degree shift over a millennium around 9000 BC. and the date has stayed about the same at 6 July. Sirius is moving towards its point of greatest distance from the south celestial pole, in its slow orbit around the south ecliptic pole over the course of the Great Year. The rest of the stars continue to precess, with the equinox now in the middle of Taurus, and Orion even closer to the equator.

Sirius 3000BC Heliacal Rising Cairo.gif 29.32 KiB


In 2000 BC, at the height of Egyptian civilization, Sirius has barely shifted its rising point and date over the last millennium, moving only by about 3° and one day. Norman Lockyer, founder of the journal Nature, and co-discoverer of helium, made intensive study of how the Egyptians aligned their temples to the heliacal rising of Sirius. It appears that after many centuries when alignments no longer worked, new temples were built on old foundations, shifting the axis slightly to put them in line with the rising point of Sirius. The equinox now occurs in Aries.
Sirius 2000BC Heliacal Rising Cairo.gif 28.03 KiB

By 1000 BC, still during the glory days of Egypt, the rising point of Sirius had shifted a further 5° north, and the equinox was in the middle of Aries. Orion is now astride the equator, with Betelgeuse having moved for the first time into the northern hemisphere.

Sirius 1000BC Heliacal Rising Cairo.gif 28.18 KiB


At the time of Christ, the moment still marking the turning point of our calendar, the great civilization of Egypt lay in ruins beneath the swords of the marauding hordes of Assyria, Babylon, Greece and Rome. The rising point of Sirius has barely moved over this time of upheaval, sitting at 110° east. The equinox point is now crossing the first fish of the constellation Pisces.

Sirius 1BC Heliacal Rising Cairo.gif 27.75 KiB


By 1000 AD, in the middle of the Dark Ages, observation of the stars had largely been forgotten except by the Arabs. The equinox point is now in the middle of the constellation Pisces. Sirius rises slightly later, on 10 July, at almost exactly the same place on the horizon where it rose at the time of Christ.

Sirius 1000AD Heliacal Rising Cairo.gif 30.61 KiB

The current situation, shown in this diagram from 2000 AD, shows the equinox nearly at the end of Pisces and just about to enter Aquarius. Sirius still rises close to the same point it has risen for the last 2000 years. Orion’s Belt has reached the celestial equator, near to its most northerly position in about 2300 AD.

Sirius 2000AD Heliacal Rising Cairo.gif 31.2 KiB


Over the next twelve or so thousand years, as shown in the remaining diagrams below for 3000 AD, 10,000 AD and 15.000 AD, we see the rising position of Sirius reverse its northerly motion, returning to invisibility from Cairo again at the end of one cycle of precession, the 25765 year-long Great Year of precession of the equinox caused by the spin wobble of the earth.

3000 AD: After its heliacal stasis over the Christian Aion, Sirius has begun its movement back to the south. The equinox is in the middle of Aquarius.

Sirius 3000AD Heliacal Rising Cairo.gif 31.47 KiB


10,000 AD: The heliacal movement over the Great Year cycle accelerates at its mid point. The September equinox is now shown, in Taurus, opposite the position of the March equinox in Scorpio.

Sirius 10000AD Heliacal Rising Cairo.gif 26.85 KiB

The year 15,000 Anno Domini: Sirius is back at the point where it becomes invisible from Cairo, with the March equinox shown once again in Virgo, and about to enter Leo, its position in the old Egyptian Zep Tepi. Sirius has returned to the heliacal point where it first appeared visible from the latitude of Cairo over the long sweep of the Holocene and the Anthropocene. However, the proper motion of Sirius, it actual shift relative to other stars, is among the fastest of all stars because it is so close to earth, only eight light years away. It appears from this diagram that over the next ten thousand years Sirius will shift to a more northerly actual location, so will not again become invisible from the north for as long as it used to. I hope humans will still be around to see it.

Sirius 15000AD Heliacal Rising Cairo.gif 23.69 KiB

[Shaula]

What evidence do you have that they knew the length of the Sothic cycle? AIUI they used the heliacal rising of Sirius to fix their ceremonial to their wandering calendar. Surely the model that they waited until a momentous event to start their year is a more parsimonious one than them having spotted a 1461 year cycle? In fact the change of the 'official' year length in 240BC or so suggests that they had not identified the more accurate long cycle. Then they added in another six-yearly correction. Why would they keep doing this sort of tinkering if they knew the right answer already?

