Stars and Atoms and the Urantia Book

by Frederick L. Beckner

Introduction

Stars and Atoms is a book by A. S. Eddington (1882-1944) published in England and in the U.S. in 1927.  This book is based on a lecture of the same title given to the British Association in August 1926. Professor Eddington was a Professor of Astronomy at the University of Cambridge.  It is a popular exposition of the then-current state of knowledge relating to the physics of stars.

Professor Eddington wrote a book on relativity, Mathematical Theory of Relativity (1923), which Albert Einstein called "the finest presentation of the subject in any language."  A biography of Prof. Eddington can be found at

http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Eddington.html

Stars and Atoms (SA) was identified by Matthew Block as a source for material contained in the Urantia Book (UB). The purpose of this paper is to present a comparison of these two writings, to examine topics and material common to both, and to determine if this material is exactly the same, essentially the same, or different. An attempt is also made to determine if the material is factually accurate when compared with present knowledge.

The results of this work leave little doubt that Stars and Atoms was one of the human sources for the scientific material in the Urantia Book. Interestingly enough, there is no trace of verbatim copying of material. The material in Stars and Atoms was read, digested, and rewritten using different language. The identical or similar use of so many concepts, numerical values, and comparisons makes a compelling case that it was source material for the UB.

Reading Stars and Atoms is then like peering over the shoulder of the archangel who prepared the UB material in Paper 41 and used information from SA for his/her own purposes. It affords a unique ability to detect errors in the UB and provides clues as to how these errors may have originated, being either in the transcription process or in the original text.
 
 

Discussion of Common Topics

There are at least twenty-two different topics which are in common between Stars and Atoms and the UB. These topics will be examined one-by-one. In this examination of these two books I focused on parallels involving measurement estimates. Certainly this treatment is not exhaustive.
 

1, and 2. Diameter of the sun and spatial distribution of the stars.  The diameter of the sun and spatial distribution of the stars is given in both the UB and in Stars and Atoms and in the same order.

"These suns have an average diameter of about one million miles, that of your own solar orb being slightly less. --- But there is abundant space to accommodate all of these enormous suns. They have just as much comparative elbow room in space as one dozen oranges would have if they were circulating about throughout the interior of Urantia, and were the planet a hollow globe." (UB458:2)

"The stars are globes comparable in size with the sun, that is to say, of the order of one million miles in diameter. The space for their accommodation is on the most lavish scale. Imagine thirty cricket balls roaming the whole interior of the earth; the stars roaming the heavens are just as little crowded and run as little risk of collision as the cricket balls." (SA9:1)

Both books give a value of the diameter of the sun which agree with one another. A modern value for this diameter is 1.39 x 109 m or 863,700 miles. The diameters given in both books are roughly correct, but the Urantia Book is technically more accurate since it specifically states that the stellar diameter is less than one million miles while Eddington makes a less specific statement.

The modern value of the diameter of the sun can be found at a web site maintained by the Lunar and Planetary Laboratory of the University of Arizona.

http://seds. lpl.arizona.edu/nineplanets/nineplanets/sol.html
Both books follow a discussion of the sun's diameter with an illustration of the spatial density of the stars.  The similarity between these two illustrations is striking, although in the UB Eddington's thirty cricket balls are replaced with a dozen oranges.  This is a definite improvement since only Englishmen are likely to be closely familiar with cricket balls, while many more people know what an orange is.
 
 

3. Number of atoms in a drop of water.  The number of atoms in a drop of water is given in the Urantia Bookas

"...one drop of ordinary water contains over one billion trillions of atoms." (UB463:7)
and as
"A drop of water contains several thousand million million million atoms." (SA9:2)
in Stars and Atoms.

Now a billion trillions of atoms is 109 x 1012=1021 atoms.  A thousand million million million atoms is 103 x 106 x 106 x 106=1021 atoms.  Here the UB is using the American definition of the word billion (109). Thus the information is essentially the same in these two passages.

A gram mole of water which weighs 18.016 grams will contain Avogadro's number of molecules, or 6.022 x 1023 molecules. Twenty five drops of water make one milliliter, so each drop has a volume of 0.04 ml.  Since the density of water is 1 gram per milliliter then each drop will weigh 0.04 gram. The number of molecules in a drop of water is then equal to 0.04 x 6.022 x 1023/18.016=1.337 x 1021.  Since each water molecule contains 3 atoms, 2 hydrogen and one oxygen, the number of atoms in a drop of water will be 4.01 x 1021.  We conclude that the statements in bothbooks are correct.

