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Sun

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Sun
Sun fromsoho big.jpg
The sun with enormous, intensely bright, active regions recorded by the SOHO Spacecraft Extreme Ultraviolet Imaging Telescope.
Symbol
Known to the ancients
Orbital characteristics
Celestial class Star
Primary Galaxy
Perigalacticon 27,600 ly2.611162e+17 km
1,745,453,735.693 AU
1.622501e+17 mi
[1]
Apogalacticon 31,800 ly3.008512e+17 km
2,011,066,260.69 AU
1.869403e+17 mi
[2]
Semi-major axis 29,700 ly2.809837e+17 km
1,878,259,998.191 AU
1.745952e+17 mi
[3]
Orbital eccentricity 0.07[2]
Sidereal year 250,000,000 a91,312,500,000 da
Avg. orbital speed 217 km/s781,200 km/h
134.838 mi/s
485,415.175 mph
Inclination 25°0.436 rad
27.778 grad
to the galactic plane
Rotational characteristics
Sidereal day 609.12 h25.38 da[4]
Solar day 27.2753 da654.607 h[5][6]
Physical characteristics
Mass 1.9891 * 1030 kg1 M☉
1,047.612 M♃
[4][5]
Mean density 1408 kg/m³1.408 g/ml
87.899 lb/ft³
[4]
Mean radius 696,000 km432,474.35 mi[4]
Equatorial radius 695,500 km432,163.664 mi[5]
Surface gravity 274.0 m/s²898.95 ft/s²
27.94 g
[4][5]
Escape speed 617.7 km/s2,223,720 km/h
383.821 mi/s
1,381,755.548 mph
[4][5]
Surface area 6,087,799,000,000 km²2,350,512,334,672.544 mi²
1 A☉
97.907 A♃
[5]
Minimum temperature 4000 K3,726.85 °C
6,740.33 °F
7,200 °R
[4][7]
Mean temperature 5777 K5,503.85 °C
9,938.93 °F
10,398.6 °R
[5]
Maximum temperature 8000 K7,726.85 °C
13,940.33 °F
14,400 °R
[7]
Composition [[Composition::92.1% hydrogen, 7.8% helium]][5]
Color #FF9933
Magnetosphere
Magnetic dipole moment at present 3.5 * 1029 N-m/T[8][9]
Magnetic dipole moment at creation 4.65 * 1029 N-m/T[8]
Decay time 19000 a6,939,750 da[8]
Half life 13170 a4,810,342.5 da[3]

The sun is the astronomical object from which we receive sunlight (heat and light also known as solar radiation). All of the planetary objects within our solar system revolve around the sun. It is classified as a G2 V star whose name comes either from the Greek, helios or from the Latin word sol).[7]

Contents

Nomenclature

The G2 class is the the second level of hottest stars within the yellow G class. A "V" star in this class is a yellow dwarf star--but the Sun is in fact in the 95th percentile in its class by size and mass of other stars in its immediate region.[7]

History

Biblical

The Bible says:
God made two great lights—the greater light to govern the day and the lesser light to govern the night. He also made the stars. Genesis 1:16

This took place during the fourth day of Creation Week. More to the point, the Sun is a part of God's creation, not a "god" in its own right.

Mythological

In contrast, virtually every other civilization has regarded the Sun as one of many gods. The Egyptians called the Sun Ra or Re, a deity whom, they said, created the world.[10] The Egyptians also called the sun-disk Aten, and for a brief period (during the reign of Pharaoh Amenhotep IV or Akhenaten), actually worshipped Aten as the one and only god of the universe.[11] In Babylonia and Assyria the sun was called Shamash, a god who, because he could see everything happening on earth, was also associated with truth and justice.[12] The Greeks at first regarded Helios as a son of heaven and earth but later came to associate the Sun with their god of truth, Apollo.

The most common theme in all the sun-worship cults is the association of the sun with truth and justice personified. The second most common theme is the regarding of the sun as the creator.