[Robert Tulip]

What evidence do you have that they knew the length of the Sothic cycle? AIUI they used the heliacal rising of Sirius to fix their ceremonial to their wandering calendar. Surely the model that they waited until a momentous event to start their year is a more parsimonious one than them having spotted a 1461 year cycle? In fact the change of the 'official' year length in 240BC or so suggests that they had not identified the more accurate long cycle. Then they added in another six-yearly correction. Why would they keep doing this sort of tinkering if they knew the right answer already?

This is from Norman Lockyer's The Dawn of Astronomy. He comments (p250) "There no doubt was a time when the Egyptian astronomer priests imagined that, by the introduction of the 365-day year, marking its commencement, as I have said, by the rising of one of the host of heaven [Sirius], they had achieved finality. But, alas, the dream must soon have vanished. Even with this period of 365 days, the true length of the year had not been reached; and soon, whether by observations of the beginning of the inundation [of the Nile], or by observations of the solstice in some of the solar temples when these had been built, it was found that there was a difference of a day every four years between the beginning of the natural and of the newly-established year, arising, of course, from the fact that the true year is 365 days and a quarter of a day (roughly) in length.

With perfectly orientated temples they must have soon found that their festival at the Summer Solstice—which festival is known all over the world to-day—did not fall precisely on the day of the New Year, because, if 365 days had exactly measured the year, that flash of bright sunlight would have fallen into the sanctuary just as it did 365 days before. But what they must have found was that, after an interval of four years, it did not fall on the first day of tlie month, but on the day following it. ...

(255) We learn from the work of Biot and Oppolzer, then, that the precessional movement of the star caused successive heliacal risings of Sirius at the solstice to be separated by almost exactly 365.25 days—that is, by a greater period than the length of the true year. So that, in relation to this star, two successive heliacal risings at the 1st of Thoth vague are represented by a period of (365.25 x 4 =) 1461 years, while in the case of the solstices we want 1506.

Now in books on Egyptology the period of 1461 years is termed the Sothic period, and truly so, as it very nearly correctly measures the period elapsing between two heliacal risings at the solstice (or the beginning of the Nile flood) on the 1st of Thoth in the vague [365 day] year."

Lockyer discusses this topic of Egyptian knowledge of the Sothic Cycle at some length. I have posted a link to his book in the astronomy thread The Dawn of Astronomy: Norman Lockyer, and will summarize further corroborating material. If his argument is incorrect I would welcome refutation of it.

[Shaula]

A summary would be good. My lecturers tended to the idea that the Egyptians were aware of problems with their calendars and made changes when they got too out of whack but that a full description of the cycle was not part of the their body of knowledge. It was not that is was outside their capabilities just that the stability required to make these sorts of long term assessments was not really there. Despite the appearance of stability the political situation was in fact pretty carnivorous.

[Robert Tulip]

The Egyptians used a calendar of 365 days, so the first day of their calendar year drifted around the seasons by the ~0.25 day difference between 365 days and the real year. The Egyptians observed the heliacal rising of Sirius as a marker of the new seasonal year for hundreds or possibly thousands of years. As I quoted above, Lockyer says the heliacal return of Sirius was close to exactly 365.25 days, slightly longer than the tropical year.

The Sothic Cycle is just the period over which this Egyptian calendar again aligns to the seasons. For example, as noted above in quote from Lockyer, if the calendar priests noted that Sirius rose heliacally on one date in their 365 day calendar, their records would show that in four years it rose on the next day, and so on. In 100 years it would rise 25 days later in the 365 day calendar. In 1461 years (365.25 x 4) it would rise one year later, completing a cycle. This is a fairly simple mathematical calculation for people who were apparently able to orient their pyramids and temples with such precision.

The main point of the opening post is to show how something that has seemed fairly constant over historical time, the heliacal position of Sirius, only seems constant because Sirius reached its most distant point from the South Celestial Pole in about 1000 AD, at which time the position of its heliacal rise stopped and reversed direction.

