The East Mebon Sun and Venus diagrams were used for three centuries to structure the two largest Barays and their surroundings

9th and 10th centuries

We noted that the azimuth of the East Baray (-1.57 degrees plus or minus some hundredths of a degree) is equal to the azimuth of a line drawn from the observer (the location used also for Mercury) to the upper platform of the East Mebon temple (on the island in the East Baray). Now, on 22 / 04 / 967, the equation of centre of the “Bhaskara” Sun was equal to -1.57°. That means that, if we locate the Sun due East from the observer, the centre of its “Bhaskara” epicycle would be in the direction of the Mebon.

A possible location could be the upper platform of this temple. The latter suggestion is probably correct because there is a relationship between this Sun diagram and the East-West length of the East Baray (7136 m plus or minus a few meters, between the midpoints of the east and west embankments). By multiplying this distance by the “Midnight” equant ratio of the Sun (0.038889), we obtain a distance of 277.5 m. This is the radius of the Bhaskara epicycle whose centre would be within a couple of meters from the central tower of the Mebon temple. This remarkable construction was probably imagined during the reign of Yasovarman I, the builder of the East Baray (about 900 AD) although the Mebon temple was consecrated in 952 AD by Rajendravarman. It is worth noting Yasovarman I also built the Bakheng temple whose centre is located on the meridian of the observer.

Reservoir

East-west width of East Mebon = radius of  Manda epicycle of Venus

The diagrams for the Sun and Venus using the Midnight parameters were used together  to create, seemingly, a remarkable geometrical construction. The location of the That Toc temple of Banteay Prei Nokor, located in the homeland of Jayavarman II, the founder of the Khmer dynasty, was determined to lie on a Sun (or Venus) apsides line running through the eastern embankment of the East Baray. Now, this apsides line crosses precisely the intersection of the Venus Sighra epicycle with the loxodrome running through the centre of both the Venus Manda epicycle and the centre of the epicycle of the Sun.

During  the 10th century, the centre of the Prasat Sralao temple was located  on the deferent of Venus.

 This temple is seemingly a component of  a huge complex which includes an arrangement of eight grid-like enclosures (discovered by the Greater Angkor Project) which plays an important role in our theory.

 The deferent of the Sun runs through the centre of this arrangement.  

 With respect to the true apsidal line, the error is small (smaller than 0.01°). It is worth noting the apsidal line from Banteay Prei Nokor is parallel to the radius of the Venus Manda epicycle and (as the "Midnight" system is involved) it is also parallel to the radius of the Sun Bhaskara epicycle. We show in the chapter on Mercury that a parallel apsidal line (ie parallel to the 22/04 apsidal lines of  Sun and Venus) was used to determine, from the Bakong temple (Roluos area), the location of the ancient observer of Angkor Thom. Another parallel apsidal line also determines the location of the main cluster of monuments built in the Kulen Range from the Beng Mealea Sun. As the areas of Banteay Prei Nokor, Roluos and Kulen are related to Jayavarman II, we suggest the three apsidal lines are the homologs of the long trips of the king between his successive capitals during the early 9th century."

The loxodrome running through Prasat Sralao and the Venus location is tangent to the epicycle of the Beng Mealea Sun.

  The longitude of the eastern dyke of the West Baray was determined after locating the midpoint of the lake (the site of the West Mebon to come) on the deferent of Venus (the West Baray was built during the first half of the century whilst the West Mebon was erected during the second half).

We noted above that the deferent of the Sun passes through the East
Mebon. Similarly the deferent of Venus passes through the West Mebon.

At the end of the 12th century, Jayavarman VII built the Ta Som temple on the meridian (blue line)of the centre of the Venus Manda epicycle.

The figure  shows a loxodrome (green line) running through the centre of the Sighra epicycle of Venus and the centre of the Ta Som temple. We’ll see in the chapter about the Saturn’s diagram of Angkor Proper that this loxodrome crosses the centre of the Sighra epicycle of the latter planet. Morever, it’s azimuth (-92.314°) is  close to the direction of the temple’s axis.

Jayavarman VII constructed the Ta Prohm temple on a loxodrome running from the summit of Phnom Bakheng to the Sun.

It should be remembered that the centre of this temple was also located on a tangent to the Sighra epicycle of Mercury running through the Krol Ko temple. Moreover, the loxodrome running from the centre of Ta Prohm to Mercury (-91.545°) is perpendicular to the loxodrome running through the observer and the centre of the Sun’s epicycle (-1.571°) and probably parallel to the temple's axis.

The loxodrome from the centre of Ta Prohm to Bat Chum is nearly perpendicular (90.21°) to the loxodrome from the latter temple to East Mebon (orange lines on the following figure).

We discovered that the distance of 221.657 kam is probably related to the period we spoke about in the Pre Rup’s chapter ie the sidereal heliocentric period of revolution of Venus (0.6152 year).

221.657 / 360 = 0.6157
Sidereal period of Venus = 0.6152 year.
Error = 0.18 day

In other words, the difference of latitude (expressed in Khmer arcminutes)  is equal to 360 sidereal  revolutions of Venus (expressed in years). The use of the factor “360” is common in the tables of Aryabhata.

