THE MATHEMATICAL AND PHYSICAL RELATIONSHIPS OF THE ROTATIONS (SPINS)

OF THE PLANETS URANUS TO EARTH, JUPITER TO SATURN, AND NEPTUNE TO VENUS AND MERCURY.

T. Frank Lee, geologist; February to April, 2007.

102 Mill Street, Ballarat, 3350, Victoria, Australia. Tel: 61-3-53316938

Introduction. The Nebular Theory of origin of the Solar System has recently been anointed as the true explanation of the origin. But it fails repeatedly to explain many physical and chemical relationships and variations of the planets and satellites. Not being happy with the “Theory” the writer in about 1992 began a study of the origin and development of the Solar System by using the method of stratigraphic superposition geology (essentially inductive, not deductive). The sequence obtained he has named “The Single Body Breakup Hypothesis of Origin of the Solar System”, an hypothesis that he has used to study and explain over forty Solar System bodies’ relationships, many unrecognised as existing by astronomers. A number of these relationships are given in the writer’s (now transferred) website page¹ The hypothesis suggests that the rotations (spins) of body pairs should be related. The relationship between Uranus and Earth was soon solved, but it has taken until now to show the relationships between Jupiter and Saturn, and between Venus, Mercury and Neptune. This paper gives these last three relationships.

Brief Description of the Hypothesis. It is necessary to know the basics of the Single Body Breakup Hypothesis in order to follow the mathematical developments that follow. It is argued that a single body of “brown body” size, containing the volumes and masses of all the present planets and satellites, orbited the Sun. It gradually developed an increasingly prolate ellipsoidal shape until it reached the Jacobi first bifurcation point and so split into a poorly stratified protoJupiter – behaving like a great centrifuge - and a relatively uniform-structured Saturn. ProtoJupiter was required to adjust internally because the total force of the system after breakup was not quite equal to the force before breakup. This was done by a discontinuous series of strings of bodies forming at the body centre and being ejected in a series of pulses along the body’s a-axis. It can easily be shown that the “brown” body had a moment of inertia factor of about a = 0.353 and the original protoJupiter had an a of 0.4. These values are critical.

The final and largest string was of Earth, Venus, Mercury, Centre of protoJupiter, Neptune, Uranus. The string underwent two impulsive forces (ejections) resulting in Uranus and Earth first being ejected (in opposite directions) then the other three bodies soon after. A diagram of this final planet-forming stage can be found in the above referred to web site¹ and also be seen in the letters column of “The Australian Geologist” magazine², pp.10-11, which briefly refers to the spin relationship between Uranus and Earth. This relationship will be given first as it is both the simplest and the first solved of the spin relationships. The several pages of calculations and support referred to in the 1996 letter were later simplified to give a near page solution. This was entered in the web site¹ relatively recently under the heading “Two Further Comments” The comment is given here in full.

1. Calculating the Rotation of Uranus Using the Rotations of Earth and protoJupiter. If the planets Earth and Uranus formed within protoJupiter as the cold body breakup hypothesis suggests, and before ejection had commenced they were rotating inside protoJupiter at the same speed as protoJupiter, then the resultant couple acting on each of the two bodies was: L = (Iw_pJ –Iw_o)/T, where: L = average retarding couple; I = moment of inertia of the planet; w_pJ = angular velocity of protoJupiter (= angular velocity of Jupiter x moment of inertia factor of Jupiter divided by 0.4); w_o = angular velocity of the planet as it finally leaves protoJupiter (= present rotation x present moment of inertia factor divided by 0.4); T = time of the planet to move through protoJupiter to separate completely from it.

Taking into account the decrease in radius of protoJupiter as the satellites, Mercury, Venus, Earth, Uranus, and Neptune left its surface (in that order), and using the diagrams and dimensions given in Paper A (or TAG Advert.1), then it can be shown that T_E = 3350 sec., approx. and T_U = 3833 sec., approx. [and noting that the present rotation of Jupiter = 1.7733482x10^-4, and of Earth = 0.7292226x10^-4 rad.sec^-1.]

Therefore L_E = (0.4 x 5.98 x 10²⁴ x 6378² x [1.1083426 – 0.6034344] x 10^-4)/3350

= 1.4665532 x 10²⁴ kg.km².sec^-1

It can be also be shown that the ratio of the couple pressures of the two internal bodies is the inverse of the ratio of the impulse pressures of the two bodies. In the case of Earth and Uranus this ratio is 3.2389964 (see earlier papers on the website) and is given as N below.

