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Tidal Locking And The Age Of The Solar System Paul Nethercott, December 2011 www.creation.com Introduction “Tidal locking (or captured rotation) occurs when the gravitational gradient makes one side of an astronomical body always face another; for example, the same side of the Earth's Moon always faces the Earth. A tidally locked body takes just as long to rotate around its own axis as it does to revolve around its partner.”1 The objective of this essay is to test current views of the age of the solar system against the observed degree of locking versus the predicted degree of locking. Tidal locking in the inner five planets [Mercury, Venus, Earth, Mars and Jupiter] is strong evidence for a recent creation of the Solar System as opposed to the evolutionist’s view that they formed 4.5 to 5 billion years ago. The tidal locking rate is how fast the planet’s day length changes per century. It is the planet’s year length [seconds] divided by the total locking time [years]. Scientist Michael Koohafkan says that we can use these formulas to arrive at the maximum age of the planets and satellites: “Rate of change of rotational speed can be calculated. If it can be represented as a function, then approximate length of time until tidal locking can be calculated. Tidal locking can help measure the age of a planet in relation to a satellite. By measuring the rate at which a planet or satellite is approaching a tidal lock, we can extrapolate back and estimate the age of a satellite or planet.” 2 “Does tidal locking only occur between a mass and a satellite? No. Tidal locking can occur between any two masses that orbit around each other. Planets can become tidally locked with the stars they orbit around, and stars in a binary system can become tidally locked together.” 2 Since many of the satellites in the Solar System are tidally locked and none of the planets are, this gives us a method to check the evolutionist and creationist models. As we shall see, none of the formulas and the ages give can be fitted into the evolutionist’s model. They either give young ages for the planets, or unbelievably old ages for moons and planets. Since evolutionists accept that the Big Bang happened 15 billion years ago and the Solar system and planets formed 5 billion years ago, they have a set time scale they can accept. Mercury Mercury is in a 2:3 orbital resonance ratio with its orbit around the Sun. If we consider it to have fully locked then it is no evidence for recent creation. God could have created it that way 6,000 years ago. If it is not fully locked then it is evidence for much younger age framework than evolutionists accept. Venus It backward rotation does not line up with tidal locking or evolution. If an asteroid hit it and reversed its rotation where is the giant impact crater? Why is its orbital eccentricity almost zero? Such a massive collision should have affected its eccentricity but there is no evidence for any massive impact. Earth The Earth is tidally locking to the Moon. 1 This is actually hastening the Sun’s tidal locking influence on the Earth. With both working together the tidal locking time and maximum possible ages is even shorter than listed in this essay. Jupiter The planet Jupiter and its moons are a miniature Solar System. If we use the tidal locking formulas in this essay and apply them to the four Galilean moons [Io, Europa, Ganymede and Callisto], we find they should have locked a long time ago. Since they are 100% locked we should expect the same of those planets [Mercury, Venus, Earth] which should lock in less than 4.5 billion years. Since Jupiter’s major moons are 100% tidally locked, the same should be true of major planets where the same formula applies within the given timescale. The fact that Mercury, Venus and Earth are not 100% locked shows the age of the Solar System to be much less than 4.5 billion years. In the case of the Earth it points to a very recent creation. Table 1. Predicted day lengths [earth Days] versus