Attached diagram shows the lineup of Sirius, Canopus, the South Ecliptic Pole, and the South Celestial Pole in 1000 AD. This moment, when Sirius and Canopus are furthest from the celestial pole, also marks a turning point of the sine curve of the location of the rise of Sirius on the horizon. The northward movement of the heliacal rise was fastest at the inflection point of the sine curve, about 5,400 BC. It slowed to a stop in 1000 AD, and is now headed south again.

Another book that discusses this topic is The Egypt Code by Robert Bauval. He contends that the Egyptians did not adjust their calendar, but kept religiously to the 365 day arrangement for a very long time, deliberately allowing their dates to slip around the seasons over at least two Sothic Cycles during the dynastic period.

Sirius and Canopus on Meridian 1000 AD.gif

[Shaula]

Bauval is red flagged for me. His stuff with Hancock was bad, bad science. He'd have to do a lot of very good stuff to get his rep back. I've not touched his stuff since then. Long chains of suppositions built on suppositions...

I'll try to have a read around. I guess my issues with the numbers is the precision with which they could be sure of their measurements over the shorter timescales. Could they have been sure enough of the number for it to have been calculable?

[Robert Tulip]

Bauval is red flagged for me. His stuff with Hancock was bad, bad science. He'd have to do a lot of very good stuff to get his rep back. I've not touched his stuff since then. Long chains of suppositions built on suppositions...

I'll try to have a read around. I guess my issues with the numbers is the precision with which they could be sure of their measurements over the shorter timescales. Could they have been sure enough of the number for it to have been calculable?

Sure there are 'red flags' in a lot of material related to this topic. Especially the speculation that Egyptian civilization is actually much older than shown in the archaeological record. However, that is a separate matter from the work on the Sothic Cycle and is not my concern here.

The precision here derives from the actual relation between the Egyptian 365 day 'revolving year' and the 365.25 day Sirius return. After four years, the heliacal rise of Sirius shifted by one Egyptian calendar day, and after forty years by ten days. This relation, as I understand from Lockyer, was stable over the period of Egyptian observation. The difference indicates that the Sirius return occurs 6 hours later on average each year, giving a Sirius heliacal year average of 365.25 days. So, any given date on the calendar will mark the heliacal rise of Sirius every 1461 years. 1461 = 365.25 x 4, so there is no mystery in this observation. It flows directly from the observation of the stability of the calendar shift by one day every four years, with the chance equality of the heliacal cycle to 365.25 rather than the exact tropical year of 365.2422 days.

[grapes]

Egyptian knowledge of this Sothic Cycle shows that they understood the period of the tropical year as 365.25 days.

From my reading of the Sothic Cycle wiki, it's not so much that they had knowledge of the Sothic Cycle, but that they used 365.25 days for the tropical year, and thought that that applied to Sirius as well.

I think we all agree that the 0.25 day is relatively easy to come up with. Determining the actual length of the Sothic Cycle is much harder.

The Egyptians used a calendar of 365 days, so the first day of their calendar year drifted around the seasons by the ~1.25 day difference between 365 days and the real year.

I'm not sure whether you're using the tropical year or the sidereal year as the real year, but surely that 1.25 day should be closer to 0.25 day?

[Robert Tulip]

1.25 day

typo. Is that one okay for me to edit to cover my tracks?

Sorry about that. This Sothic Cycle knowledge question was a minor point in the OP, which was mainly intended to show how the heliacal position of Sirius as viewed from Egypt shifts over the course of earth's spin wobble period.

From my position in Australia, Sirius is visible on any clear night. At the date of its heliacal setting on 29 July it rises 3.5 hours before dawn.

[grapes]

Go ahead and edit! My post will remain though, in case anyone ever needs a quickie to impugn your scholarship.

[Robert Tulip]

The path of the heliacal rising of Sirius over the period of precession of the equinox is plotted in the attachments to the opening post. Part of the reason for presenting this material is to help refute unscientific ideas about precession. Over the 26,000 year cycle of precession, the rising point of Sirius moves relatively rapidly when it is orthogonal to the axis between the celestial and ecliptic poles (inflection points ~5400BC and 7500AD) and appears to barely move at all when it crosses this axis (~1000 AD and ~12000 BC). This apparent stasis during centuries of historical time, as the rising point of Sirius turns from moving northward to southward, was used by writers such as Homann to make incorrect claims that Sirius does not precess and that precession is due to some other mechanism than lunisolar torque.