Orbital characteristics and galactic relationships

The Sun orbits the galactic center at a distance less than half the total estimated radius of the galaxy, and in an orbit inclined about 25° from the galactic plane. The eccentricity of the Sun's orbit is 0.07, about average in comparison to the eccentricities of the planets and dwarf planets of the solar system. At present the Sun lies 50 light years north of the galactic plane and is continuing to climb north of it as it approaches perigalacticon.[13]

Properties and Characteristics

The sun accounts for 99.8% of our solar system's total mass. With a mass of 2 x 1030 kg, an atmospheric temperature of about 5800 K, and a luminosity of 4x1020 megawatts, the sun is by far the most extraordinary object during the day-time sky and of our solar system. However within our Milky Way galaxy it is one of probably 100 billion of the same types of stars.

The tremendous light and heat that the sun releases (solar radiation), and the delicate position that the Earth occupies in relation to the sun, combine to make the sun an integral part of sustaining life.

Core temperatures reach 15,000,000 K (K = Kelvin) while the sun's surface or photosphere temperature is 5,800 K. When the photosphere is hit by the heat of the sun the temperature drops to a minimum of 4,000 K. It then continues further until it encounters a thin layer of atmosphere roughly 10,000 kilometers deep called the chromosphere and reverses trend to rise to 8,000 K. Even further is another part of the sun's total atmosphere called the corona that blends in with interplanetary space.

Energy production and transport

The standard model of the solar system asserts that the Sun produces its energy through nuclear fusion.[14] The sun uses a type of nuclear fusion called the proton-proton chain reaction. This is when a nucleus with one proton (hydrogen) is fused with another proton, creating a two particle nucleus. Then it fuses to become a three particle, then finally a four particle. The final four particle nucleus contains two neutrons and two protons, which is the element called helium. There are also energy and many other products that are released. The favored model for energy production relies on tremendous pressures resulting from the sun's own mass to overcome the natural electrostatic repulsive forces that normally keep hydrogen atoms from coming together and fusing.[7]

The model for hydrogen fusion includes these three equations:

{}^0_{-1}\!e + {}^1_1\!\mbox{H} + {}^1_1\!\mbox{H} \to {}^2_1\!\mbox{H} + {}^0_0\!\nu + \mbox{1.44 MeV}

{}^2_1\!\mbox{H} + {}^1_1\!\mbox{H} \to {}^3_2\!\mbox{He} + \gamma + \mbox{5.49 MeV}

{}^3_2\!\mbox{He} + {}^3_2\!\mbox{He} \to {}^4_2\!\mbox{He}+ {}^1_1\!\mbox{H}+ {}^1_1\!\mbox{H} + \mbox{12.85 MeV}

Here, e represents an electron, H means hydrogen, He means helium, γ represents a gamma photon, ν represents a small, uncharged particle called a neutrino that is not supposed to have any proper mass, and the energy unit eV, or electron volt, is the product of the charge on a single electron and the standard unit of electromotive force or electromotive potential.

The energy produced varies as the fourth power of the temperature--and at the temperatures thought to prevail in the sun's core, matter exists, not as ordinary matter with atomic nuclei and electrons, but as plasma--a form of super-hot matter in which atoms are totally denuded of their electrons.

The first equation above is assumed to be the rate-limiting step. The neutrinos produced should have an energy of 0.26 MeV--too little energy to be detectable by current technology. But processes occurring after this step ought to produce higher-energy neutrinos that would be detectable. Such neutrinos have been detected, but at a flux much smaller than predicted. This indicates that the presumed rates for these subsequent processes are higher than the true rates, or else the neutrinos produced somehow transform to a different type of neutrino that would be unobservable. That in turn would imply that neutrinos do have rest mass.[7]

According to current models, some of this energy is transferred to the surface by convection in the outer 20-30% of the body of the sun.[14] Helium in this convective zone rises to or near the surface, releases its heat, and then sinks back to the center. Helium absorbs radiation more readily than does hydrogen, and for that reason the sun is always getting marginally brighter with the passage of time.[7]

The remaining energy is transferred in the gamma photons, which must take a "random walk" to reach the corona of the Sun. Current models suggest that the sunlight generated by these processes takes 50 million years to reach the surface.[14]

Problems with the Standard Model

The standard model asserts that the power plant inside the Sun is a particular form of chain-reaction nuclear fusion. This has never been directly measured nor proven. The multi-stage sequence of reactions to achieve this fusion have never been successfully repeated in a loop (e.g. a fusion reactor). This is because each stage fully consumes the available fuel as it proceeds to the next stage. There is not even a theoretical model through which such a sustained/repeating chain-reaction can be achieved. Experiments with tokamak-style and the JET (Joint European Torus)[15] showed fusion is possible through alternative methods, but never translated to the type of fusion purported in the Sun.