actual day lengths Tidal Locking Formula Cornell Formula Wikipedia Formula Ohio Uni Formula Guilott’s Formula Correia’s Formula Edson’s Formula Castillo-Rogez Formula Actual Predicted Mercury 88 88 88 88 88 88 88 58 Predicted Venus 225 225 225 104 225 225 225 243 Predicted Earth 365 301 365 29 92 13 365 1 Predicted Predicted Mars Jupiter 10 472 3 20 1 90 1.025 5 0.413 Table 2. Maximum ages [Million years] Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Tidal Locking Guilott’s Formula Seager's Formula Correia’s Formula Edson’s Formula Castillo Formula Leger's Formula Robuchon's Formula Peale's Formula Barne's Formula Schubert's Formula Carter's Formula Heath's Formula Melnikov's Formula Grießmeier's Formula Cornell Formula Wikipedia Formula Ohio Uni Formula Mercury 1753 1753 42 Venus 662 796 662 573 9.5 662 1948 2131 102 1323 19 88 1 3619 4341 3619 3627 15 3619 2577 106 315 960 237 Earth 139 139 49 344 7 20 7 17 0.13 7 154 170 1 15 1.4 4 5 Mars 1277 1277 226 51 136 51 114 0.7 51 1419 2115 38 103 35 134 10 Jupiter 220 190 Table 3. Percentage of Tidal Locking Process Planet's Name Mercury Venus Earth Mars Jupiter Year Length Seconds 7,600,530 19,414,140 31,558,150 59,354,294 374,247,821 Day Length Seconds 5,080,320 21,081,600 86,400 88,906 35,510 Percentage Locked 66.84% 108.59% 0.27% 0.15% 0.01% The Shortest Day Length Possible What is the fastest speed the planet could have been rotating in the beginning? How long would the original day length have been? T 2R V V f , F mV 2 F , R GM f , 2 R f F , T = Day length, seconds R = Planet’s radius, metres f = Current Surface gravity force, Newtons F = Current Equatorial Centripetal force, Newtons V = Current Equatorial Velocity, Metres/Second = Final Equatorial Velocity, Metres/Second Table 4. Shortest Planetary Day Lengths. Formula 1 Planet's Name Mercury Venus Earth Mars Jupiter Shortest Day Length, Seconds 5,052 5,201 5,070 5,898 10,669 Shortest Day Hours 1.40 1.44 1.41 1.64 2.96 The Equatorial Bulge Thus the relative difference 3 between equatorial and polar radii is h = Equatorial Bulge height, metres W = Angular axial rotational velocity, radians/second R = Planet’s radius, metres G= Gravitational constant M = Mass of the planet, kilograms t = Day length, seconds c = Velocity of light 1 W2 R3 h , 2 GM Another formula 4 gives the actual height in metres: 2 t 2GM hR 2 , c c 2 4 Planets maximum age. T = Tidal locking time, years. d = Original day length, seconds y = Current year length, seconds: d Age T , y 1. Guillot’s Formula Dr. Guillot from Department of Planetary Sciences, University of Arizona 5, 6 gives a formula we can use to determine tidal locking times. According to his formula the Earth has been orbiting the Sun less than 150 million years. R m a , t Q Gm M R 3 Planets Name Mercury Venus Earth Mars Jupiter 2 6 Maximum Age Million Years 1,753 9,519 139 1,277 164,988,229 Giant Planets At Small Orbital Distances By T. Guillot, And A. Burrows The Astrophysical Journal 1996 Volume 459, Pages L35–L38 http://iopscience.iop.org/1538-4357/459/1/L35/pdf/1538-4357_459_1_L35.pdf Q is the planet’s tidal dissipation factor, is the planet’s primordial rotation rate, M is the star’s mass, m is the planet’s mass, R is the planet’s radius, G is the gravitational constant a is the planet’s orbital radius 2. Correia’s Formula Dr. Alexandre Correia from Santiago University, Portugal 7 gives yet another formula we can use to determine tidal locking times. According to his formula the Earth has been orbiting the Sun less than 50 million years. M is the star’s mass, m is the planet’s mass, R is the planet’s radius, g is 640 k is the planet’s Love number G is the gravitational constant a is the planet’s orbital radius N is the planet’s mean orbital motion 2 3 9GM kgR t 6 ma Astronomy & Astrophysics, August 7, 2008 Manuscript 0388 By Alexandre C. M. Correia Earth-Like Extra-Solar Planets Planets Name Mercury Venus Earth Mars Jupiter 5 4 3kgR n t 2 (mR 3)G http://arxiv.org/PS_cache/arxiv/pdf/0808/0808.1071v1.pdf Maximum Age Million Years 42 