In this topic, Eddington's treatment seems more precise than that of the UB, since 4 is more closely "several" than merely being "over one."
 
 

4. Thickness of calcium layer. The thickness of the calcium layer in the chromosphere of the sun is given in the following passage in the Urantia Book:

"This explains why there is a calcium layer, a gaseous stone surface, on the sun six thousand miles thick; ..." (UB462:1)
Stars and Atoms states that
"The layer of calcium suspended on the sunlight is at least 5000 miles thick." (SA70:3)
By inspection we see that these two statements contain essentially the same information, although one number is an absolute thickness, and the other is a minimum thickness.

Current science states that the thickness of the calcium layer, or chromosphere, is 2000 km, or about 1,243 miles thick. This information can be found at

ht tp://solar.physics.montana.edu/YPOP/Spotlight/SunInfo/Structure.html.

Another source, http://ousrvr2.oulu.fi/~spaceweb/textbook/sun.html, gives this thickness as 10,000 km or 6,214 miles which is in agreement with the UB value. At this point in time I am unable to conclude whether the UB value is correct or in error.

Another issue to be considered is just what is the chromosphere in relation to the "calcium layer?"  Most determinations of the thickness of the chromosphere are based on measurements of radiation from hydrogen, not calcium.

Also, does this layer include the thickness of the spicules which themselves are about 6,000 miles high?
 
 

5. Use of the word "sunbeam".  Both the Urantia Bookand Stars and Atoms use the word "sunbeam" to describe the solar radiation which supports the calcium in the chromosphere. Compare

"The ordinary atmosphere of the sun terminates rather abruptly, but above it there is a deep though very rarefied layer called the chromosphere consisting of a few selected elements which are able to float --- float, not on the top of the sun's atmosphere, but on the sunbeams." (SA70:2)
in Stars and Atoms with
"This calcium atom moves outward by alternate jerks of forward propulsion, grasping and letting go the sunbeam about twenty-five thousand times each second." (UB462:2)
and also the passage quoted from the UB in the discussion of topic 8, the excitation rate of calcium. The similarity of the use of the non-technical term "sunbeam" in both books lends credence to the hypothesis that Stars and Atoms was used as a human source for some of the discussions in Paper 41 of the Urantia Book.

Technically speaking, the "sunbeam" to which this passage alludes is not visible light, but X-radiation of a wavelength of about 14 nm as shown below in topic 7.
 
 

6. Composition of the chromosphere.  The elements to be found in the sun's chromosphere mentioned in Stars and Atomsare found in the following passages:

"The light and nimble hydrogen atom is fairly good at it [i.e., riding the sunbeam], but the ponderous calcium atom does it best." (SA70:2)

"Therefore somewhere between the star and the telescope there exists a stationary medium which imprints these lines on the light. This time it is not the earth's atmosphere. The lines belong to two elements, calcium and sodium, neither of which occur in the atmosphere." (SA66:1)

In addition to calcium, the Urantia Book mentions the element sodium inthe following passage:
"The sodium atom, under certain modifications, is also capable of light and energy locomotion." (UB462:1)


One can see from these passages that Eddington mentions hydrogen, sodium and calcium as constituents of the sun's chromosphere.  The UB mentions only sodium and calcium.  Eddington does mention sodium and calcium together in one location, while the reference to hydrogen occurs several pages later. The UB information is thus essentially the same as a subset of the information on this topic in Eddington's book.
 
 

7. Duration of excited state of calcium.  Eddington states the duration of the excited state of calcium in the following passages:

"Milne's result is that an electron tossed into the higher orbit remains there for an average time of a hundred-millionth of a second before it spontaneously drops back again. I may add that during this brief time it makes something like a million revolutions in the upper orbit." (SA73:1)

"It is not necessary that the time should be at all closely the same for different elements; but laboratory measurements for hydrogen also give the period as a hundred-millionth of a second, so there is no fault to find with the astronomical determination for calcium." (SA73:2)

Here Eddington gives not only the time in seconds but the duration of the excited state in terms of the number of revolutions of the electron.