From the above equations and information the following equality can be made:

L_U = L_E x N x r_U³/r_E³ = I_U x (w_pJ – w_oU)/T_U

and arranging and substituting in it gives:

(w_pJ –w_oU) = 1.4665532 x 10²⁴ x 3.2389964 x 26150³ x 3833/(6378³ x 0.4 x 26150² x 86.6 x 10²⁴)

= 0.5297700 x 10^-4 rad.sec^-1

Therefore w_oU = (1.1083426 – 0.5297700) x 10^-4

= 0.5785726 x 10^-4 rad.sec^-1.

Thus w_U present = w_oU x 0.4/0.23 = 1.0062132 x 10^-4 rad.sec^-1 or 17.35 hours for a revolution.

This compares with a measured value of 17.29 hours.

Note: The ratio of the present rotation times of Earth and Uranus = 17.29/23.934 = 0.7224, which is the reciprocal of the ration of the forces of Earth and Uranus on the centre of protoJupiter immediately before ejection began. The same reciprocal obtains for the forces of Earth and Uranus in their present orbits on a point X at 5.3 AU from the Sun, where the “brown body” was located before breakup, when the planets and point X lie on the same radius form the Sun. (See for example TAG Advertisement 1³.

2. The Rotational Relationship of the Couple Jupiter-Saturn. ProtoJupiter and Saturn came from the initial breakup of a rotating prolate ellipsoid, the “brown body”. Although they would have had opposed movements of fluid at their near-touching surfaces, they were still enclosed in a uni-directional fluid. In effect, then, and provided they were near spherical, it can be written that: R_pJ x w_opJ = R_S x w_oS If we apply the formula to protoJupiter and present-day Saturn, assuming the rotation of protoJupiter was the same as Jupiter is now, i.e., w_eJ = 1.7733482x10^-4 rad.sec^-1 and w_eS = present rotation of Saturn = 2.1702141 x 10^-4 rad.sec^-1, then:

R_pJ x w_eJ = 74007 x 1.7733482 x 10^-4 = 131240.18 x 10^-4 km.rad.sec^-1

R_S x w_eS = 60100 x 2.1702141 x 10^-4 = 130429.87 x 10^-4 km.rad.sec^-1

That is, the two products are only 0.62% different and so it can be written that w_eS = w_eJ x R_pJ/R_S.

This suggests that the rotations of Jupiter and Saturn should be related. It is now necessary to prove this is so.

In my 1994 book⁴, pp 72 –87, the moment of inertia factor of the “brown” body was built up shell by shell from the centre outwards to give an a of 0.4 for protoJupiter and 0.353 for the “brown” body. These figures may be incorrect by a small amount as at the commencement of Solar System studies I used a mass of 1999x10²⁴ kg for Jupiter. instead of the real value of 1899x10²⁴kg, The larger figure was taken from Cole†, my original source of information. The difference caused by this error must be slight, or later work using a = 0.4 for protoJupiter would not have given the correct answers that they did.

Later, in my 1997 booklet⁶, pp 29-32, I showed that there appears to be physical relationships between Saturn and the other planets using an a both of 0.4 and 0.353; with me hesitatingly deciding that 0.4 was more likely to be correct. The decision made no difference to later work as Saturn never came into the calculations – until now. In the following test, therefore, the a values of 0.4 and 0.353 will be used for calculations and the Saturn a giving the nearest value to that calculated for protoJupiter accepted as the true value.

It is first required to determine the angular rotations of protoJupiter and Saturn immediately after separation. This is done as follows using the following formula w_o = w_e x a_e/a_o. where

w_opJ = w_epJ x 0.25/0.4 = 1.1083426 x 10^-4 rad.sec^-1

w_oS = w_eS x 0.22/0.4 = 1.1936178 x 10^-4 “

or w_oS = w_eS x 0.22/0.353 = 1.3525414 x 10^-4 “

Note that 1.1083426 = 1.23^1/2 within 0.06% (Also the ratios of the masses of M_pJ and M_J = 2101/1899 = 1.0637 or 1.23^1/2 within 0.24%.) and 1.1936178 = 1.19¹ within 0.30%

