TWO MORE SOLAR SYSTEM BODY RELATIONSHIPS DEDUCED USING THE SINGLE BODY BREAKUP HYPOTHESIS

AND NOT EXPLAINABLE BY THE NEBULA THEORY

The Mass Relationship Between Jupiter and Saturn.

Calculating the Rotations of Mars and Uranus Using That of Earth.

T. Frank Lee, Geologist.  June, 2008.

 

 

1.  The Mass Relationship Between Jupiter and Saturn.

     This has to do with the splitting of the original “brown body” into protoJupiter and Saturn and the separation of the two bodies.  I leave it to the reader to work out how this happened,  I am only interested in bringing the formula to his attention.

     Using values:  Jupiter – mass = 1899x1024 kg,  orbit distance = 5.203 AU,  orbit speed = 13.1 km.sec-1.

                             Saturn – mass = 568.6x1024 kg, orbit distance = 9.539 AU, orbit speed = 9.6 km.sec-1

 

                then the formula       MS/MJ              =  Orbit-dJ2/Orbit-dS2      =  Orbit-sJ4/Orbit-sS4;

                                               = 0.2994207        = 0.2971673                       = 0.2884030

 

2.   Calculating the Rotation of Mars Using That of Earth.

Introduction.  It is necessary to be acquainted with the breakup sequence of protoJupiter as given in the later papers in website www.franklee-geologist.com or on the conference posters 33IGC and AESC2008.

     It was determined some 13 years ago that the formula LX = (IwpJ – IwoX)/T - where L = average lateral retarding couple, I = moment of inertia of the planet, wpJ = angular velocity of protoJupiter, woX = angular velocity of the planet as it finally leaves protoJupiter, T = time for the planet to separate from protoJupiter -  allowed one to calculate the rotation of Uranus using that of Earth.  The formula developed from it is:

LU = LE x N x RU3/RE3 = IU x (wpJ – woU)/TU         N is defined below.

     The determination is a relatively simple matter as the two bodies suffered the same impulse force, and conditions were basically the same for both during their passage through protoJupiter.  It was clear to the writer at the time, and became even clearer over the following years of study, that the same calculation could not be done for Neptune using the rotations of Venus and/or Mercury. Instead a  formula was finally developed using the orbit speeds of the planets.  (See website).  This was because Venus and Mercury interfered with one another during ejection from protoJupiter.  The interference actually stopped Mercury’s rotation and very nearly did the same to Venus.

     A few years back I wondered if it was possible to calculate the rotation of Mars using that of Earth, as I had done for the axial tilt of Mars, but it was only a few months ago that an  attempt was made to develop the formula required.  And, as found so often in my studies of the Solar System, by thinking “simple” and not looking at the problem as being complicated the formula for Mars given below came out in a matter of a few weeks.  Such a long time because the study was carried out in “fits and starts”.

Determining the Rotation of Mars.  To use Earth’s rotation to calculate that of another body not ejected at the same time it is necessary to mathematically adjust the impulse pressure conditions of Earth within protoJupiter to that of the body being considered.  These mathematical adjustments are entered into the Earth/Uranus formula.  For Mars the necessary adjustments are as follows.

     Adjustment 1.  N is the adjustment needed for position within protoJupiter.  In effect it is to move one position to another.  It is the ratio of the lateral pressures, i.e., the “rotation” pressures slowing down the two rotating bodies being compared within the larger, gaseous body.  The lateral pressure ratio is the inverse of the outward, ejection pressure ratio, which decreases as a straight line outwards from the centre of the gas body.  This ratio in turn equals the inverse ratio of the distances of the centres of the two bodies from the centre of protoJupiter at the instant of impulse.  So Mars, as Mars was nearer the centre of protoJupiter at ejection ( = 10589 km) than Earth was when it was ejected ( = 23356 km), began with a lesser pressure.  Thus in the formula, Earth’s value must be multiplied by N = 10589/23356 = 0.4533739.

     An aside is required here.  It is important both in the construction of the formula and in deducing a more precise beginning of the internal breakup of protoJutiter.  As will be seen from diagrams in my web page and on the 2008 posters, the internal breakup sequence of protoJupiter was believed to be: 1. Separation into two bodies – “silicate”, point X (centre of protoJupiter), “gaseous” with “icy” core.  2. Separation of satellites – string Europa,/Moon/Io/Mars, then Earth/Venus,/Mercury composite body, point X, Neptune/Uranus composite body with string Satellite X?/Ganymede/Titan/Callisto beginning at its centre.  The first attempt to determine the rotation of Mars, using this sequence, gave an impossible answer.  But when the string  Europa/Moon/Io/ Mars/silicate composite body was placed with the composite body centre coinciding with point X the correct answer was obtained.  Thus a problem I have worried over for years – did the “silicate” and “gaseous” spheres move simultaneously outwards (I inclined to believe they did.) or did one move first and so precipitate the movement of the second to retain force equality? And if so which one?  The calculation of the tilt of Mars has solved this problem; the “gaseous” sphere with its “icy” core moved first, causing the “silicate” satellites to develop and be ejected before the main “silicate” sphere moved.

     Adjustment 2. P is the ratio required for the adjustment of impulse size.  It is the number to apply to adjust the formula for size of the two impulse pressures of Earth and Mars.  The impulse pressures can be calculated using the formula pdt = M x (V2-V1)/(pR2), where V = orbit speed about the Sun.  For bodies on the Sun side of Jupiter V1 = 12.9 km.sec-1 and for bodies beyond Jupiter V2 = 12.9 km.sec-1.  For bodies orbiting Jupiter M x (V2 – V1) becomes M x V.  Calculation shows for Earth pdtE = 7.9080423 x 1017 kg.km-1.sec-1, and for Mars pdtMs = 1.9760657 x 1017 kg.km-1.sec-1.  The ratio P is therefore 0.2498805      (= 4.0019126-1) because the impulse pressure for Mars was smaller than that for Earth.