The _Urantia_Book also gives these quantities in the passage

"The agility of this acrobatic calcium electron is indicated by the fact that, when tossed by the temperature-Xray solar forces to the circle of the higher orbit, it only remains in that orbit for about one-millionth of a second; but before the electric-gravity power of the atomic nucleus pulls it back into its old orbit, it is able to complete one million revolutions about the atomic center" (UB 462:3)


Notice that while the UB and SA disagree on the duration when given in seconds by a factor of 100, they agree on the number of revolutions of the electron in this time.  Obviously the duration in seconds is in error in one of the two books. Certainly Eddington intended to give the duration as a hundred-millionth of a second since he gives the same number more than once.

It is possible to estimate the time required for the electron to make 106 revolutions in the following crude manner which Pauling and Wilson (Introduction to Quantum Mechanics, 1935) call the "old" quantum mechanics. If the electron is in a circular orbit of radius r, the electrostatic attractive force of the nucleus will just be balanced by centrifugal force. Thus one may write

F=Z e2/r2=m v2/r
where Z is the charge of the nucleus, e is the charge of the electron (4.77 x 10-10 esu), m is the mass of the electron (9.10938188 x 10-28 gram) and v is its velocity in cm/s.

The electron angular momentum will be quantized such that

mvr=n h/(2 pi)
where n is the orbital quantum number and h is Planck's constant (6.62606876 x 10-27 erg-sec). Solving these two equations for v
and r one finds
v=2 pi Z e2/(n h),  and r=n2 h2/(4 pi2 m Z e2)
We are interested in the velocity of the 19th electron, the 20th being removed by ionization. This electron is the 4s1 electron of the
calcium atom.  An accurate value of the ground state energy of this electron in the singly-ionized calcium atom is -.335571 Hartree, or -1.463 x 10-11 erg. This information can be found in the NIST atomic data table at
http://physics.nist.gov/PhysRefData/DFTdata/Tables/20Ca.html
This energy will be equal to the negative of the kinetic energy of the electron, m v2/2. Equating these two and solving for v gives the
velocity of the electron as
v=(2E/m)0.5=1.792 x 108 cm/s
Substituting this velocity into our equation for velocity and solving for Z with n=19 gives Z, the effective atomic number=15.78. Thus the screening constant due to the presence of the inner electrons reduces the effect of the nuclear charge (20) by a factor of 0.789.

Now that the effective value for Z is known, we can calculate the radius of the electron orbit from our equation for r above, giving

r=1.227 x 10-7 cm.
for the radius of the ground state orbit. The energy of the first excited state (n=20) can be estimated as (19/20)2 of the energy of the ground state. This energy is thus 1.320 x 10-11 erg. The velocity of the excited electron can be calculated as before to give 1.708 x 108 cm/s.

Again calculating r using this velocity and n=20 gives

r=1.360 x 10-7 cm.
The number of revolutions made by the electron per second is given by
f=v/(2 pi r)
Substituting for v and r from above we obtain
f=(2 pi)2 Z2 m e4/(n3 h3)
Substituting the values of velocity and orbital radius we obtained above, we find that the rotational rate of the excited electron is
f=1.999 x 1014 rev/s.
The time to make 106 revolutions will thus be
106/1.999 x 1014=0.5 x 10-8 sec
or very near a hundred-millionth (10-8) of a second as Eddington stated.

As a check on our work we can calculate the energy and wavelength of the photon required for photoionization of this excited state of calcium.  The difference of the n=19 and n=20 energies given above is 1.430 x 10-12 erg.  The wavelength of this photon is then 13.9 nm, which is in the X-ray wavelength region, in agreement with the UB.

We must thus conclude that the UB time of one millionth of a second is an error. It is possible that the word "hundred" was inadvertently left out of the manuscript by the typist when it was transcribed from the handwritten version. Otherwise we must assume that this error was made by the author of this paper.
 
 

8. Excitation rate of calcium.  The excitation rate of the calcium ions in the sun's chromosphere is given in the following passage in the UB:

"By tossing this nineteenth electron back and forth between its own orbit and that of its lost companion more than twenty-five thousand times a second, a mutilated stone atom is able partially to defy gravity and thus successfully to ride the emerging streams of light and energy, the sunbeams, to liberty and adventure." (UB462:2)


The excitation rate given by Eddington is in the passage

"After remaining in the excited orbit for a little while the electron comes down again spontaneously.  The process has to be repeated 20,000 times a second in order to keep the atom balanced in the chromosphere." (SA72:1)
There is good agreement between these two statements.  Eddington's number of 20,000 times per second is the minimum excitation rate required to keep the calcium atom at a stationary level in the chromosphere. The higher rate of 25,000 times per second given in the UB is that required for the calcium atom to escape from the chromosphere, and naturally would be higher. These two statements then are mutually self consistent and contain essentially the same information.