In looking at precession and ancient knowledge, Norman Lockyer demonstrates that shifts in precession and obliquity as predicted by Newtonian mechanics match to realignments of ancient monuments such as at Karnak and Denderah. To start to understand how astronomy may have figured in ancient thought requires a solid empirical foundation.

[grapes]

Part of the reason for presenting this material is to help refute unscientific ideas about precession. Over the 26,000 year cycle of precession, the rising point of Sirius moves relatively rapidly when it is orthogonal to the axis between the celestial and ecliptic poles (inflection points ~5400BC and 7500AD) and appears to barely move at all when it crosses this axis (~1000 AD and ~12000 BC). This apparent stasis during centuries of historical time, as the rising point of Sirius turns from moving northward to southward, was used by writers such as Homann to make incorrect claims that Sirius does not precess and that precession is due to some other mechanism than lunisolar torque.

Homann claimed that Sirius lacked precession even today. I was caught up in that argument, even to the point of analyzing his own backyard data and publishing my analysis in a response to an online journal article of his. I wasn't aware of this effect or I might not have ever even tried to figure out what he was doing.

[Robert Tulip]

Homann claimed that Sirius lacked precession even today. I was caught up in that argument, even to the point of analyzing his own backyard data and publishing my analysis in a response to an online journal article of his. I wasn't aware of this effect or I might not have ever even tried to figure out what he was doing.

Thanks Grapes. Homann's claims present a case study in the psychology of false belief. An artifact of observation, the apparent stasis of Sirius against precession, has been used to build a fantastic framework of ideas that ignores contrary evidence. This wrong way of thinking has evolved into further efforts to find a binary partner for the sun such as an invisible black hole or brown dwarf, once its proponents found the original Sirius claim was untenable. It all goes back to a wrong inference drawn from observation of Sirius over historical time, ignoring how this observation fits simply into a slow astronomical cycle of the earth against the stars caused by the wobble of the spin axis of the earth.

[Alsor]

What is the current position of Sirius in the sky in Egypt at midnight on new year, and what was, say, 100 years ago?

[Tensor]

Robert, silly question. How has the modifications to the current calendar affected the helical rising? Since the Julian, (and the modification to it by the Gregorian), don't the calendar changes assist in keeping the rising from moving a great deal?

For instance, from records, we know that Sirius was at the meridian at midnight on New Year Eve in 1582 (or one minute after midnight on 1 Jan 1583). But 10 days were dropped from the calendar in 1582 (at least among the Roman Catholic countries) during the change to the Gregorian calendar, so if that change hadn't occurred, Sirius would have been have been on the meridian on December 21st, not at midnight between Dec. 31 and Jan 1.

The days were dropped of course, due to the addition of days caused by precession. I'm using midnight on New Years here as I am not sure of the rising date during 1582. Since you are showing a rising date ~July, I would assume the rising date would jump back 10 days in 1583, correct?

[Robert Tulip]

Robert, silly question. How has the modifications to the current calendar affected the helical rising? Since the Julian, (and the modification to it by the Gregorian), don't the calendar changes assist in keeping the rising from moving a great deal?

For instance, from records, we know that Sirius was at the meridian at midnight on New Year Eve in 1582 (or one minute after midnight on 1 Jan 1583). But 10 days were dropped from the calendar in 1582 (at least among the Roman Catholic countries) during the change to the Gregorian calendar, so if that change hadn't occurred, Sirius would have been have been on the meridian on December 21st, not at midnight between Dec. 31 and Jan 1.

The days were dropped of course, due to the addition of days caused by precession. I'm using midnight on New Years here as I am not sure of the rising date during 1582. Since you are showing a rising date ~July, I would assume the rising date would jump back 10 days in 1583, correct?

Tensor, I'm pretty sure that the software I used, SkyGazer 4.5, uses Gregorian dates for pre-Gregorian period. I will check that and confirm. The deletion of ten days for the Gregorian calendar change was not related to precession, as I understand it, but was solely due to the fact that the Julian calendar wrongly included leap years on all the centuries. The difference between the Julian figure of 365.25 and the correct 365.2422 days caused the ten day drift of the solstices and equinoxes against the calendar over 1500 years. 2000 was a leap year, but 2100, 2200 and 2300 will not be.

