THE SINGLE BODY BREAKUP ORIGIN OF THE SOLAR SYSTEM.
A list of the simpler property and body relationships revealed and/or explained by it.
An amplification of the poster presented.
T. Frank Lee, MAppSc, BSc, DipCE, FAus IMM, MGeol.Soc Aust.
102 Mill Street, Ballarat, Victoria, 3350, Australia. Tel: (61) 3 53316938.
Over time a spinning, dominantly gaseous but moderately density-graduated, increasingly prolate ellipsoidal “brown” body split into two unequal parts as required by the Jacobi bifurcation rule for a rotating mass of gas. The rule states that separation occurs when the ellipsoid’s a-axis “radius” attains the length of 1.5x the radius of a sphere containing the volume of the original ("brown") body. 1.5 = 1.232.
Of the two resultant unequal parts, the smaller, almost perfectly gaseous body, Saturn, remained unaffected by what followed. The “brown” body was a closed force system. Because the body was not a pure gas the split was imperfect and force after was not equal to force before breakup. Equality could only be made via the larger, density differentiated body, “protoJupiter”, and was done by internal adjustment. The body’s denser core broke initially into two parts, a “silicate” and a “gaseous”. This caused collapse of its outer layers, resulting in a central impulse force sufficient to drive out some of the central, denser matter. The result was a repetition of this mechanism until force balance was attained.
The following notes give some of the consequences of the breakup.
Such a mechanism of ejection as described above requires that the ejected matter display certain kinetic properties. Only two are given here.
Saturn is excluded as it is not an ejected body. With the ejected planets on a common radius from the Sun, and protoJupiter at 5.3 AU (See later notes for the calculation of this distance.) the sum of the forces of Uranus, Neptune, and Pluto exerted on protoJupiter must equal the sum of the forces of Mars, Earth, Venus, and Mercury. –Newton’s Third Law. And such is the case.
The ejected planets would have moved outwards from protoJupiter until each body was captured by the Sun. This capture would have taken place after the protoJupiter remainder, Jupiter, had reached its present orbit distance of 5.2 AU. (In my early studies I assumed 5.3.) Thus the sum of the angular momenta of the ejected planets about Jupiter must equal or be slightly less than their angular momenta about the Sun. And such is the case.
The ratio mass of Jupiter to mass of Saturn is equal to the ratio of Saturn’s orbit distance from the Sun squared to Jupiter’s orbit distance from the Sun squared. i.e. MJ/MS = OrbitS2/OrbitJ2.
Note that the radius of a sphere having the combined volumes of Neptune and
Uranus divided by the radius of a
sphere having the combined volumes of Earth, Venus, and Mercury gives a value
of (32089/7913) = 4.055 = 1.198. The radius
ratio of Uranus to Earth is 4.10,
and of Neptune to Venus 4.09.
Combine the masses and volumes of Neptune and Uranus (A) and the masses and volumes of Mercury, Venus, and Earth (B) to form two spherical bodies touching at point C. Then the forces exerted by A and B at point C are almost equal.
The hypothesis explains why the hydrogen/helium ratios of the gaseous
planets increase from Neptune to Uranus to Jupiter to Saturn as against the
order from the Sun of Jupiter, Saturn, Uranus, Neptune; the latter order being
predicted originally by the Nebula Theory.
Explains why the deuterium/hydrogen ratio in the planet
atmospheres decreases in the order Venus, Mars, Earth, Neptune, Uranus,
Jupiter/Saturn.
It requires a description too long
to give here, but a simple explanation can be given using the hypothesis to
explain the distribution of the noble
gases in the planets of our Solar System.
The formula x = 2 x 0.724n (= 2 x 1.38-n) gives the orbit distances from the Sun of all but two of the planets. The two failures are as for the Titius-Bode Law for Neptune and Pluto. The formula is, however, more accurate than the old law.
Determine the distance of orbit (X) about the Sun of a body containing all the masses of the planets and satellites including Saturn, using the formula S(m)/X2 = S(m/d2). X will be found to be closely 5.3 AU. The speed of a body at that distance is 12.9 km.sec-1. Then the speeds of the planets about the Sun are given by the formula v = 12.9 x 1.23n for n = 6 (Mercury), 5 (Venus), 4 (Earth), 3 (Mars), 2 (inner edge of asteroid belt), 1˝ (Ceres), 1 (outer edge of asteroid belt), 0 (Jupiter), -1 (no body possible), -1˝ (Saturn), -2 (Chiron), -3 (Uranus), -4 (Neptune), -5 (Pluto), etc (?).