The standard model asserts that the Sun transports heat using convection. If this is true, it is only body in human existence that does so.

The standard model asserts that the Sun's magnetic field is a result of its rotation. The Sun however, if proportionally reduced to the size of a beach-ball, would be off-tolerance from being a perfect sphere by less than the width of a human hair[16]. The only thing in human existence "more" spherical than the Sun are artificially-manufactured plastic ball-bearings. If the Sun rotates, it should show flattening at the equator, yet it does not.

Coronal heating is an unexplained anomaly. The standard model requires that the area nearest the surface should be the hottest visible part of the Sun. However, Sun's surface is around 6000 degrees Kelvin and the photosphere is around 4000 degree Kelvin. As we rise 200km above this, the temperature rapidly rises to over 1 million degrees Kelvin, and up to 20 million degrees Kelvin as far as one Solar diameter away from the Sun[17]. The only explanation offered for this extreme difference is an effect called "magnetic reconnection" which has never been proven[18]. In fact, no observation of magnetic fields of any kind have shown a propensity to break or reconnect, as this is not the nature of a magnetic field.

An important observation: The standard model purports that the Sun's core is 15 million degrees Kelvin, yet over 1 Solar diameter away from the surface, the temperature is over 20 million degrees Kelvin. The hottest part of the Sun is not even a part of the Sun's mass. The standard model has never sufficiently explained this.

Sunspots

The earliest observations of sunspots might have been made in the fourth century BC by the Greeks. Chinese astronomical records dating back to 28 BC include descriptions of changing dark patches on the sun that might have been sunspots.[19]

Galileo Galilei in 1613 was the first astronomer to study sunspots in any detail. It was a revolutionary observation, and one that clashed greatly with Western man's ideas of the heavens, propounded chiefly by Aristotle, as a perfect, unblemished place.[19][20]

An amateur astronomer, Heinrich Schwabe, was the first to note the sunspot cycle in 1843.[21] The sunspots are dark on account of their cooler temperature. This in turn is due to strong magenetic fields which allow the transport of heat via convective motion in the sun. At times these sunspots can be 50,000 miles in diameter and appear in two bands, one being north and the other south in the direction of the sun's equator.

Observations have also shown that the number and location of sunspots come and go in a semi-periodic 9.5 to 11-year solar cycles. At the start of this cycle they are about 30 degrees from the equator. Midway through, the cycle of the number of sunspots observed is maximum, usually about 15 degrees from the equator. Near the end of this on average 10.8-year cycle, the sunspots are very near the equator.[22][23]

Star Spots

The sunspot effect is visible on other stars such as Betelgeuse[24]. However, some star-spots are massive, covering 10,000 times the area of a common sunspot and a very large proportion of the star itself[25], with no explanation in the standard model.

The solar magnetosphere

The magnetosphere oscillates in synchrony with the sunspots in a twenty-two-year cycle. The current amplitude of that cycle is 3.5 * 1029 N-m-T. This amplitude has been decaying since creation, but relatively slowly, with a half-life of 13,170 Julian years. In fact, according to Humphreys[8], the sun's magnetic field has lost perhaps 25 percent of its strength since creation.

Measurements of the sun's magnetic dipole moment have not been exact enough to demonstrate whether the amplitude of the field's oscillations is constant or decaying. If those oscillations are in fact decaying, then the Sun cannot be a dynamo.[8]

Problems for uniformitarian theories posed by the Sun

Uniformitarians commonly estimate that the Sun is about 4.5 billion years old, has consumed about half its nuclear fuel (hydrogen), and will begin to die within about 5 billion years.[26]

But they also must admit that the sun continues to brighten as it continues to fuse hydrogen into helium. In fact, by uniformitarian estimates, the sun ought to be 40% brighter today than it was when the planets formed and 33% brighter than it was when life purportedly first formed (3.8 billion years ago by evolutionary assumptions). This is called the Faint Young Sun anomaly. In short, the Earth would have been covered with ice at the time life supposedly formed. If the Earth was in fact hot enough at that time, then the Earth ought to be much hotter today than it once was. The evolutionary timeframe applied to the fossil record is incongruous with these conditions.[7][27] Uniformitarians answer that the Earth's atmosphere might be compensating for this increased brightness. (But these are often the same scientists who insist that industrial and transport-related introduction of carbon dioxide into Earth's atmosphere threatens to overheat the Earth, with potentially disastrous results.)