2,577 49 226 7,595 3. Edson’s Formula Dr. Adam Edson from Department of Meteorology, The Pennsylvania State University 8 gives yet another formula we can use to determine tidal locking times. According to his formula the Earth has been orbiting the Sun less than 350 million years. We change this formula to get t rather than a. Firstly isolate the sixth root: Pt a 0.024 3 M 6 Q Raise both sides to the power six: Pt a 6 3 0.024 M Q Isolate T from P and Q: Q a t 3 p 0.024 M 6 Icarus, 2011, Volume 212, Pages 1–13 By Adam Edson Terrestrial Planets Orbiting Low-Mass Stars P is the original rotation period of the planet in hours t is the time period from formation M is the mass of the star a is the planet’s orbital radius Planets Maximum Age Name Mercury Million Years Venus 24,860 Earth 344 Mars 4,288 www3.geosc.psu.edu/~jfk4/PersonalPage/Pdf/Edson_etal_Icarus_11.pdf 4,320 4. Castillo-Rogez Formula Dr Castillo-Rogez, Jet Propulsion Laboratory, California Institute of Technology 9 gives yet another formula we can use to determine tidal locking times. According to his formula the Earth has been orbiting the Sun less than 8 million years. Icarus, Volume 190 (2007), Pages 179–202 3kGM 2 r 5 dt d 6 Ca Q d 3kGM a 6 dt CD Q 2 5 Planets Maximum Age Name Mercury Million Years Venus 3,619 Earth 7 Mars 51 662 spin (ω, in rad/s) as a function of time, t, is governed by G is the universal constant of gravity, M stars’s mass, a Planets’ equatorial radius, C the polar moment of inertia, and D the semi-major axis. The dissipation factor Q and the tidal Love number k2 Based on current tidal locking formulae and the derived maximum tidal locking times and the degree to which the planets are tidally locked, one concludes that either: 1. The planets had impossibly fast initial spin rates, or 2. The solar system is much less than 4.5 billion years old Tidal locking is consistent with a young age for the solar system. Robuchon and Schubert publications. 10, 11 give the identical formula in their http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/40960/1/07-1357.pdf 5. Barnes’ Formula Using formula 22-24 by Barnes 12 we get young ages for the solar system. According to his formula the Earth has been orbiting the Sun less than 200 thousand years. Astrobiology, Volume 8, Number 3, 2008, Page 559 W 2 19 2 1 e , T 2 Planets Name Mercury Venus Earth Mars 2 , t 8mQa 6 W, TL 2 3 45GM kR Maximum Age Million Years 6.76 14.64 0.13 0.65 Where , is the initial spin rate (radians per second) a, is the semi-major axis of the planet around the sun W, satellites orbital spin e, satellites eccentricity Q, is the dissipation function of the planet. G, is the gravitational constant M, is the mass of the parent, kilograms m, is the mass of the planet, kilograms k, is the tidal Love number of the planet R, is the radius of the planet, metres. t = Initial day length, seconds T = Orbital period, seconds TL, tidal locking time seconds www.astro.washington.edu/users/rory/publications/brjg08.pdf 6. Leger’s Formula Using formula 25 by Leger 13 we get young ages for the solar system. According to his formula the Earth has been orbiting the Sun less than 30 million years. Astronomy And Astrophysics, 2009, Volume 506, Page 299 | n W | ( IQ k ) t (3M 2m)( R a)3 (GM a 3 ) Planets Name Mercury Venus Earth Mars Maximum Age Million Years 796 4,341 20 136 T= Seconds M= Mass of the star, kilograms m=mass of the planet, kilograms n is the mean orbital motion W is the primordial rotation rate of the planet a, is the semi-major axis G, is the gravitational constant R, is the radius of the planet, metres. Q the planetary dissipation constant, k the Love number of second order I = 0.4 7. Peale's Formula Peale 14 gives a formula we can use to determine tidal locking times. According to his formula the Earth has been orbiting the Sun less than 20 million years. Icarus, 1996, Volume 122, page 168. 