In the formula directly above, the three bodies having the greatest differences between their calculated and measured orbit speeds are Neptune, Venus, and Mercury. These differences, with other physical data, allow the calculation of the rotation of Neptune.
The rotation of Uranus can be calculated using those of Jupiter and Earth. See website www.franklee-geologist.com.
To calculate the rotation of Saturn use the following formula: RotS = rotJ x RpJ/RS, where RpJ is the radius of a sphere containing the volumes of all the other planets and satellites except Saturn (= 74007 km)
The axial tilt of Saturn can be calculated using the following formula:
tiltS = (tiltJ x RpJ x MpJ x apJ)/(RS xMS xaS) plus the angle between the orbital planes of the two planets about the Sun. a = moment of inertia factor (apJ = 0.4).
It can be shown that the rotations of Venus and Mercury are related and that the axial tilt of Mercury must be zero or close to zero. See website.
Shows why the ratios of the radii of
Uranus to Earth, Neptune to Venus are the same and are equal to the ratios of
their axial tilts (Neptune 720° + tilt, Venus 180° + 2.67°, not 180° - 2.67°).
ie. Ra/Rb = tilta/tiltb.
Using only the physical dimensions
of the planets and the formula given directly above it is possible to derive a
simple formula relating the axial tilts of Neptune and Venus to that of Earth.
Ie.,
TiltX =
8.189035 x tiltE x RX/RE for X = Venus or Neptune.
Translate Mars and Moon to
Jupiter. Then the ratio of their axial
tilts is closely 2, as is the ratio of their radii; ie. RMs/RMn
= tiltMs/tiltMn » 2.
Place in line in the following order
the bodies Europa, Moon, Io, Mars, Earth, Venus. The ratios of the radii of touching couples are closely RMn/REu =
1.231/2, RIo/RMn = 1.231/4, RMs/RIo = 1.233, RE/RMs = 1.233, RV/RE = 1.23-1/4. This suggests that Earth and Moon did NOT
form by impact.
Note that RE/RV = 1.0542, closely
1.231/4 and RU/RN = 1.0566, closely 1.231/4.
Also, ME/MV = 1.2279, closely 1.23 and MN/MU = 1.1894, closely 1.19.
Both 1.23 (commonest) and 1.19 (second commonest) are Universe ratios.
The formula d = 2 x 0.981n gives the densities of the major satellites and the
unself-compressed density of Mars, where n = +6, Callisto; +4, Titan; +2,
Ganymede; 0, Triton; -22, Europa; -27, Moon; -30, Io; -33, Mars. As Moon and Titan lie neatly in a
mathematical sequence of a common physical property the suggestion is that they
formed similarly and at the same time as the other bodies. Note: 0.981-16 = 1.36.
Further support for the planetary and satellite relationship suggested in the previous note: make a table of all solid – “silicate” and “icy” – bodies’ densities (D), radii (R), and their quantities 1000 x D/R. As will be seen below the groups of values 1000D/R suggests a close relationship of the bodies within the groups and a probable relationship of the groups, with Mars and Mercury marking the end of groups. This sequence of numbers is highly unlikely to be fortuitous.
Name
D R 1000D/R Name D R 1000D/R
Callisto 1.81 2400 0.75417 Europa 3.04 1560 0.71635-2
Titan 1.85 2560 0.72266 Moon 3.34 1738 0.72136-2
Ganymede 1.93 2640 0.73106 Io 3.55 1829 0.71778-2
Mars 3.76 3396 1.231/2
Name D R 1000D/R
Earth 5.515 6378 0.747691/2
Venus 5.24 6050 0.750161/2
Mercury 5.43 2439 1.234
The formula y = 26.2 x 0.724n gives the approximate orbital distances in Jupiter radii of the Jupiter satellites about their “parent” Jupiter for: n = 0, Callisto; 2, Ganymede; 3, Europa; 5, Io. This, together with the above-given body relationships, suggests that Titan may once have been at orbit distance n = 1 and Moon at orbit distance n = 4.
When the two bodies Moon and Titan are placed as suggested in the previous note, and the six bodies are placed on a common diameter from Jupiter – “silicate” bodies on one side, “medium icy” on the other, then: the ratios of the forces exerted on Jupiter by the bodies Io/Ganymede = 4.034, Moon/Titan = 4.01, and Europa /Callisto = 3.623; and the sum (Io+Moon+Europa)/(Ganymede+Titan+Callisto) = 3.97. These values point to the Moon and Titan once being located, even if very briefly, about Jupiter. If so, then Moon and Titan must be captured bodies. See www.franklee-geologist.com for discussion.