The Gregorian calendar will not stop the Sirius rising date from changing due to precession. Over the next ten thousand years the rising point will migrate back to due south, and will also move around the year. I need to make my analysis more precise by using Sun and Sirius both exactly on the horizon instead of the rough diagrams linked in the OP to calculate the speed of this drift. This use of both on the horizon does not give the observable heliacal rising though, which happens when Sirius is about 7 degrees west of the solar right ascension. At the latitude of San Francisco this now happens on August 7.

Alsor, I will check the answer to your question and revert.

[grapes]

The days were dropped of course, due to the addition of days caused by precession.

Precession doesn't "add days" so much as it causes the yearly occurrence of an astral phenomenon to change relative to the seasons. The orbit of the earth is defined by those astral phenomena, but we prefer to keep the calendar adjusted so that the seasons are marked in a consistent fashion.

But you know all this.

Tensor, I'm pretty sure that the software I used, SkyGazer 4.5, uses Gregorian dates for pre-Gregorian period. I will check that and confirm. The deletion of ten days for the Gregorian calendar change was not related to precession, as I understand it, but was solely due to the fact that the Julian calendar wrongly included leap years on the centuries. The difference between the Julian figure of 365.25 and the correct 365.2422 days caused the ten day drift of the solstices and equinoxes over 1500 years. That is why 2000 was not a leap year.

I think you mean, that is why 2000 was a leap year.

Over a 400 hundred year period, the best-fit correction requires 97 leap years, so leap years were skipped in 1700, 1800, and 1900, but not 2000. In some parts of the world.

[Robert Tulip]

You are quick Grapes! I managed to edit my mistake before I saw your post, hence no 'last edited' line.

[Robert Tulip]

What is the current position of Sirius in the sky in Egypt at midnight on new year, and what was, say, 100 years ago?

It is close to bang on the meridian in both. Precisely, Sirius crosses the meridian at Cairo at New Year at 11.55 pm in 2011 and at 11.54 pm in 1911, according to SkyGazer. 100 years is a very short time for precession.

I thought this would be the case everywhere on earth where Sirius is visible, but checked Johannesburg and found that Sirius crosses the meridian at new year at seven past twelve.

One thousand years ago Sirius crossed the meridian at the latitude of Egypt at 10.55 pm. I thought this would mean it basically shifts about one hour per millennium, but checking for 1 AD the time is 10.33 pm, and for 1000 BC it is 10.21 pm. I would have thought this time difference would be the same in times equal sides of Sirius's point furthest from the South Celestial Pole, in 1093 AD, assuming the software is accurate. SkyGazer uses Coordinated Universal Time, which is Gregorian, so ancient sky maps should be commensurate with modern ones.

[Alsor]

A. 1 deg / 72 y

B. 360 deg / 24 h = 15 deg / 1h = 1 deg / 4 min

100 years: 100/72 * 4 min = 5 min 33 s

SkayGazer probably mixed times - a local with the universal...

But no, there should be calculated astronomical time.

01/01/2011 - 01/01/1911 0:0 = 36525.00 d

...
and yet something is not right:

100 * 365.2563 = 36,525.63 days
therefore, those 36,525 days is 100 orbits of the Earth minus 0.63 d.

0.63 d is part: 0.63/365.2563 = 0.0017 of full orbit, which is 0.62 degrees = 2235''

Precession: 100 * 50''= 5000''- more than twice.

It is certain - a consequence of the precession.

On the other hand, the calculated time period from 01.01.1911 to 01.01.2011 is also sure (the error is small).

So we have a contradiction.

[Robert Tulip]

A. 1 deg / 72 y
B. 360 deg / 24 h = 15 deg / 1h = 1 deg / 4 min
100 years: 100/72 * 4 min = 5 min 33 s
SkyGazer probably mixed times - a local with the universal...
But no, there should be calculated astronomical time.
01/01/2011 - 01/01/1911 0:0 = 36525.00 d
...
and yet something is not right:
100 * 365.2563 = 36,525.63 days
therefore, those 36,525 days is 100 orbits of the Earth minus 0.63 d.
0.63 d is part: 0.63/365.2563 = 0.0017 of full orbit, which is 0.62 degrees = 2235''
Precession: 100 * 50''= 5000''- more than twice.
It is certain - a consequence of the precession.
On the other hand, the calculated time period from 01.01.1911 to 01.01.2011 is also sure (the error is small).
So we have a contradiction.