Extensive studies made over the years has led to the observation that most property relationships contain a power of one of the three numbers 1.23, 1.19, and 0.724 (1.23 x 1.19 x 0.724^-1 = 2.02169 or 1.19⁴ within 0.82%) and as 0.724^-1 = 1.38122 it is quite possible that the rotation of Saturn immediately before separation from the initial protoJupiter was 1.38122 x 10^-4 rad.sec^-1 and immediately after separation was, as given by w_eS for a = 0.353, equal to 1.3525414 x 10^-4. This possibility (probability?) is suggested because my numerous studies of physical relationships within the Solar System have shown there is generally a decrease of about 2% when a dynamic event occurs. ( See, for example, Advertisement 4⁵, where a 2% reduction is used for the accuracy of the formula q_X = 8.189035 x q_E x R_X/R_E when determining the tilt of a planet of one ejection event using the tilt of another in a later ejection event..) Occasionally the decrease is about 4%, suggesting two dynamic events took place. Saturn underwent only one dynamic event, and so 1.38122 x 0.98 = 1.35254. Whether such happened or not (and I subscribe to it) it is clear that the moment of inertia factor of Saturn at separation was 0.353, not 0.4.

_{It is therefore necessary to compare the R x wo values:}

_{for protoJupiter, 74007 x 1.1083426 x 10-4 = 8.2025111 km.rad.sec-1;}

_{and for Saturn, 60100 x 1.3525414 x 10-4 = 8.1287903 “}

_{The ratio is Saturn/protoJupiter = 0.99101, i.e. the two values are within 0.91% of one another.}

_{The equation RpJxweJ = RSxweS is thus a simplification of RpJ x wopJx0.4/0.25 = RS x woSx0.353/0.22, i.e., 13.1240 compared to 13.04299, a near equality, and so} the equation w_eS = w_{eJ x} R_pJ/R_S given at the beginning of this section is a valid one; it is merely a simplification of a slightly more complex equation. It consequently leads to the conclusions that the rotations of Jupiter and Saturn are related and that the two planets did come into existence at the same time.

3. Relating the Rotations (Spins) of Venus and Mercury, and Showing How They Can Be Used to Calculate the Rotation of Neptune. Some years ago I developed the formula v = 12.9 x 1.23ⁿ to give the orbit speeds in km.sec^-1 of the planets about the Sun; and so allowing the distances of the planets from the Sun to be determined quite closely (using the approximate formula d = KM/v² ). The formula is briefly discussed in an earlier paper on my web site¹ and given more fully in my booklet⁶. The formula is much more accurate than the Titius-Bode Law. As an aside I point out here that the number 12.9 in the formula is that speed a body would have at a distance of 5.3 AU from the Sun; and 5.3 AU is the distance from the Sun at which a body having a mass equal to the sum of the masses of the planets and satellites of the Solar System would exert the same force on the Sun as does the sum of the forces of the planets and satellites at their present orbits, i.e., F = GS(m)/5.3² = GS(m/d²).

I stated at the time of development of the formula v = 12.9 x 1.23ⁿ that the formula showed both Neptune and Pluto to be correctly placed and so there was no need for explanations for their apparent orbital discrepancies indicated by the Titius-Bode Law. Such “explanations” were rife at the time. It is the Titius-Bode Law that is in error as it is based on linear measurement. It should be based on velocity.

The accompanying table (See below) gives the speeds of the planets as calculated using the formula, their measured average speeds, and the percentage differences between the two.

Note that the three planets with the greatest discrepancies between calculated and measured orbit speeds are Mercury, Venus, and Neptune; the first with the greatest discrepancy and the other two of equal discrepancies. These bodies, according to the Single Body Breakup Hypothesis were ejected simultaneously from the centre of protoJupiter and so it is no surprise that the two larger bodies have equal, or near equal, discrepancies.

To study the rotation relationships between the three bodies one to the other it is necessary to give a more detailed description of the formation of the planets (Mars excepted) as given by the hypothesis. The differentiated “heavy” gas plus “silicate” core of protoJupiter divided into two spherical bodies, the gaseous/”icy” and the silicate, lying touching at the centre of protoJupiter. From these were ejected the “icy” and mainly hydrous silicate satellites (including Mars). This left two major differentiated bodies at the centre, a Neptune/Uranus sphere (Neptune as its core) and a Mercury/Venus/Earth sphere (Mercury as core). These two bodies in turn broke up into a string of five bodies, viz., Uranus, Neptune, centre of protoJupiter, Mercury, Venus, and Earth. This resulted in a major collapse or “caving in” of the outer parts of protoJupiter, causing the creation of an impulsive force at the centre sufficient to drive out Uranus and Earth; but not sufficient to eject Neptune, Mercury, and Venus. I suggest that this impulsive force caused Mercury and Venus to be sufficiently pressed together as to almost stop the rotation of Venus, for the bodies were rotating prior to this instant. Why almost? Because if its rotation was completely stopped, and then the impulsive force which drove the three bodies outwards in the final readjustment of protoJupiter to give Jupiter, the later imposed rotation on Venus by this impulse would have given Venus