6 wr CQ t 2 5 3Gm kR Planets Name Mercury Venus Earth Mars Maximum Age Million Years 573 3,627 17 114 T= Seconds w, is the initial spin rate (radians per second) G, is the gravitational constant m, is the mass of the planet, kilograms k, is the tidal Love number of the planet R, is the radius of the planet, metres http://audiophile.tam.cornell.edu/randpdf/gladman.pdf 8. Carter’s Formula Joshua Carter gives a formula 15 we can use to determine tidal locking times. According to his formula the Earth has been orbiting the Sun less than 160 million years. The Astrophysical Journal, 2010, Volume 709, Page 1221 4QC R m a W t 9 Gm M R 3 2 6 Planets Name Mercury Earth Mars Maximum Age Million Years 1,948 154 1,419 W is the planet’s initial angular rotation frequency, m is the planet’s mass, M is the stellar mass, Q is the specific dissipation factor R is the Planet’s radius a is the Orbital radius G is the Gravitational constant http://audiophile.tam.cornell.edu/randpdf/gladman.pdf 9. Heath’s Formula Martin Heath gives a formula 16 we can use to determine tidal locking times. According to his formula the Earth has been orbiting the Sun less than 160 million years. IAU Symposium, Volume 213, 2004, Page 228 Q r t 2 PM 0.027 6 Planets Name Mercury Venus Earth Mars Maximum Age Million Years 2,131 12,263 170 2,115 Where Q is a friction parameter P is the initial rotation period of the planet, M is the mass of the parent star, And r is the planet's orbital semi major axis (all in cgs units). 10. Melnikov’s Formula A. V. Melnikov gives a formula 17 we can use to determine tidal locking times. According to his formula the Earth has been orbiting the Sun less than 160 million years. 3 E (1 e) 1 3e 2 e 4 8 2 T Planets Name Mercury Earth Mars Wi W f W 2 45 pr n W 38Q Icarus, 2010, Volume 209, Pages 786–794 4 45 pr 2 n 4 W E 38Q Maximum Age Million Years 1,948 154 1,419 Wi = Initial rotation rate Wf = Final rotation rate p = Density, kilograms per cubic metre R= planets radius, metres N = Mean orbital motion e= Eccentricity m = Planets rigidity, Newtons per square metre E = Ratio for large eccentricity orbits 11. Griessmeier’s Formula J. M. Griessmeier gives a formula 18, 19 we can use to determine tidal locking times. According to his formula the Earth has been orbiting the Sun less than 16 million years. R3 M 4 (Wi W f ) p T Q p M GM 9 p s Qp 3Q 2k 2 5 2 d R p 6 Icarus, Volume 209 (2010), Pages 786–794 Icarus, Volume 199 (2009), Pages 526–535 Planets Name Mercury Venus Earth Mars Maximum Age Million Years 1,323 7,237 15 103 Wi = Initial rotation rate Wf = Final rotation rate Mp = Mass of the planet Ms= Mass of the Star Rp = Radius of the planet d= Orbital radius Q = Tidal dissipation factor k = Planet’s love number 12. Cornell University Formula Astronomers at Cornell University have devised a formula 46 we can use to arrive at this value. By doing these calculations we can determine the maximum time that these planets have been orbiting the Sun. 3 GmR5 T k sin( 2 ), 2 a6 1 , tan( 2) Q t MR 2 W T 2 , 3 n C ( A B) 2 , 2 C Planets Name Mercury Venus Earth Mars Jupiter Tidal Locking Time Million Years 28 290 1,800 76,000 400,000 t= Tidal locking time in seconds e = The lag angle T = Tidal torque n = Mean orbital motion A = Satellite's moment of inertia about long axis a = Solid body angular acceleration in dimensionless units B = Satellite's moment of inertia about intermediate axis C = Satellite's moment of inertia about the spin axis W, is the initial spin rate (radians per second) a, is the semi-major axis of the motion of the planet around the sun Q, is the dissipation function of the planet. G, is the gravitational constant M, is the mass of the Sun m, is the mass of the planet k2, is the tidal Love number of the planet R, is the radius of the Sun. m = Precession of perihelion, degrees per day http://astrosun2.astro.cornell.edu/academics/courses/astro6570/Tidal_evolution.pdf 12. Cornell University Formula Astronomers at Cornell University have devised a formula 46 we can use to arrive at this value. By doing these calculations we can determine the maximum time that these planets have been orbiting the Sun. Planets Name Mercury Venus Earth Earth