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Benvenuti in queste pagine dedicate a scienza ed arte. Amelia Carolina Sparavigna

Wednesday, June 15, 2016

On the Karnak Temple and the Sun Hierophany

The Karnak Temple and the Motion of the Earth's Axis

Article published on SSRN Journal.
Abstract: The Karnak Temple complex comprises a vast mix of temples, chapels and other buildings. Its construction began during the reign of Senusret I in the Middle Kingdom and continued during the Ptolemaic period. The temple was the main place of worship the Amun-Ra, the Sun God. Not surprisingly his temple has its axis aligned along the sunrise azimuth on the winter solstice. Here we will discuss how the motion of the Earth’s axis has altered, in four thousand years, this alignment of half a degree.



Sun hierophany at the temple on the winter solstice

Sunday, June 12, 2016

Newgrange and the axial tilt


The Newgrange  stone age passage tomb on the Winter Solstice is described by the site:
Above the entrance to the passage at Newgrange there is an opening. This opening allows sunlight to penetrate the passage and chamber at sunrise around the Winter Solstice. A narrow beam of light penetrates the opening and reaches the floor of the chamber, "gradually extending to the rear of the passage. As the sun rises higher, the beam widens within the chamber so that the whole room becomes dramatically illuminated. After 17 minutes the sunbeam leaves the chamber and retreats back down the passage. When Newgrange was built over 5000 years ago, the winter solstice sunbeam would have made its way to the back recess of the central chamber. Due to changes in the tilt of the Earth's axis the sunbeam now stops 2 metres from the back recess". 
What is this tilt? It is the obliquity of the ecliptic. Here in the figure we can see it.


The angle of the Earth's axial tilt varies with respect to the plane of the Earth's orbit. These slow 2.4° obliquity variations are roughly periodic, taking approximately 41,000 years to shift between a tilt of 22.1° and 24.5° and back again. Currently the Earth is tilted at 23.44 degrees, decreasing. 
At the time of Newgrange building, the til was of about 24 degrees.


If we want to evaluate the effect of this tilt shift on the sunrise and sunset azimuths on solstices, at the Newgrange latitude, the influence of the tilt on the sunrise azimuths on solstice is about a degree.  This explains the two metres back from recess.

Hardknott fort sunrises on summer solstice

As told by Ben Johnson on the Hardknott Roman Fort at 
"A trip to the Roman fort at Hardknott in Cumbria is probably not for those of a nervous disposition!! The drive up the steep, winding, narrow road through Hardknott and Wynose passes is often tricky and always a little frightening ... , but this adds to the experience, as the setting of the fort is spectacular and the scenery incredible."

I would like to add something to these worlds.
Let me use the following shapshot from the Photographer's Ephemeris.


We can see how the Roman fort wakes up on the summer solstice.
Viewed from the center, the sun rises along the direction of the NE gate.
The sunset corresponds to the NW gate.
This year the moon is 98%, that is full moon! Fantastic!

More on the Hardknott fort at

Saturday, June 11, 2016

On precession

Polaris is the brightest star in the constellation Ursa Minor. Very close to the north celestial pole, it is currently the pole star. But Odysseus, the Greek king of Ithaca, and the ancient mariners, did not use this star for their voyages. Why? because of precession (cerchio che più tardi in cielo è torto).

a very detailed and clear discussion on precession, with illustrations,

Here I am adapting a part of this excellent discussion.

The Earth is like a spinning top. Then the Earth’s rotational axis gyrates, with a period of 26,000 years. This motion is called axial precession, or "precession of the equinoxes".  Precession occurs because the Sun's gravity induces torque, which pulls the Earth's equatorial bulge toward the ecliptic. 
The axis of precession is perpendicular to the ecliptic and is aligned with the ecliptic axis. This axis projects to two points, the north and south ecliptic poles, which are inclined 23.5º to the celestial poles.

Note that axial precession affects the direction of the Earth's axis, but it does not affect the angle of its tilt relative to the ecliptic. Thus, precession affects the time of year in which various constellations are visible. The precssion does not affect the axis tilt, which is constant, and so the seasons themselves continue just like they are now.

Our standard Gregorian calendar is based on the solar, or tropical year, the time it takes the Sun to return to the same equinox, which is defined by the direction of the Earth's axis relative to the Sun. Since the seasons are intrinsic to the tropical year, our Gregorian calendar is calibrated so that the March equinox always falls on either March 20 or 21. This forces the seasons to occur during the same months, regardless of precession. However, the stars visible in the evening will slowly change. Figure 1 (of the given link) shows the winter solstice in the north, with the constellation Taurus prominent at midnight. If the Earth's axis were pointing in the opposite direction, Taurus would still be prominent at midnight, but it would be the summer solstice. So, for the solar calendar, the seasons occur in the same months, but we view different constellations during those months.

Besides the axial precession of 26,000, there is also a small oscillation of the tilt. Taking approximately 41,000 years the tilt shifts from 22.1° to 24.5° and back again. Currently the Earth is tilted at 23.44 degrees,  decreasing. If we want to evaluate the effect of this tilt shift on the sunrise and sunset azimuths on solstices, for instance at the Newgrange latitude, for Newgrange passage tomb that was built 5,000 ago, the influence of the tilt on the sunrise azimuths on solstice is about a degree (see  http://stretchingtheboundaries.blogspot.it/2016/06/newgrange-and-axial-tilt.html )