an axial inclination unrelated to that of Neptune. But it has been shown in earlier work (e.g, Advertisement 4⁵ and on the website¹ ) that the tilts of Neptune and Venus are related by the formula tilt_N/tilt_V = radius_N/radius_V, where tilt_V = (180 + a)° - not -a - and tilt_N = 720° + its field-measured tilt. And of course, a slightly more complicated formula relates the tilts of these planets to those of Earth and Uranus.

Using the same argument for Mercury, its present rotation axis is vertical and so it can be argued that this body ceased rotating within protoJupiter when pressed against Venus. And if Venus came to an almost complete stop, why wouldn’t it be expected that the much smaller Mercury stopped?

Then came the largest and last impulse, causing the three last planetary bodies to be ejected. Neptune, being the sole “gaseous” planet of the three, moved outwards unhindered. However, it was a different story for the oppositely retreating Venus and Mercury.

From the above table the difference between the calculated and known speeds of Mercury is 44.7- 47.9 = -3.2 km.sec^-1, and between those of Venus is 36.3-35.0 = +1.3 km.sec^-1. The ratio of the two numbers

Planet	V=12.9x1.23n km.sec^-1 For n = n		Measured speed km.sec^-1	%age difference calculated/measured
Mercury Venus Earth Mars Inner edge asteroid belt Ceres Outer edge asteroid belt Jupiter No body possible Saturn Chiron Uranus Neptune Pluto Belt planetoids	6 5 4 3 2 1.5 1 0 -1 -1.5 -2 -3 -4 -5 -6	44.7 36.3 29.5 24.0 19.5 17.6 15.9 12.9 10.5 9.5 8.5 6.9 5.6 4.6 3.7	47.9 35.0 29.8 24.1 19.4 17.9 13.1 9.8 Not available Av. Rad, a = 13.7 6.8 5.4 4.7	-6.7 + 3.7 -1.0 -0.4 +0.5 -1.7 -1.5 -1.0 +1.5 +3.7 +2.1

(omitting signs) is 3.2/1.3 = 2.46154, while that of 3.2/(3.2+1.3) = 0.71111 or 0.724 within 1.81% (or 1.19^-2 within 0.70%), and 1.3/(3.2+1.3) = = 0.28889 or 0.724⁴ within 4.89% (or 1.36^-6 within 0.04%). From experience I find the appearance of Universe ratios in the calculations suggests the method of attack of the problem is correct.

Next, observe that the sum of the calculated speeds divided by the sum of the two measured speeds gives (44.7+36.3)/(47.9+35.0) = 0.9777, or 0.98 within 0.30% (i.e., 0.724^1/16 within 0.24%). Again, the change of condition gives a 2% decrease in value, but here we have an apparent reversal.

The Hypothesis states that the two bodies were ejected simultaneously. But Mercury, between Neptune and Venus, was given a greater ejection speed (because of its size) than Venus. It had, in some way, to pass Venus. In my opinion it could only have done so by rolling at least one quarter of the way around Venus – and in the orbital plane? – as the two bodies moved outwards. It would rotate about its axis 2pR_V/2pR_My = 6050/2439 = 2.48052 times the rotation of Venus – and in the opposite direction – a number only 0.77% different to the ratio calculated for the differences of the speeds given above, i.e., 2.46154. (Note that R_V/R_My = 2.48052.)

The two bodies, according to the Hypothesis, are closely similar in composition (dominantly Mg/Fe silicates) and so their moments of inertia and coefficients of friction should be closely similar. If any sliding took place between the faces of the two bodies then movement would be of equal amount for both. Thus the movements of the two spheres would have behaved as two cog wheels, i.e., R_a x w_a = R_b x w_b. In this case, Venus R_V x w_V should equal Mercury R_My x w_My if the above assumptions as to the relative movements of the two bodies is correct. And the equality exists, as Venus = 6050x(36.3-35.0) = 7865, and Mercury = 2439x(47.9-44.7) = 7805; i.e., within 0.77% of one another. The above thus supports the sequence of events for the two bodies at the beginning of the final ejection impulse.