Earth Earth Mars Mars Mars Jupiter Jupiter Locking Time Million Years 28 290 1,800 1,800 1,800 1,800 76,000 76,000 76,000 4,400,000 4,400,000 Maximum Age Million Years 18.68 314.78 1.38 4.31 1.61 0.19 34.03 39.23 7.22 220.09 66.75 Original Day Seconds 8,020 8,400 62,064 10,800 58,000 83,000 62,064 58,000 83,000 17,010 30,052 Current Year Seconds 7,600,530 19,414,140 31,558,150 31,558,150 31,558,150 31,558,150 59,354,294 59,354,294 59,354,294 374,247,821 374,247,821 Current Day Seconds 5,080,320 21,081,600 86,400 86,400 86,400 86,400 88,643 88,643 88,643 35,730 35,730 http://astrosun2.astro.cornell.edu/academics/courses/astro6570/Tidal_evolution.pdf 13. Wikipedia Website Formula The Wikipedia website 48-53 gives another formula we can use to determine tidal locking times. Several universities uphold this on their physics websites. 6a R 10 t 10 mM 2 6 Planets Name Mercury Venus Earth Earth Earth Mars Mars Mars Jupiter Jupiter Tidal Locking Time Million Years 132 884 5,443 5,443 5,443 298,713 298,713 298,713 3,793,047 3,793,047 University of Oklahoma, Physics Department, Wikipedia Hyperlink http://www.nhn.ou.edu/%7Ejeffery/astro/astlec/lec005.html Swarthmore College, Physics Department, Wikipedia Hyperlink http://www.sccs.swarthmore.edu/users/08/ajb/tmve/wiki100k/docs/Tidal_locking.html University of Oklahoma, Physics Department, Wikipedia Hyperlink http://www.nhn.ou.edu/%7Ejeffery/astro/astlec/lec012.html Maximum Age Million Years 88 960 4 5 1 134 154 28 190 58 Original Day Length Seconds 8,020 8,400 62,064 58,000 83,000 62,064 58,000 83,000 17,010 30,052 t = Years a = Planet’s Orbital radius, metres R = Planet’s radius, Metres m = 3 x 1010 m = Mass of the planet, kilograms M= Mass of the Sun, kilograms Santa Barbera University, Physics Department, Wikipedia Hyperlink http://scienceline.ucsb.edu/search/DB/show_question.php?key=1291229393&task=category&method=&form_keywords=&form_category=astronomy&start = Buffalo State University, Physics Department, Wikipedia Hyperlink http://www.physics.buffalo.edu/phy302/topic3/index.html http://en.wikipedia.org/wiki/Tidal_locking 14. Ohio University Formula The Ohio University website 6 a t 10 (m / M ) AU 12 70 gives yet another formula we can use to determine tidal locking times. Planets Name Mercury Venus Earth Mars Tidal Locking Time Years 1,433,709 217,953,706 1,733,312,966 6,548,184,125 Maximum Age Million Years 1 236 5 10 t = Years a = Planet’s Orbital radius, metres AU = Astronomical Unit, Metres m = Mass of the planet, kilograms M= Mass of the Sun, kilograms http://www.astronomy.ohio-state.edu/~pogge/Ast141/Unit5/Lect34_Habitability2.pdf 15. Roberts Formula wCa6 t 3 Im kGM 2 R 5 Planets Name Mercury Venus Earth Mars Jupiter Saturn Maximum Age Million Years 0.04 0.49 0.09 2.40 51.31 4,459.93 Maximum Age Years 42,597 491,841 94,833 2,404,319 51,307,096 4,459,934,721 C is the polar moment of inertia, m is the mass of the planet R is the mean radius of the planet G is the gravitational constant w is the rotation rate I is the moment of inertia a is the orbital radius k is the Love number http://www.lpi.usra.edu/meetings/lpsc2009/pdf/1927.pdf 16. Robuchon’s Formula d 3kGM a dt 2D 6QC 2 5 dt 3kGM 2 a 5 d 2 D 6QC 2 D QC t 3kGM 2 a 5 6 8pa 4 r C 15 Icarus, 2010, Volume 207, Pages 959-971 Planets Name Mercury Venus Earth Mars Maximum Age Million Years 662 3,619 7 51 r is the planet’s current polar radius C is the Polar moment of inertia D is the Semi-major axis of the orbit Q is the tidal dissipation factor G is the gravitational constant a is the Current equatorial radius p is the density of the planet Saturn’s Moon Iapetus Astronomers know that this moon 20 is tidally locked to Saturn. Using formula 1 the time needed would be 4,624 million years. In order to get around this problem astronomers claim that there are deposits of short live radioactive isotopes 21 underneath the moon’s surface. These heated up the planet and changed its elasticity. Such a claim is of course totally unprovable. “While most of the satellites despin rapidly, Iapetus, mainly because of its large distance from Saturn, requires longer than the age of the solar system to despin to synchronous rotation.” 