The excitation rate, f, required to balance a calcium atom against the sun's gravity can be calculated as follows. In order for the calcium atom to remain stationary in the chromosphere, the distance it falls between absorption of XRay photons must be equal to the distance it rises in the same time due to the transfer of momentum of the photon to the atom.

The downward acceleration, a, of a calcium atom at a distance r from the center of the sun but outside the interior of the sun is given by

a=F/mc=G ms /(rs2)
where F is the force of gravity, ms is the mass of the sun (1.99 x 1033 g), G is the universal gravitational constant (6.673 x 10-8 cm3 gm-1 s-2), mc is the mass of the calcium atom, and rs is the radius of the sun (6.95 x 1010 cm).

The distance the atom falls in the time between photon impacts is given by

fall=a/(2f2)
In order for the calcium atom to be at rest, this downward fall due to gravity must be exactly balanced by the upward rise due to the absorption of the momentum of the Xray photons required for photo-ionization of calcium. The momentum, p, of a photon is given by
p=h/lambda
so the maximum possible upward rise of a calcium atom of mass mc (40 x 1.659 x 10-24 g) in a time 1/f due to absorbing a photon of a wavelength, lambda, travelling radially outward is equal to
rise=p/(mc f)
Equating the rise and fall and solving for f gives
f=G ms lambda mc/(2 rs2 h)
Substituting the values given above and using the wavelength of the Xray photon as 13.9 x 10-7 cm as found in section 7 above, we find that
f=18,450 photons/s.
This number is an underestimate of the actual excitation rate required since the photons will not all be travelling radially outward. Our calculated rate using this crude model is thus in reasonable agreement with both Eddington's value of 20,000 photons per second to balance the calcium atom, and with the UB's value of 25,000 photons per second required to eject the calcium atom from the chromosphere. We thus conclude that both excitation rates given are reasonably accurate.
 
 

9. Mass of the sun.  The mass of the sun is mentioned in both SA and the UB.

"The mass of the sun is - I will write it on the blackboard - 2000000000000000000000000000 [2 x 1027] tons." (SA:2)

" The mass of your sun is slightly greater than the estimate of your physicists, who have reckoned it as about two octillion (2 X 1027) tons." (UB459:5)

These two statements agree exactly numerically, although we don't know precisely which "tons" are being used.  Being a scientist, Eddington is most likely to be using metric tons here.  In the U.S., the word "ton" most commonly denotes 2000 lbs, which is 2000/2.2046 kg=.90719 metric ton.

The currently-accepted mass of the sun is 1.99 x 1033 g. This is the equivalent of 1.99 x 1027 metric tons (1000 kg). Thus we must conclude that if the UB is using units of metric tons, its statement disagrees with the current value which is slightly less than 2 x 1027 metric tons rather than being slightly greater than that value. On the other hand, if the UB value is in U.S. tons, which is more likely, then the sun's mass would be 1.99 x 1027 / .90719=2.19 x 1027 U.S. tons, and the UB statement is correct.
 
 

10. Prominence of iron lines in spectrum of the sun.  Eddington discusses the reason for the occurrence of iron lines in the solar spectrum in

"In the sun the most prominent spectrum is iron. We do not infer that the sun is unusually rich in iron; we infer that it is at a comparatively low temperature near 6000(deg) favorable for the production of iron spectrum." (SA58:1)
The UB discusses the same phenomenon in the passage:
"For example: Solar spectra exhibit many iron lines, but iron is not the chief element in the sun. This phenomenon is almost wholly due to the present temperature of the Sun's surface, a little less than 6,000 degrees, this temperature being very favorable to the registry of the iron spectrum." (UB462:5)
These two passages agree in the statement that it is the low temperature of the sun's surface which makes the iron lines predominate.  Both passages use the word "favorable" to describe the effect of the sun's surface temperature on the production/registry of iron spectra.  Eddington states that this temperature is favorable for the "production" of these spectra, while the UB states that it is favorable for the "registry" of the same.  A question for further study is whether the UB statement is an improvement on Eddington's statement or not.
 
 

11. Two distinct periods of sun formation.  It is very interesting to observe that both Eddington and the UB discuss an earlier formation of stars prior to the most recent one.  Eddington mentions this in this passage about the presence of heavy elements in young stars.