The number of seconds for Mercury to rotate once in cog-wheel motion would have been 2px2439/3.2 = 4789 sec. and for Venus 2px6050/1.3 = 29241sec. The ratio of these two numbers is 6.105907 (= 1.435985⁵), with Mercury rotating in the direction as for the other planets and Venus counter-clockwise, its direction of rotation being that of the remaining rotation discussed above.

The present ratio of the rotations of the two bodies is 243.01 days/58.646 days = 4.143676 (1.426745⁴). Thus the initial rotation of Venus, i.e., after being nearly stopped by Mercury and at the commencement of cog-wheel rotation, must have been 6.1015907/4.143676 x 243.01 = 1.473548 x 243.01 = 358.087 days.

Note the ratios 6.105907, 4.143676, and 1.473548: they are approximately whole number powers of one number, near 1.4454 (the average of the three figures) i.e., within 2.07% of 1.19² (or 4.65% from 0.724^-1), i.e., the three ratios are related, showing that the movements of the two bodies were, and still are, related.

Now to show that the rotations of Venus and Mercury are related to Neptune.

I wrote in my booklet “Further Studies of the Solar System”^c in 1997 (p.32) “It is certainly beyond me to determine the variable force couple slowing down each planet as it passed through protoJupiter, but it is within my capability to attack the problem by ratios. The resultant couple acting on one of the lesser planets is: L [= J in the present paper] = (Iw_p – Iw_o)/T, where L = the average retarding couple, I = moment of inertia of the planet, w_p = angular velocity of protoJupiter, w_o = angular velocity of the planet as it finally leaves protoJupiter = w_o of earlier calculations, T = time for the planet to separate from protoJupiter.” This suggests a test of the above calculated original rotations of Venus and Mercury at the commencement of the final ejection.

It has been argued above, and fairly certainly proved, that at the instant of the final impulsive force, driving out Neptune, Venus, and Mercury from the centre of protoJupiter, Mercury was tight against Venus and had stopped rotating relative to Venus. But Venus was still rotating counter-clockwise, to the other planets. This means that Mercury, in effect temporarily stuck to Venus, was also rotating counter-clockwise to the other planetary bodies. Its rotation relative to them would be near that of Venus. The final impulsive force would have driven out this sub-system Venus/Mercury and have added to Venus’s rotation. At the same time Mercury would have cog-wheel rotated in the reverse direction to that of Venus.- at (3.2 – 1.3) km.sec^-1. It would have taken some 2x2.5x6050/(3.2-1.3) = 5000 seconds (Even assuming (3.2 – 0) gives 2970 sec.) to rotate one quarter of the way around Venus before separating. During the same time Venus would have moved out from the centre of protoJupiter some 5000x(35.0 – 12.9) = 110500 km (or 2970x(35.0 – 12.9) = 65637 km). The radius of protoJupiter was at that time approximately 73000 km. Thus the two bodies were out of, or nearly out of, protoJupiter before the cog mechanism ceased and so there is no need to determine drag by the fluid of protoJupiter on the two inner bodies’ rotations; it is quite minor. We can therefore determine the couples J of the rotating bodies Venus and Mercury as follows.

Rotation of Venus at beginning of “cog” movement = -358.087 days

= -2p/(3600x24x358.087) = -2.0308487x10^-7 rad.sec^-1;

Rotation of Venus at end of “cog” movement = -243.01 days

= -2p/(3600x24x243.01 = -2.9925539x10^-7 rad.sec^-1;

Rotation of Mercury at beginning of “cog” movement is approximately that of Venus

= -2.0308487x10^-7 rad.sec^-1;

Rotation of Mercury at end of “cog” movement = +58.646 days

= +2p/(3600x24x58.646) = +1.2400173x10^-6 rad.sec^-1.