21 Mercury’s orbital eccentricity = 0.205630 Iapetus orbital eccentricity = 0.0286125 This means that Mercury’s eccentricity is over seven times that of Iapetus. Dr Conor Nixon claims that the reason Mercury is not tidally locked is that it eccentricity stops this happening. 22 If this is so, then objects that do not have this obstacle should lock. Since the tidal locking time for the Earth is 1.8 billion years and the age of the Earth is supposed 4.5 billion years, it should be 100% locked. This means that the Earth’s current day length should be 8,766 hours. Evolutionists admit that the moon Iapetus’ eccentricity has never varied: “The time needed for the eccentricity to evolve is much larger than the age of the Solar System, unless the initial eccentricity is very close to its present value. Similar reasoning based on Peale (1999) indicates that the semi-major axis evolution has been negligible over Iapetus’ lifetime. Thus, little dynamical evolution has taken place postdespinning and Iapetus’ present semi-major axis and eccentricity are indicative of its initial state.” 23 Iapetus has locked even though the time needed is greater than the evolutionist’s chronology allows. Planetary Migration To explain how planets like Jupiter, Saturn, Uranus and Neptune formed in the first place evolutionists have invented the theory of planetary migration 24. This would not affect tidal locking times of Saturn, Uranus and Neptune because they are so great. According to this theory these planets formed much closer to the Sun than what they are now, and then later migrated out to their current positions. “In both cases, the initial semi-major axes of Jupiter, Saturn, Uranus, and Neptune are 5.4, 8.7, 13.8, and 18.1 AU, respectively”. 25 Even if Saturn, Uranus and Neptune were this much closer to the Sun it would not affect their tidal locking. We know that planetary day lengths come in pairs: Earth-Mars Jupiter-Saturn Uranus-Neptune 24 10 16 - 24.6 10.5 17 Hours Hours Hours Since Uranus and Neptune are outside the tidal locking zone their day lengths are unchanged. Since Saturn’s orbit is outside the tidal locking influence of the Sun its day length is unchanged. If their day lengths were within one hour of each other from the beginning like Uranus and Neptune, Jupiter’s day length has only changed by one hour because Saturn has been unaffected by tidal locking. This would reduce its age down to less than 60 million years. If the Earth and Mars original day lengths only differed by one hour this would reduce the Earth’s maximum age to 500,000 years. Since the day length of Uranus and Neptune is unchanged we can assume that day lengths were not radically different in the past. If the Earth had the same day length as either of these planets in the beginning how long would it take to slow to its present value of 24 hour [86,400 seconds] day? The Age Of The Earth Earth’s original day length = 23 hours Maximum age = 194 thousand years Earth’s original day length = Uranus current day length [62,063 seconds] Earth’s Maximum age = 1.4 million years Earth’s original day length = Neptune’s current day length [58,000 seconds] Maximum age = 1.6 million years The Age Of Mars Mars’ original day length = 23.hours Maximum age = 7.2 million years Mars’ original day length = Uranus current day length [62,063 seconds] Mars’ Maximum age = 34 million years Mars’ original day length = Neptune’s current day length [58,000 seconds] Mars’ Maximum age = 39 million years The Age Of Jupiter Jupiter’s shortest possible day length = 17,010 seconds Maximum age = 220 million years Jupiter’s original day length = 30,052 seconds Maximum age = 66 million years Evolutionists Admit Major Problems Evolutionists admit major problems in their theories on the origin of planetary rotation. The theory of a magnetic field solving the problem would require the Sun’s field to be more powerful than a neutron star. “The mechanism also provides explanations for the formation of planetary spin, why axes of spin can be tilted, and the lack of angular momentum in the sun. But the magnetic fields that are required are extraordinarily large, being generally greater than those of neutron stars.” 