Place the bodies Mars, Io, Moon, and Europa in line and touching along an X-axis. Calculate for each the value of pdt = Mv/pR2, where v is the speed in km.sec-1 about Jupiter (For Mars v = speed about the Sun minus 12.9 km.sec-1). Moon v is unknown. Plot the values of pdt from the body centres in the Y-axis direction. Join the three points. A straight, sloping line is obtained. Using the value for pdtMoon obtained from this graph calculate vMoon. Use the formula v = (K/d)1/2 to determine d. The value obtained will be closely that for the Moon using the formula y = 26.2 x 0.724n, where n = 4. Apply the same method on satellites Ganymede, Titan, and Callisto. The value of n for Titan will be 1. The conclusion must be that the Moon and Titan were originally members of the Jupiter family of satellites.
The orbit speed of the Moon about protoJupiter, if it once was in orbit about protoJupiter as suggested above, would have been approximately 16.05 km.sec-1. The speed of Earth relative to protoJupiter at 5.3 AU (see earlier note) when exiting from protoJupiter was 16.9 km.sec-1. That is, the two speeds are closely similar. This allows a simple explanation to be given for the capture of the Moon by the Earth.
Place the following planets in line and touching: Earth, Venus, Mercury, pointX, Neptune, Uranus. Determine the distances L of the centres of each body from point X.
Then LU/LE is inversely proportional to MU x (12.9 – vU)/(pRU2) divided by ME x (vE – 12.9)/(pRE2), where v is the orbit speed about the Sun.
It will also be found that the ratio of the forces exerted on point X by Earth and Uranus is 0.724, while the ratio of the forces of Earth and Uranus in their present orbits on a point X at 5.3 AU, when the three bodies are in line on the same radius, is 0.722. The ratio of the two planet rotation times is 0.722.
The ratio numbers 1.23 and 1.19 given in some of the above notes occur repeatedly in Solar System body and chemical relationships, and are the two most common ratio numbers (1.23 by far the most common) in Universe body relationships, from galaxies to the spacing of electrons in atoms. A third number, 0.724 = 0.9816 =1.38-1, is almost unique to our Solar System. Its equivalent in the Universe is 1.37 or 1.36. 1.36 can be written as 0.981-16. Note the density formula for satellites given above.
It is significant that 1.19 x 1.23 x 1.36 = 2.00 and that 1.191.19 = 1.23, while 1.231.232 = 1.368. These numbers, then, are not random numbers. When they, or powers of them,appear in ratio relationships the relationships are mostly of significance.
How did the meteorites and comets come into existence? The mechanism is roughly analogous to that of a volcano. As the “silicate” and “icy” bodies were ejected from protoJupiter they were accompanied by “spatter”, “spray”, and small lumps of matter. In the case of the meteorites the dominant silicate to iron types would mirror the compositions of the accompanying planet (including Mars), with lesser intermediate types before and after planet ejection. The various types would become mixed over time due to different velocities and orbit forms to give the distribution we now see 4.6 x 109 years later.
If “spatter” accompanied ejection of a “silicate” planet as described above, the total “spatter” would, on average, approximate the parent’s velocity, but there would be a wide range of trajectory angles to the Solar System orbit plane. After half an orbit about the Sun the bodies would tend to meet over a limited time span. Over geological time the span would increase and the concentration decrease at each “meeting”.
The equation 3 x (multiple of the planet orbit times [including Ceres and Pluto]) about the Sun in Earth years = 4.6 x 109, the age of the Solar System. Therefore the first meeting of like bodies would have been at 2˝ x 4.6 x 109 = 3.84 x 109 years. This is closely the known age of maximum major impacts on Earth and Moon (and Mars?). This is support for the hypothesis.
The hypothesis permits a simple mechanism to be outlined by which the Earth’s magnetic field, variations of the field, and its reversals can be explained. See website.
Comparing the known planetary values of 55Cancri to those of our Solar System by using equations developed from the hypothesis suggests that both systems had a similar origin of Single Body Breakup style.
Ellipsoidal galaxies with associated quasars obey at least some of the kinetic rules that governed the development of our Solar System.
20/3/2008
“A man was taken to the zoo and shown the giraffe. After gazing at it a little in silence: ‘I don’t believe it’, he said.”
At head of chapter VIII in “Clouds of Witness”,. by Dorothy L. Sayers.