Let's see. Instead of the calendar figure of 36525, if we use the tropical figure of 36524.22, the difference against the sidereal period is not 0.63 but 1.41.

Plugging this into your equation, 2235 x 1.41/0.63 = 5002. This seems to resolve the contradiction.

[Alsor]

Let's see. Instead of the calendar figure of 36525, if we use the tropical figure of 36524.22, the difference against the sidereal period is not 0.63 but 1.41.

Plugging this into your equation, 2235 x 1.41/0.63 = 5002. This seems to resolve the contradiction.

But we know that it has been exactly 36,525 days, every 86400 seconds (with an accuracy of order of milliseconds).

[grapes]

But we know that it has been exactly 36,525 days, every 86400 seconds (with an accuracy of order of milliseconds).

Well, just go back 400 years then. There's only been 97 leap days in that time so on average each year is (400 x 365 + 97) / 400, which is 365.2425 days. Easy enough.

[Robert Tulip]

The accuracy of the number of days since 1911 is calendrical, not dynamic. I think the device of leaving out the leap day on three out of four century years means the meridian transit time of Sirius at new year would not track smoothly across the centuries, but would have a bump around the century years that do not have a leap day. Since we are now just passed the middle of a two century period without an adjusting Gregorian non-leap century to align the calendar and the seasons, it is not surprising that astronomy software shows a discrepancy between time of meridian transits and expected precessional values over this period. The software is probably accurate as far as the calendar is concerned, but reflects the calendar's inaccuracy, over the intra-century short term, in not using the precise orbital period as the measure of the year.

[grapes]

Thanks Grapes. Homann's claims present a case study in the psychology of false belief. An artifact of observation, the apparent stasis of Sirius against precession, has been used to build a fantastic framework of ideas that ignores contrary evidence.

Homann may have been influenced by this effect but he ultimately did the scientific thing and spent years observing Sirius himself. His observations, as he reported them, were at odds with your theory.

However, as I found out later, his observatory was set up in his yard. He didn't make meridianal observations because a tree or something was in the way--so he took sightings at an angle. He seemed to be aware of the problem with this, so only compared observations at about the same time of year--obviously you can't make an observation exactly a real year (whatever that means to you ) later because of the obscuring effect of our central body. Weirdly, or not, his measurements got better, over the years, so that his early data seemed to support his position, but his later data did not. He depended upon that early data, and died soon after. His son carried on the crusade.

[Alsor]

The accuracy of the number of days since 1911 is calendrical, not dynamic. I think the device of leaving out the leap day on three out of four century years means the meridian transit time of Sirius at new year would not track smoothly across the centuries, but would have a bump around the century years that do not have a leap day. Since we are now just passed the middle of a two century period without an adjusting Gregorian non-leap century to align the calendar and the seasons, it is not surprising that astronomy software shows a discrepancy between time of meridian transits and expected precessional values over this period. The software is probably accurate as far as the calendar is concerned, but reflects the calendar's inaccuracy, over the intra-century short term, in not using the precise orbital period as the measure of the year.

But it does not matter - the program calculates ideal case.

Probably uses a different day length to calculate the number of days (implicitly).
This error is common - 'matching' length of the day, because of precession.

Therefore, in a short period of time, the error is significant, and in the long interval (in thousands of years), the error is small, because then it is decisive orbital phase.

[Hornblower]

But it does not matter - the program calculates ideal case.

Probably uses a different day length to calculate the number of days (implicitly).
This error is common - 'matching' length of the day, because of precession.

Therefore, in a short period of time, the error is significant, and in the long interval (in thousands of years), the error is small, because then it is decisive orbital phase.

Can you tell us, in appropriate mathematical detail, what you mean by "decisive orbital phase"?

Honestly, I cannot follow your line of thought in this post.

[grapes]

Yeah, which "program"?

[Robert Tulip]

I think Alsor may have been referring to my use of the program SkyGazer 4.5 to analyse the positions of Sirius over time. I don't agree with his phrase 'ideal case' because the software is simply using the calendar in a mechanical objective way. The problem Alsor seems to be raising with his rather obscure phrase 'decisive orbital phase' is the error introduced by calendar time, measured within a century. The measured time when Sirius crosses the meridian at new year (and so the heliacal rising as well) does not exhibit the smooth linear path produced by precession over this relatively short period because of our convention of assigning leap years in the Gregorian system. The smooth path of precession will only be only visible when we take a longer period, over centuries or thousands of years.