26 John Lowke cites NASA scientist Jack Lissauer’s article saying: “It is difficult for the nebular hypothesis to explain the origin of planetary spin” 27 Thayer Watkins from San Hoses University says that the planets obtained the rotational energy from orbiting debris in the Solar System: “As the proto-planets acquire mass they also acquire angular momenta. The mechanism for the acquisition of angular momentum in the planetary sweep of the ring resulted in rotation periods for the planets that are largely independent of their masses. Jupiter is nearly three thousand times more massive than Mars but its rotation speed is only about sixty percent faster.” 28 “The small level of statistical dependence of rotation period on mass is apparently not due to the correlation of mass with other factors affecting the rotation period. There is an effect of mass on rotation period that arises from the gravitational coalescence and contraction of the material of the planets which could account for the second order level of dependence of rotation period on mass.” 28 “The second order differences in the periods of rotation can be accounted for by the gravitational contractions of the planets. A larger gaseous planet contracts more than a smaller rocky planet and thus its rotation speed increases more.” 29 The Origin Of Planetary Spin If the planets formed by evolution why do they have different day lengths? If a planet derived its rotational energy from the orbital velocity of the surrounding material we would expect that the closer to the Sun the shorter the day length. The material that Mercury accreted from had ten times the orbital velocity/kinetic energy that the material Pluto came from. Pluto’s day length however, is ten times shorter than Mercury. If we compare the day length [seconds] to the orbital velocity [metres/second] there is no relationship. If tidal resonance forces caused the day lengths we would expect the year/day ratio to be less than or equal to one. The year day ratio is the year length [seconds] divided by the day length [seconds]. Planets Name Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto Year/Day Ratio 1.4966 0.9209 365 668 10,540 25,140 41,043 75,062 339,326 Velocity/Day Ratio 48.36 145.68 707.49 3.64 6.81 3.7 5.43 11.88 14.6 The Origin Of Planetary Spin “The origin of planetary rotation and obliquity (inclination of the spin axis with respect to the orbital plane) is an open question.” 30 If matter were hitting a planet it is most probable that it would be random and depending on which side it hits it would increase or decrease the planet’s rotation. Much of the matter would hit at the wrong angle and provide no rotational energy at all. The craters on the Moon and other satellites do not show any special pattern in this area. Sergei Nayakshin 31, 32 has put forward a new theory that the planets formed from rotating gas clouds up to 50 AU from the Sun. Instead of the standard accretion model, he proposes that the planets condensed from individual rotating gas clouds. Because the nebula would be so big with their original density as one kilogram per cubic kilometre, he has to place them at vast distances from the Sun so that they do not overlap each other. After formation they migrate to their current distance from the Sun. Unfortunately the nebulae that the moons of the planets would form from overlap the planets and each other. Exo solar planets have not migrated in this fashion as many orbit very close to their parent star. Jupiter’s Moon Io Europa Ganymede Callisto Orbital Radius Kilometres 421,700 671,034 1,070,412 1,882,709 Cloud Radius Million Kilometres 1,286 1,047 1,531 1,381 The Origin Of Planetary Spin “The origin of these large and coherent planetary spins is difficult to understand (e.g., Dones & Tremaine 1993) in the context of the “classical” Earth assembly model (e.g., Wetherill 1990).” 