"The presence of sodium and calcium in the cosmical cloud, of helium and nebulium in the diffuse nebulae, of titanium and zirconium in large quantities in the atmospheres of the youngest stars, bears witness that the evolution of the elements is already far advanced during the diffuse prestellar stage - unless indeed our universe is built from the debris of a former creation." (SA105:1)
The UB describes a first period of sun formation in
"50,000,000,000 years ago this first period of sun dispersion was completed; the nebula was fast finishing its tertiary cycle of existence, during which it gave origin to 876,926 sun systems." (UB654:8)
and a second period in
"10,000,000,000 years ago the quartan cycle of Andronover began. ... The nuclear eruptions which were to inaugurate the second nebular sun cycle were imminent." (UB655:1)
Thus the UB does describe the process of stellar formation as occurring in two distinctly different time periods, as suggested by Eddington.  Astronomers talk of Type I and Type II stars, the Type II being older than 10,000,000,000 years and lacking in metals, while the Type I stars, such as the Sun are younger and are rich in metals.
 
 

12. Constancy of internal temperature.  Both the UB and Eddington discuss how the interior temperature of stars is essentially independent of the surface temperature over a wide range of conditions.

"A confusion between internal temperature and surface temperature is responsible for some of the mistakes of the older theories. To outward view the star cools from 12,000(deg) to 3,000(deg) in passing down the series, but there is no such change in its internal heat. The central temperature remains surprisingly steady. (No special reliance can be placed on the slight falling off apparently shown by Krueger 60.)  It is very remarkable that all stars of the main series have a central temperature of about 40 million degrees as nearly as we can calculate."(SA110:1)

"There exists a regulating blanket of hot gases (sometimes millions of degrees in temperature) which envelops the suns, and which acts to stabilize heat loss and otherwise prevent hazardous fluctuations of heat dissipation.  During the active life of a sun the internal temperature of 35,000,000 degrees remains about the same quite regardless of the progressive fall of the external temperature." (UB463:4)

By comparing these two passages we find that both books give essentially the same information concerning the constancy of internal temperature of stars, this temperature being nearly independent of the external temperature. This is in agreement with current knowledge of stellar structure.
 
 

13. Energy in a drop of water.  Both books discuss the energy obtainable from a drop of water.

"... by annihilating a single drop of water we should be supplied with 200 horsepower for a year." (SA102:2)

"You will realize what high temperature means by way of the acceleration of ultimatonic and electronic activities when you pause to consider that one drop of ordinary water contains over one billion trillions of atoms. This is the energy of more than one hundred horsepower exerted continuously for two years." (UB463:5)

As we have seen in the discussion on the number of atoms in a drop of water, a drop of water weighs about 0.04 grams. Using Einstein's equation relating energy and mass we find that this mass is equivalent to an energy of 3.6 x 1019 ergs, or 3.6 x 1012 joules.

A hundred horsepower is equivalent to 74,570 Watts, so one hundred horsepower for two years is an energy of 74,570 x 2 x 365 x 24 x 60 x 60 Watt-seconds, or 4.7 x 1012 joules. So we see that both books contain essentially the same information and that that information is basically correct.
 
 

14. Age of the sun.  Both books also give numerical values for the age of the sun. Eddington states an upper limit:

"The upper limit to the present age of the sun is 5.2 billion [5.2 x 1012] years however great its initial mass." (SA114:1)
As Eddington states in the preface of his book, he uses the term billion in the English usage meaning 1012, rather than 109 as we use the word in the United States. The UB gives the age of the sun in the passage:
"Your sun is now passing out of its six billionth year. At the present time it is functioning through the period of greatest economy. It will shine on as of present efficiency for more than twenty-five billion years." (UB465:5)
Eddington's upper limit on the sun's age is about a thousand times the current estimates. The currently-accepted age of the sun is 4.5 billion, that is, 4.5 x 109, years. One must conclude that the _Urantia_Book_ statement is much more accurate than the information given by Eddington and is near the current estimates. Some current thinking says that the Sun will persist in hydrogen burning for 10 billion years.
 