At first sight, this result could be due to chance but we think it is not the case because it is confirmed by the toponymy :

Phu = mountain

Phek = Venus

Moreover, it is worth remembering the distance of 221.657 kam was measured between two particular places:

- The northernmost sacred mountain

- The location "A" on the parallel of the sacred hill which determined the “Prime Meridian” of Angkor.

The Bat Chum temple, built on the parallel of the Bakheng's crest, was consecrated on 953 ie 1 year after the East Mebon which is the main component of the Sun & Venus diagrams.

11th century

The Mountain of Venus

The northernmost Khmer sacred mountain, the Phu Phek mountain, stands in north-east Thailand on a meridian which crosses the East Baray. A small temple was built near the summit, probably during the 11th century. We have measured a distance of 416.968 km (221.657 kam) between the parallel of the Phu Phek summit and the parallel of the Phnom Bakheng crest. It should be noted the “summit” and the “crest” are, in both cases, the intersection of the crest with the meridian of the temple built near the top of the hill

 The central tower of Banteay Kdei was not located exactly on the loxodrome from Bat Chum to Ta Prohm. As a consequence, the near right angle we described   two paragraphs above is lowered from 90.21°  to 89.82° if it is measured from Banteay Kdei instead of  Ta Prohm. It is worth noting  the mean angle is equal to 90.015°.  So, the Banteay Kdei’s centre could have been  located to correct the Ta Prohm's inaccuracy by creating an counteracting error of - 0.18° which provided a precise mean orthogonal loxodrome. This would have been possible because the Banteay Srei temple was obeying less constraints (in the context of the planetary diagrams) and because its centre was situated at only 1151 m from the Bat Chum’s centre.

Jayavarman VII shortened the 10th century baray (Sras Srang) located to the east of Banteay Srei. He also built a nice landing stage on the western embankment of the reservoir. The overall proportions of the resulting Banteay Kdei-Sras Srang complex were determined by « Midnight » parameters related to the Venus diagram.

East-west length including temple and baray = 1666 m

East-west length of fourth enclosure = 717 m (we measured the southern wall)

Distance from south-west corner of fourth enclosure to north-west corner of reservoir = 994 m

Distance from centre of landing stage to fourth enclosure = 154 m

Distance from fourth enclosure to third enclosure = 249 m

The central tower of Banteay Kdei was located approximately halfway between the corresponding structures of Bat Chum and  Ta Prohm. We have determined the precise position of this central tower : it  was built 11 m to the north-west of the precise midpoint (M).

This created a difference of 22 m between the distances measured from the two other temples.

By dividing 22 m by the average of the latter distances, a nearly perfect Venus eccentricity can be calculated.

1151 - 1129 = 22 m

(1151 + 1129) / 2 = 1140 m

22 / 1140 = 0.0193

True Venus eccentricity = 0.0194

These distances were measured on « Google Earth ». We used the median axes of the enclosures (or gopuras)and the outer corners of the embankments.  

East-west length of central platform of landing stage = 14 m

This was measured on the 1/500 EFEO plan.

Jayavarman  VII constructed also the Banteay Kdei temple between Ta Prohm and Bat Chum, to the west of the ancient reservoir called  « Sras Srang. ». The south-north axis (4.4° west of north) of the Banteay Kdei temple was oriented to another monument built by Jayavarman VII : the Krol Ko temple (we have seen the latter is crossed by a loxodrome from Ta Prohm which is tangent to the Sighra epicycle of Mercury).

Last modification : 19 / 01 / 2009

Copyright 2008  Jean-Pierre Lacroix & Robert Bywater  

jpl@ancientcartography.net

rab1@ancientcartography.net

  12th century

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The original photo (without diagram) is in the public domain

(NASA)

Pre Rup : eastern second enclosure

This file is licensed under Creative Commons Attribution 2.0

Full resolution‎ (2,272 × 1,704 pixels, file size: 1.29 MB

EFEO : 1/500 plan

EFEO : 1/500 plan

  Beng Mealea

  Courtesy of Moyra Farrington

Corresponding Java applet :

please click on image

There is possibly a relationship between the number of towers and the “Midnight” eccentricity of Venus.

We noted that the latter can be calculated from the following formula:

Ev = 1 / (e x x 6)

With  Ev = Venus eccentricity

           e =  2.718 = Euler number (basis of natural logarithms)

           3.1416

This formula provides Ev = 0.0195 (Midnight value = 0.0194)

The Khmer arcminute was most probably used to determine the larger dimensions of the Angkor site :

- the western embankment of the West Baray was located 11 kam from the eastern embankment of the East Baray (measured between the midpoints on each dyke).

- there is a  difference of longitude of 15 kam between the median axis of the West Baray's western dyke and the centre of another Sun's epicycle (discussed in detail later) located on the eastern slope of the Chau Srei Vibol hill, one of the more spectacular sites on satellite images, as it is surrounded by a huge moat.

- In the Dangrek Range, the temples of Ta Bai Baek, Ta Muen Thom, Ta Khwai and Preah Vihear  were built on the same loxodrome and  located at selected integers of kam from one another.

Landing stage of Sras Srang (from EFEO plan)