Uniformitarians have also had to admit that the sun rotates about 200 times more slowly than the nebula hypothesis would predict, simply on account of the contraction of the solar mass into its present volume. This violates of the Law of Conservation of Angular Momentum. This "angular momentum" problem has been apparent for hundreds of years and remains unresolved to this day.[27]. In fact (see Anomalies section above) the Sun is near-perfectly spherical, suggesting that it does not rotate at all (otherwise the equator would bulge and the poles would be flattened).

The sun's equatorial plane is inclined 7.25° to the ecliptic. (See Earth.) By the nebula hypothesis, that inclination should be zero. The errant inclination poses an especially acute problem for the orbit of Neptune. Uniformitarians have speculated that a collision with an even larger object knocked the sun off a true perpendicular to its present inclination--but no scientist has offered a convincing speculation as to what that object might be.[27]

Conventional astronomers, Carl Sagan among them, insist that our star is mediocre and unremarkable. Yet the G-type of star is relatively rare, and furthermore its mass and position in the galaxy lie within very narrow tolerances for the support of life. The sun is also a singular star, not part of a binary--also a rare finding--and is remarkably stable in its energy output. These facts combine to make the sun an unusually hospitable star for a planet to have life on it.[27]

Finally, the only reason that uniformitarians can cite for a great age of the Sun is the apparent great age of the Earth.[7]. At least one astronomer has frankly admitted that the Sun itself gives no clue to any such tremendous age, and that the acceptance of a very young age of the Sun, like the six-thousand-plus years calculated by James Ussher, might logically follow from a modicum of new evidence:[27][28]

There is no evidence based solely on solar observations, Eddy stated, that the sun is 4.5-5 x 109 years old. "I suspect," he said, "that the Sun is 4.5-5 billion years old. However, given some new and unexpected results to the contrary, and some time for frantic recalculation and theoretical readjustment, I suspect that we could live with Bishop Ussher's value for the age of the earth and sun. I don't think we have much in the way of observational evidence in astronomy to conflict with that."

Gallery

Satellites

The satellites of the Sun include all the planets and dwarf planets, and most of the asteroids.