The moments of inertia for the two planets are closely:

I_V = 0.4x4.87x10²⁴x6050² = 7.130167x10³¹

I_My = 0.4x0.33x10²⁴x2439² = 7.852312x10²⁹

On the assumption that the “cog” movement began with the final impulsive force that ejected the three bodies, we can write (where J is the impulse couple):

J_V = 7.130167x10³¹x(-2.9925539 – 00)x10^-7

J_My = 7.852312x10²⁹x(+1.2400173 – 00)x10^-6

But to these two bodies must be added the couples that they had immediately before the impulse, i.e.

J_Vo = 7.130167x10³¹x(-2.0308487)x10^-7

J_Myo = 7.852312x10²⁹x(-2.0308487)x10^-7 approximately;

or, combining J_V and J_Vo : 7.130167x10³¹x(-2.992539 – 2.0308487)x10^-7

and J_My plus J_Myo : 7.852312x10²⁹x(+1.2400173 – 0.2030849)x10^-6

The total couple on the “silicate” side of the centre of protoJupiter (i.e., ignoring signs)

= (3.5817699 + 0.13316849)x10²⁵ = 3.73899512 x 10²⁵ kg.km².sec^-1 -----------------------A

While Venus and Mercury, “locked” together, were moving outwards through protoJupiter in the Sun’s direction, Neptune was moving outwards unhindered outwards through protoJupiter in the opposite direction. The only retarding couple on its rotation was that of the medium it was passing through and it has been shown in earlier work that its couple at separation from protoJupiter is given by the formula

J_N = 0.4x103x10²⁴x24750²x(1.1083426 – 0.7859403)x10^-4/(71900/[12.9 – 5.4])

= 8.4871751x10²⁵ kg.km².sec^-1 ------------------------------------------------------------------B

where 1.1083426x10^-4 is the rotation of protoJupiter in rad.sec^-1 and 0.7859403x10^-4 is the rotation of Neptune at the surface of protoJupiter = present rotation x 0.29/0.4.

The ratio B/A = 2.269908 ------------------------------------------------------------------------------------C

As has been shown elsewhere, the ratios of the impulse pressures calculated for the planets Uranus to Earth and Neptune to Venus were equal to the ratios of their distances from the centre of protoJupiter when forming the internal string; respectively U/E = (2x24750+26150)/(2x(2439+6050)+6378) = 3.2390;

and N/V = 24750/(2x2439+6050) = 2.2648243 -------------------------------------------------------- D

i.e., C/D = 1 within 0.22%. This shows that Neptune is related to Venus plus Mercury.

It is therefore possible to calculate the rotation of Neptune using those of Venus and Mercury by using the formula:

(J_V+J_Vo+J_My+J_Myo)x2.269908 = 0.4x103x10²⁴x24750²x(1.1083426 – w_No)x10^-4/(71900/[12.9-5.4]), where the couples J are treated as positive values, followed by w_Np = w_Nox0.4/0.29, where w_Np is the present core rotation of Neptune.

The fact that the ratio of the impulse pressures of the two sides is in accord by adding two impulse couples for both the lesser planets suggests to me that the three bodies had already begun to move outwards from protoJupiter before the final impulse force took place.

Conclusions. In sum, this paper shows, ignoring Mars, that it is possible to use the rotation (spin) of a planet to calculate the rotation of another planet; specifically, Jupiter/Saturn, Uranus/Earth, and Neptune/Venus+Mercury. This can only be done using the Single Body Breakup Hypothesis. The Nebula Theory requires the rotations to be unrelated.

References.

1. www.franklee-geologist.com

2. “The Australian Geologist”, Newsletter No. 99, June 30,1996, pp.10-11.

3. “The Australian Geologist”, Newsletter No. 118, March 31, 2001, pp.10-11. Advertisement 1 “The Breakup of a Single Body to Form the Planets and Satellites: The Main Steps with Proofs.” .

4. “The Origin and Development of the Sun and the Planets” by T.F.Lee, 1994. ISBN 0 646 19165 9. Limited copies.

5. “The Australian Geologist”, Newsletter No.125, Dec.20,2002, pp. 46-47, “Physically Based Equations Relating the Axial Tilts of the Planets”.

6. Further Studies of the Solar System – studies from 1994 to early 1997” by T.F.Lee – geologist. Melbourne. ISBN 0 646 31840 3. Limited copies. (Also in 2^nd. edition with additions to Sept., 1997.)

7. Cole, G.H.A. “Early Physical Conditions of the Planets and Satellites “ in Surveys in Geophysics 11: pp.1-54; 1990. Kluwer Academic Publishers, Netherlands. (See Table II, p.5)