     Adjustment 3.  S is the ratio for the rate of change of the impulse pressures; the rapidity at which the pressures changed over distance; the gradients of the graphs constructed for the two impulse events.  For Earth it is the gradient between Uranus and Earth, and calculation gives 1.0420058 x 1013dt kg.km-2.sec-1.

     Mars belongs to the ‘silicate”-satellites ejection sequence and was the last of the satellites to be ejected.  The pdt values when plotted against distance for the bodies Europa, Moon, Io, and Mars give a very near straight line gradient.  However, as both Mars and Moon suffered capture and removal from the control of Jupiter the writer believes the most accurate slope value is between Io and Europa.  This value will be used in the present calculation for Mar’s rotation.  The gradient is 0.9146826 x 1013dt kg.km-2.sec-1.  And as the gradient for Earth is greater than that for Mars the S to be entered in the formula to determine the rotation of Mars is,  S = 0.9146826/1.0420058 = 0.8778095 (= 1.1391993-1).

     Adjustment 4.  This, the final adjustment, comes from the writer’s many years of study of the Solar System.  It has been mentioned a number of times in his papers.  When a change of state by breakup of protoJupiter took place (and of the body which preceded it) a loss of approximately 2% of force, energy, etc. occurred.  I have previously used the figure 0.98 and will use this now.  In the case of Mars, that body formed before Earth.  Thus the ejection pressure environment for Mars would have been about 102% (x0.98-1) greater than for Earth’s environment.  It is therefore necessary to include the number 0.98-1 in the formula.

The Calculation of the Rotation of Mars.  It is now possible to write out the formula that allows the rotation of Mars to be calculated using that of Earth and protoJupiter.  It is:

LMs =LE x R3Ms/R3E x N x P x S x 0.98-1 = IMs x (wpJ – woMs)/TMs

where  N = 0.4533739,  P = 0.2498805,  S = 0.8778095,  wpJ = 1.1083426 x 10-4 rad.sec-1

T = time for Mars to pass completely out of protoJupiter = (74007 -7193)/(24.1 – 12.9) » 5966 sec.

 

Thus,   1.4665532 x 1024 x 33963/63783 x 0.4533739 x 0.2498805 x 0.8778095 x 0.98-1

=  0.4 x 0.64 x 1024 x 33962 x (1.1083426 – woMs) x 10-4/5966

Therefore, 2.2465384 x 1022 = 4.9487109 x 1022 x (1.1083426 – woMs)

Giving, 1.1083426 – woMs  =  0.4539644    Thus  woMs = 0.6543782, which has to be multiplied by 10-4

wMs present = woMs x apJ/aMs present,  where a is the moment of inertia factor.

Therefore wMs present = 0.6543782 x 10-4 x 0.4/0.365  =   0.7171268 x 10-4 rad.sec-1

Rotation of Mars in hours = 2p/(3600 x 0.7171268 x 10-4) = 24.338 hours.

The measured value is 24.623 hours, i.e., 1.17% different..

 

3.  A Revised Calculation of the rotation of Uranus.  It is considered advisable to recalculate the rotation of Uranus.  This is because more accurate physical measurements have been determined since the original calculation in about 1994.  The following values are taken from “Physics and Chemistry of the Solar System” (revised edition), 1997, by John S. Lewis; Academic Press, p.216.

Uranus:  mass 86.77 x 1024 kg,  radius 25660 km,  (Interior rotation 17.24 ±0.01 hours.

The formula for Uranus is LU = LE x R3U/R3E x N  = IU x (wpJ – woU)/T

where  N = (2x24552+25660)/(2x[2439+6050]+6378)  =  3.2010618

T »  (72881 – 2x24552)/(12.9 – 6.8)  =  3897.67 sec, say 3890 sec.

 

Thus 1.4665532 x 1024 x 256603/63783 x 3.2037329

= 0.4 x 86.77 x 1024 x 256602 x (1.1083426 – woU) x 10-4/3890

giving  1.1083426 – woU  =  0.52037329

thus woU = 0.5879693, which must be multiplied by 10-4

wU present  =  woU x apJ/aU  = 0.5879693 x 10-4 x 0.4 x 0.23 = 1.0225553 x 10-4 rad.sec-1

Rotation of Uranus in hours = 2p/(3600 x 1.0225553 x 10-4) = 17.068, say 17.07 hours.

i.e., 1.01% different to the measured value of  17.24 hours.

 

Comments.  I have no doubt that “experts” on the subject of the properties of the planets will label the above work on calculating planetary rotations as useless and meaningless.  Why?  Because, they will point out, such relationships between planets are impossible according to the Nebula Theory.   And theory in present-day science takes precedence over fact.

     The formulae developed above show that the rotations of the bodies Uranus, Earth, and Mars are related; and an earlier paper (see website) has shown that the rotation of Neptune can be calculated using the orbit speeds of Venus and Mercury.  Again, in that paper, it has been shown that there is a relationship between the rotations of Venus and Mercury – and why the rotations are “peculiar”.

     For the Nebula Theory to be considered a valid explanation of the origin of the Solar System it must be able to explain the rotation relationships.  So far, all attempts have failed to even validly explain how the planets obtained their rapid rotations.  The same criticism can be levelled at its explanations for the axial tilts of the planets – both tilt and the relationships of the tilts that exist.  I do not expect the Theory to be ever able to explain the relationships.

     On the other hand, the Hypothesis used here in this paper explains both rotations and tilts; and for the many other Solar System property relationships that the fraternity of scientists do not even seem to know about.