This table lists all planets and dwarf planets. To sort by any listed property, use the sortation device in the column header.
Perihelion Aphelion Eccentricity Sidereal year Inclination Mass Sidereal day
Earth 1470900000000.983 AU147,090,000 km
91,397,488.666 mi
1521000000001.017 AU152,100,000 km
94,510,558.339 mi
0.016710220.0167 365.2563661 a365.256 da 8.72664625997E-75.0e-5 °8.726646e-7 rad
5.555556e-5 grad
5.9736E+241 M⊕5.9736e+24 kg
0.00315 M♃
86164.223.935 h0.997 da
Jupiter 7405200000004.95 AU740,520,000 km
460,137,795.276 mi
8166200000005.459 AU816,620,000 km
507,424,143.005 mi
0.048390.0484 4330.58662511.857 a4,330.587 da 0.02277654673851.305 °0.0228 rad
1.45 grad
1.8987E+27317.721 M⊕1.8987e+27 kg
1 M♃
357309.925 h0.414 da
Mars 2066200000001.381 AU206,620,000 km
128,387,715.74 mi
2492300000001.666 AU249,230,000 km
154,864,342.241 mi
0.09350.0935 686.981.881 a686.98 da 0.03228859116191.85 °0.0323 rad
2.056 grad
6.4185E+230.107 M⊕6.4185e+23 kg
3.380471e-4 M♃
88642.4424.623 h1.026 da
Mercury (planet) 460000000000.307 AU46,000,000 km
28,583,074.843 mi
698200000000.467 AU69,820,000 km
43,384,136.642 mi
0.20560.206 87.9690.241 a87.969 da 0.122173047647 °0.122 rad
7.778 grad
3.302E+230.0553 M⊕3.302e+23 kg
1.739085e-4 M♃
50673601,407.6 h58.65 da
Neptune 4.44445E+1229.709 AU4,444,450,000 km
2,761,653,195.339 mi
4.54567E+1230.386 AU4,545,670,000 km
2,824,548,387.417 mi
0.01130.0113 60189.5475164.79 a60,189.548 da 0.03087487446781.769 °0.0309 rad
1.966 grad
1.0243E+2617.14 M⊕1.0243e+26 kg
0.0539 M♃
5799616.11 h0.671 da
Saturn 1.35255E+129.041 AU1,352,550,000 km
840,435,606.061 mi
1.5145E+1210.124 AU1,514,500,000 km
941,066,670.643 mi
0.05650.0565 10759.2229.457 a10,759.22 da 0.04337143191212.485 °0.0434 rad
2.761 grad
5.6846E+2695.124 M⊕5.6846e+26 kg
0.299 M♃
38361.610.656 h0.444 da
Uranus 2.7413E+1218.324 AU2,741,300,000 km
1,703,364,849.28 mi
3.00362E+1220.078 AU3,003,620,000 km
1,866,362,940.428 mi
0.04570.0457 30681.615300284.002 a30,681.615 da 0.01298524963480.744 °0.013 rad
0.827 grad
8.6832E+2514.53 M⊕8.6832e+25 kg
0.0457 M♃
-62064-17.24 h-0.718 da
Venus 1074800000000.718 AU107,480,000 km
66,784,975.742 mi
1089400000000.728 AU108,940,000 km
67,692,177.682 mi
0.00670.0067 224.7010.615 a224.701 da 0.05916666164263.39 °0.0592 rad
3.767 grad
4.8685E+240.815 M⊕4.8685e+24 kg
0.00256 M♃
-20997000-5,832.5 h-243.021 da
Ceres 3809820115292.547 AU380,982,011.529 km
236,731,246.725 mi
4468273011322.987 AU446,827,301.132 km
277,645,612.829 mi
0.079541620.0795 1680.9731634.602 a1,680.973 da 0.18476760574610.586 °0.185 rad
11.763 grad
9.47E+201.584675e-4 M⊕9.47e+20 kg
0.0129 M☾
326709.075 h0.378 da
Eris 5.6742472091E+1237.93 AU5,674,247,209.1 km
3,525,813,753.368 mi
1.45902802611E+1397.53 AU14,590,280,261.1 km
9,065,979,840.917 mi
0.440.44 203590.35557.4 a203,590.35 da 0.77072867103444.159 °0.771 rad
49.066 grad
1.66E+220.00278 M⊕1.66e+22 kg
0.226 M☾
288008 h0.333 da
Pluto 4.436824613E+1229.658 AU4,436,824,613 km
2,756,914,999.528 mi
7.375927931E+1249.305 AU7,375,927,931 km
4,583,189,132.342 mi
0.248807660.249 90614.8725248.09 a90,614.873 da 0.29917997705417.142 °0.299 rad
19.046 grad
1.305E+220.00218 M⊕1.305e+22 kg
0.178 M☾
-551856.672-153.294 h-6.387 da
Use a JavaScript-enabled browser to view this element. Browse the result list directly.DECADECENTURYNeptune1846-09-23T00:00:000Date of discovery 23 September 184623 September 1846
3 Tishrei 5607 He
2 Ethanim 5850 AM

Discoverer Heinrich L. d'Arrest, Urbain Le Verrier, John Couch Adams, Johann Gotfried Galle
Name origin Roman god of the sea
Celestial class Gas giant, Solar system, Planet
Uranus1781-03-13T00:00:000Date of discovery 13 March 178113 March 1781
16 Adar 5541 He
47 Adar 5784 AM

Discoverer William Herschel
Name origin Roman (and Greek) name for heaven and father of Saturn.
Celestial class Gas giant, Solar system, Planet
Ceres1801-01-01T00:00:000Date of discovery 1 January 18011 January 1801
16 Teveth 5561 He
15 Teveth 5804 AM

Discoverer Giuseppe Piazzi
Name origin Roman goddess of agriculture
Celestial class Solar system, Dwarf planet
Eris2003-10-21T00:00:000Date of discovery 21 October 200321 October 2003
25 Tishrei 5764 He
25 Ethanim 6007 AM