 

15. Distance to Andromeda.  The distance to the neighboring Andromeda galaxy is given in these two sources. Stars and Atoms gives the distance in the following passage:

"With the naked eye you can see the Andromeda nebula as a faint patch of light. When you look at it you are looking back 900,000 years into the past." (SA93:2)
The UB gives the distance to Andromeda in this passage:
 
"There are not many sun-forming nebulae active in Orvonton at the present time, though Andromeda, which is outside the inhabited superuniverse, is very active. This far-distant nebula is visible to the naked eye, and when you view it, pause to consider that the light you behold left those distant suns almost one million years ago." (UB170:1)
The current estimate of the distance to the Andromeda galaxy is 2 million light years. We must conclude that the information in both sources essentially agree, but that the information in both sources does not agree with the current estimate. This may be a case of intentionally not revealing scientific information not known at the time. It is also possible that unknown effects cause the dimming of light when passing through such long distances, which would make Andromeda seem farther away than it really is.
 
 

16. Rate of mass loss. Another topic discussed in these two books is the rate of loss of mass of the sun. Eddington states

"The sun is losing 120 billion [1.2 x 1014] tons annually ... " (SA111.3)
while the UB states
"Your own solar center radiates almost one hundred billion tons of actual matter annually, ..." (UB465:3)
Now the luminosity of the sun is 3.9 x 1033 ergs/s. Using the Einstein energy/mass equation one finds that an energy of 3.9 x 1033 ergs is equivalent to a mass of 4.33 x 1012 grams.  The sun must thus lose a mass of 4.33 x 1012 grams per second, or 1.366 x 1017 kilograms per year due to the mass converted to the energy of sunlight. This is the same as 1.366 x 1014 metric tons per year.

Stated another way, this is 150.2 x 1012 short tons (1 short ton=2000 lbs) annually. This is an underestimate of the total mass loss since it is based on radiation only.

The sun also loses mass in the form of neutrinos, and other material particles. This is probably the "actual matter" that the UB speaks of.  Another term for this is the solar wind. This solar wind consists of 95% protons, 4% doubly ionized helium, and the rest other heavier elements and electrons. The solar wind at the Earth's orbit contains on the average 8.7 protons/cm3 travelling at a velocity of 468 km/s. The "actual mass" ejected by the sun must certainly be greater than the mass of this solar wind. The mass ejected per second of these protons, mps, can be calculated using

mps=4 pi r2 v rho mp
where r is the radius of the earth's orbit (1.496 x 1013 cm), v is the average proton velocity (4.68 x 107 cm/s), rho is the proton density (8.7 protons/cm3) and mp is the mass of the proton (1.6726 x 10-24 gm).

Using these values one computes that mps=1.92 x 1012 gm/s, or 4.309 x 109 lbs/s. This is the equivalent of 2.15 x 106 US tons/s or 67.9 x 1012 tons per annum. This is probably an overestimate since the density of the solar wind is greatest in the region +/- 20 deg about the plane of the Earth's orbit.

This mass estimate can agree with the UB statement only if the word billion in the UB signifies 1012, the English usage of the word, the same as Eddington, instead of 109, the US usage. So either the UB value of mass loss per annum is wrong, or the UB uses the word "billion" in two different, inconsistent ways (see topic 3 for a useage of "billion" in the US style. Eddington states that he is using the English definition of a billion, that is, a billion is 1012, rather than the American useage where a billion is 109.
 
 

17. Exterior and interior temperature of the sun.  Both books treat the subject of the interior and exterior temperature of the sun. Eddington states that

"This 6000(deg) is only the marginal heat of the great solar furnace giving no idea of the terrific intensity within. Going down into the interior the temperature rises rapidly to above a million degrees, and goes on increasing until at the sun's centre it is about 40,000,000(deg). (SA14:2)

"Temperatures are expressed i n degrees Centigrade." (SA6:1)

The UB gives values for these temperatures in the following passage:
"The surface temperature of your sun is almost 6,000 degrees, but it rapidly increases as the interior is penetrated until it attains the unbelievable height of about 35,000,000 degrees in the central regions.  (All of these temperatures refer to your Fahrenheit scale.)" (UB463:2)
It is very curious that these two sources give the same numerical value for the temperature of the sun's surface, but they use different units; Eddington giving his value in degrees Centigrade, while the UB states that its value is in degrees Fahrenheit.

At http://science.msfc,nasa,gov/ssl.pad.solar/interior.htm one sees that the sun's surface temperature is given as 5,700 C or 10,292 F, and the interior temperature is 15,000,000 C or 27,000,000 degrees F.

Another source gives the interior temperature of the sun as 17,000,000 C, or 30,600,000 F. Thus the data in SA and the UB agree in numerical magnitude, but disagree in the units used. Eddington is correct concerning the surface temperature, while the Urantia book is more nearly correct concerning the internal temperature. The Urantia book is incorrect concerning the surface temperature, while Eddington overstates the internal temperature.