I find this interesting because as Alsor has noted, the time Sirius crosses the meridian at new year would initially be expected to precess by one degree of arc every 71.6 years with precession. Clock time over the last century does not produce this result because of the tiny error in clock time, which we correct with the deletion of leap days at three out of every four century years.

My interest in this thread was to examine the heliacal rising of Sirius, especially how the movement of the rising point of Sirius relates to precession. My calculation from SkyGazer was that Sirius reached its most northerly point in 1094 AD, a point in time that effectively marked a type of 'solstice' in the position of Sirius at the horizon over the precessional period. Over the 26,000 year period of precession, Sirius has barely started moving south again. The 920 years since the turning point equates to about two weeks in comparison to a year.

Whether this 'solstice' is the source of Homann's erroneous theory that Sirius does not precess I really don't know, but it looks possible.

[grapes]

Whether this 'solstice' is the source of Homann's erroneous theory that Sirius does not precess I really don't know, but it looks possible.

Perhaps you can help me straighten something out that has been bugging me.

Can you use that program to get the times (as close as you can but nothing excessive) of the meridian transits of Sirius on the following dates? Thanks.

1999 May 4
2000 May 4

ETA: The Sirius Reseach Group has pulled off the original data from their links at their website, and there is a message that they are about to pull the plug on the whole website. O well. http://siriusresearchgroup.com/

EETA: It's not linked, but the data is still available: http://www.siriusresearchgroup.com/article1.htm

The front page says:

Please feel free to copy or download a selection of articles, presentations and papers for future reference:

1994:

Date -- local time of transit

06.04. -- 21h11'50''

18.10. -- 08h25'18"

t1: 45992 s

n: 195

t2: 46002.34 s

t3: -10.34 s

------------------------

1995:

06.04. -- 21h12'48"

19.10. -- 08h22'19.5"

t1: 46228.5 s

n: 196

t2: 46238.25 s

t3: -9.75 s

---------------------------

1996:

14.04. -- 20h38'19"

26.10. -- 07h51'45"

t1: 45994 s

n: 195

t2: 46002.34 s

t3: -8.34 s

----------------------------

1997:

22.04. -- 20h07'51"

01.12. -- 05h31'11.5"

t1: 52599.5 s

n: 223

t2: 52607.81 s

t3: -8.31 s

--------------------------

1998:

05.04. -- 21h15'37"

22.10. -- 08h09'25"

t1: 47172 s

n: 200

t2: 47181.89 s

t3: -9.89 s

-----------------------------

1999:

05.04. -- 21h16'36.5"

19.10. -- 08h22'12"

t1: 46464.5 s

n: 197

t2: 46474.16 s

t3: -9.66 s

-------------------------------

2000:

05.04. -- 21h13'41"

31.10. -- 07h32'03"

t1: 49298 s

n: 209

t2: 49305.08 s

t3: -7.08 s

------------------------------

2001:

09.04. -- 20h58'59"

15.10. -- 08h35'59"

t1: 44580 s

n: 189

t2: 44586.89 s

t3: -6.89 s

------------------------------

2002:

10.04. -- 20h55'08"

11.10. -- 08h51'47"

t1: 43401s

n: 184

t2: 43407.34 s

t3: -6.34 s

------------------------------

2003:

06.04. -- 21h11'55"

15.10. -- 08h37'03"

t1: 45292 s

n: 192

t2: 45294.62 s

t3: -2.62 s

------------------------------

2004:

09.04. -- 20h57'08"

25.10. -- 07h54'55"

t1: 46933 s

n: 199

t2: 46945.98 s

t3: -12.98 s

------------------------------

2005:

10.04. -- 20h54'15"

11.10. -- 08h50'54"

t1: 43401s

n: 184

t2: 43407.34 s

t3: -6.34 s

------------------------------

2006:

23.04. -- 20h06'05"

31.12. -- 03h35'26"

t1: 59439 s

n: 252

t2: 59449.18 s

t3: -10.18 s

------------------------------