Discoverer David Rabinowitz, Chad Trujillo, Michael Brown
Name origin Greek goddess of discord
Celestial class Solar system, Dwarf planet
Pluto1930-01-01T00:00:000Date of discovery 19301930
5690 He
5933 AM

Discoverer Clyde W. Tombaugh
Name origin Greco-Roman god of wealth and the underworld
Celestial class Solar system, Dwarf planet
2003-10-21T00:00:00

References

  1. Trapp, Andrew. "Timescales in Open, Flat, and Very Large Closed Universes." From Now Until the End of Time... Accessed January 17, 2008.
  2. 2.0 2.1 Author unknown. "Entry for 'Apogalacticon'." <http://everything2.com/> July 22, 2001. Accessed January 17, 2008.
  3. 3.0 3.1 Calculated
  4. 4.0 4.1 4.2 4.3 4.4 4.5 4.6 Williams, David R. "Sun Fact Sheet." Goddard Space Flight Center (NASA), September 1, 2004. Accessed January 17, 2008.
  5. 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 Harvey, Samantha. "Sun Facts and Figures." NASA, April 26, 2007. Accessed January 17, 2008.
  6. This day is actually a synodic day and is the period for the same point on the Sun's equator to appear again directly facing the Earth.
  7. 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 "Entry for 'Sun'." Encyclopædia Britannica, 2008. Encyclopædia Britannica Online. Accessed March 5, 2008.
  8. 8.0 8.1 8.2 8.3 8.4 Humphreys, D. R. "The Creation of Planetary Magnetic Fields." Creation Research Society Quarterly 21(3), December 1984. Accessed April 29, 2008.
  9. Estimated
  10. Dunn, Jimmy. "Re (Ra) and Re-Horakhty." <http://www.touregypt.net/>. Accessed March 5, 2008.
  11. Dunn, Jimmy. "The Egyptian God Aten Before and After Akhenaten." <http://www.touregypt.net/>. Accessed March 5, 2008.
  12. MacKenzie, Donald A. "Chapter XI: The Golden Age of Babylonia." Myths of Babylonia and Assyria, IndyPublish.com (ISBN 1421962977), December 30, 2005, pp. 240-259. Accessed March 5, 2008, at <http://www.sacred-texts.com/>
  13. LeDrew, Glenn. "Our Galactic Home." AstroNotes, 1997. Accessed January 17, 2008.
  14. 14.0 14.1 14.2 "Sunspots: Modern Research, Page 2." The Exploratorium, 1998. Accessed March 5, 2008.
  15. http://en.wikipedia.org/wiki/Joint_European_Torus
  16. http://www.scientificamerican.com/gallery/well-rounded-sun-stays-nearly-spherical-even-when-it-freaks-out/
  17. http://en.wikipedia.org/wiki/Corona
  18. http://en.wikipedia.org/wiki/Sun
  19. 19.0 19.1 "Sunspots: History." The Exploratorium, 1998. Accessed March 5, 2008.
  20. Paul describes a region called the "third heaven" as the actual "heaven" where God has His throne. See II_Corinthians 12:2 . But the Bible was not yet readily available to laymen in Galileo's day, and Western man might naturally confuse God's heaven with the lesser "heaven" that we call "outer space" today.
  21. "The Sunspot Cycle." The Exploratorium, 1998. Accessed March 5, 2008.
  22. "The Sun." Curious about Astronomy? Ask an Astronomer, Cornell University, October 18, 2007. Accessed March 5, 2008.
  23. "Factors Affecting Global Temperature." Ponder the Maunder. Accessed March 5, 2008.
  24. http://www.scientificamerican.com/gallery/star-spots-on-betelgeuse/
  25. http://www.noao.edu/noao/noaonews/dec99/node2.html
  26. "Entry for the Sun." Gateway to the Future, <http://library.thinkquest.org/>. Accessed March 5, 2008.
  27. 27.0 27.1 27.2 27.3 27.4 Psarris, Spike. Our Created Universe. Seattle Creation Conference, 2007. Video presentation, 55 minutes.
  28. Eddy, John. Remarks at a seminar reported in Geotimes, 23:18, September, 1978. Quoted in Pierce, Larry, "The Forgotten Archbishop", in James Ussher, The Annals of the World, Larry Pierce, ed., Green Forest, AR: Master Books, 2003 (ISBN 0890513600), pp. 891-2.
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