The Urantia book statement would be correct if the statement in parentheses said that only the interior temperature was in degrees Fahrenheit. Was the parenthetical sentence in the original handwritten manuscript, or was it added by human hands later? Why was the figure of 35,000,000 degrees used instead of Eddington's 40,000,000?  Was this an attempt to correct Eddington's overestimate?
 
 

18. Value of light energy.  Both books attempt to estimate the value of a pound of light.

"There is no real reason why you should not buy a pound of light from an electric light company - except that it is a larger quantity than you are likely to need and at current rates would cost you something over (pound sign)100,000,000." (SA98:0)

"As you value energy and power on your world, sunlight would be economical at a million dollars a pound." (UB460:6)


The amount of energy in a pound of light, or anything for that matter, can be computed from Einstein's equation, E=m c2.  A pound is equal to 453.6 grams, so the energy contained in a pound is 4.077 x 1023 ergs, or 4.077 x 1016 Watt-sec.  This is equivalent to 1.13 x 1010 kWh.  At a current price of $0.05 per kWh this energy would be valued at $5.65 x 108, or five hundred and sixty five million dollars. It would indeed be economical at a million dollars per pound. Eddington's estimate appears to be a reasonable one; the UB does not really estimate the value.
 
 

19. Density of the Companion of Sirius.  The two books possibly are discussing the red dwarf companion of Sirius in the following passages:

"Working out the sum more accurately we find that the Companion of Sirius is a globe intermediate in size between the earth and the next larger planet Uranus. ... The actual density works out at 60,000 times that of water - just about a ton to the cubic inch. (SA 50:0)

"One of your near-by suns, which started life with about the same mass as yours, has now contracted almost to the size of Urantia, having become forty thousand times as dense as your sun.  The weight of this hot-cold gaseous-solid is about one ton per cubic inch. And still this sun shines with a faint reddish glow, the senile glimmer of a dying monarch of light." (UB460:1)


The specific gravity of the sun is 1.41, so therefore the UB density is 56,400 times that of water.  This is in good agreement with the value given by Eddington.  It is interesting how Eddington says that it is "intermediate in size between the earth and the next larger planet Uranus", while the UB provides the same information by saying that it "has now contracted almost to the size of Urantia."  Both statements imply that it is just slightly larger than Urantia.

It seems clear that the information in these passages is essentially the same and that both books are correct.
 
 

20. Density of giant suns.  Both books contain a reference to the same density for giant suns.

"Betelgeuse, for example, has a density of about a thousandth that of air." (SA64:1)

"The massive sun of Veluntia, one of the largest in Orvonton, has a density only one one-thousandth that of Urantia's atmosphere." (UB460:3)

Although the UB makes it clear that Veluntia is not the same star as that referred to below which has the same characteristics as Betelgeuse, it makes reference to the same density value. This numerical value is essentially the same between the two books.
 
 

21. Characteristics of Betelgeuse.  Eddington gives the surface temperature, diameter, and mass of Betelgeuse, the yellow star in the arm of Orion.

"Betelgeuse has a surface temperature of 3000 deg." (SA78:1)

"The diameter is about 300 million miles. Betelgeuse is large enough to contain the whole orbit of the earth inside it, perhaps even the orbit of Mars." (SA82:2)

"This gives the mass equal to 35 x sun." (SA82:3)

Compare these with the passage from the UB
"Another of the Orvonton giants now has a surface temperature a trifle under three thousand degrees.  Its diameter is over three hundred million miles--ample room to accommodate your sun and the present orbit of the earth. And yet, for all this enormous size, over forty million times that of your sun, its mass is only about thirty times greater."(UB460:4)
The agreement concerning surface temperature is not truly clear, since Eddington is using units of degrees Centigrade, while the UB doesn't specify the units of temperature being used here.

The two passages agree exactly concerning diameter and make use of the same explanatory comparison. The masses given are not exactly the same but are reasonably close. This then is a question for further study.  Is the density estimate given by the UB more in agreement with current knowledge than Eddington's estimate?
 
 

22. Cosmic background temperature.  An interesting side observation made during this work is that Eddington makes an astonishing prediction of the temperature of the cosmic background in 1927!  He gives this temperature in the following passage:

"We generally think of interstellar space as excessively cold. It is quite true that any thermometer placed there would show a temperature only about 3(deg) above absolute zero." (SA69:2)
The discovery of the 2.7 degree above absolute zero background temperature was made more than 30 years later by Penzias and Wilson, and earned them the Nobel prize.  Eddington had a value within 10% of the measured value decades previously.  He does not say how he arrived at this value however.

The UB also treats the question of the cosmic background temperature in the following passage:

" Gravity presence and action is what prevents the appearance of the theoretical absolute zero, for interstellar space does not have the temperature of absolute zero." (UB473:4)
Is it radiation or gravitation which causes the non-zero background temperature?  Modern science measures this temperature by observations of the spectrum of the background microwave radiation.

Both these passages give information that is essentially accurate in light of present knowledge.
 
 

Conclusions

The comparison of the passages from these 22 topics leave little doubt that Stars and Atoms was a source for material in the Urantia Book, or was at least known to the writer of this material.

This comparison also reveals three certain and two possible errors in the Urantia Book.  The first certain error relates to the time the excited electron in the calcium atom spends before returning to its ground state. Eddington gives this time as " a hundred-millionth of a second," while the Urantia Book gives it as ".. it only remains in that orbit for about one-millionth of a second."  If the Urantia Book had said "a hundred" instead of "one" it would have agreed with Eddington.  It is clear from the independent calculation given above that the value in the Urantia Book is in error. I am not aware of this error having been previously noticed.

The second certain error is in the surface temperature of the sun.  The Urantia Book specifically says that this temperature is 6000 degrees Fahrenheit, while the correct value is near 6000 degrees Centigrade.  This error might have been introduced in editing the book since it involves a parenthetical statement. This error has been known for some time, as it has been mentioned in previous writings of this type.

The third certain error is in the statement of the annual loss of mass by the sun.  Either the UB is inconsistently using the word "billion" to mean different values in different parts of the book, or its value of the annual loss of mass of "actual matter" by the sun is apparently in error.

The first possible error relates to the age of the sun. The UB gives this as 6 billion years, while current estimates of this age are around 4.5 billion years. It is hard to see how this numerical difference could have been a typographical error. The UB statement directly contradicts the information in SA, so it obviously was not the source for the UB value.

In 1927, when SA was written it was thought that the stars were trillions of years old. If the UB value was written in that time frame then it either corrects an error of the then-contemporary science, or it is merely repeating the erroneous value given by Eddington, depending on whether the word "billion" is used in the American or English sense.  I am not sure at this time when the value of billions of years was correctly found by human science.  This is an interesting question for further research.

The second possible error is in the distance to the Andromeda galaxy.  Current estimates give this distance to be about 2,000,000 light years.  This is twice the value given in the Urantia Book and SA.

Given the fact that these errors exist in the science content of the Urantia Book, what then are we to make of them?  Do these errors invalidate the superhuman origin of the revelation?  The skeptic would say that it does, I, however, say that this is insufficient reason to dismiss superhuman origin.

My reasons for believing this are as follows. Superhuman is not synonymous with infallibility.  The first two certain errors could easily have been human errors in transcription from the handwritten text. The third certain error reflects a confusion between the terms "billion" as used by different English-speaking countries.  This could have been a translation error by the original author.  The first possible error may not be an error since it is based on a mathematical model and not actual measurements.  The second possible error may be due to the limitations placed on the revelators, as the value given in the UB was the best value known to human science at the time Paper 41 was written.

Clearly, the possibility of errors in the scientific content is admitted by the revelators.

"We full well know that, while the historic facts and religious truths of this series of revelatory presentations will stand on the records of the ages to come, within a few short years many of our statements regarding the physical sciences will stand in need of revision in consequence of additional scientific developments and new discoveries.

These new developments we even now foresee, but we are forbidden to include such humanly undiscovered facts in the revelatory records.  Let it be made clear that revelations are not necessarily inspired.  The cosmology of these revelations is not inspired.  It is limited by our permission for the co-ordination and sorting of present-day knowledge.

While divine or spiritual insight is a gift, human wisdom must evolve." (UB1109:3)

Weighing these few errors against the weight of the spiritual content of the Urantia Book and the spiritual fruits discernable in its readers, one must conclude that this is insufficient evidence to dismiss the possibility of a superhuman origin of this revelation. On the other hand, readers of the UB should not rely on a presumed inerrancy in scientific content as proof of its superhuman origin.

Acknowledgement

The author gratefully acknowledges the assistance of Matthew Block in proof reading drafts of this paper and in providing valuable suggestions for improving its accuracy and clarity.