33 According to Schubert 34 the original rotation rate for satellites in the Solar System was 5 to 10 hours. According to Schlichting 34, 35 the Earth’s original day length was 4 hours. Dr. Lissauer: “The origin of the Solar System is one of the most fundamental problems of science. Together with the origin of the Universe, galaxy formation, and the origin and evolution of life, it forms a crucial piece in understanding where we, as a species, come from.” 36 “However, the growth of solid bodies from mm size to km size still presents particular problems. The physics of inter particle collisions in this regime is poorly understood. Furthermore, the high rate of orbital decay due to gas drag form size particles implies that growth through this size range must occur very rapidly.” 37 “The origin of planetary rotation is one of the most fundamental questions of cosmogony. It has also proven to be one of the most difficult to answer (Safronov 1969, Lissauer & Kary 1991).” 38 “Our various tabulated results are not mutually consistent, because we have considered several possible scenarios of planetesimal mass distribution and giant planet growth. The accuracy of these assumptions is open to some question, but clearly our analysis is more applicable to some planets than to others. For instance, solar tidal forces invalidate all of our results for Mercury and Venus, and it is unreasonable to think that no systematic component exists for the rotation of Jupiter and Saturn.” 39 The Origin Of Planetary Spin Alan W. Harris and William R. Ward: “We discuss briefly the possibility of alteration of obliquity through resonance in Section 3; however, the obliquities of the outer planets must be regarded as an unsolved problem.” 40 Luke Dones And Scott Tremaine: The origin of planetary spins is poorly understood, for several reasons: (i) The spins of several of the planets (at least Mercury, Venus, and Pluto) have been modified by tidal friction, so their primordial spins are unknown. (ii) The planets probably acquired their rotations by accreting spin angular momentum along with mass as they grew from the protoplanetary disk. (iii) The physical parameters of the solar nebula, such as the velocity dispersion of planetesimal amounts of gas and solid bodies, have not been well constrained. (iv) Any model in which the planets form by accreting gas and small bodies predicts that the planets should have nearzero obliquity, and whatever process created the substantial observed obliquities may also have modified the magnitudes of the spins (Harris and Ward 1982, Tremaine 1991, Ward and Rudy 1991). (v) At present, planetary perturbations cause the obliquity of Mars to vary chaotically over a wide range, and the obliquities of the other terrestrial planets may have been chaotic in the past (Laskar and Robutel 1993; Laskar et al. 1993; Touma and Wisdom 1993). 41 The Origin Of Planetary Spin K. Tanikawa And S. Manabe: “In order to calculate the angular momentum acquired by a proto planet, we need models of flux and mass distributions of planetesimals and eccentricity and semi major axis distributions of planetesimal orbits. However, we do not have information on these quantities. Therefore it is very difficult to treat the entire problem of calculating the angular momentum of planets. Here we make a simple assumption and try to obtain a qualitative result on the final angular momentum of planets.” 42 Thierry Montmerle: “There are however four main problems in the above scenario, which have not yet been solved.” 43 “Thus, at present, astronomers are only able to draft general trends without being able yet to further constrain the main steps that allow to go from sub-micron size grain to km-sized bodies, and this is a major problem in particular for theories of the formation of the solar system.” 44 “In principle, the 200 known exoplanetary systems should also give us clues about planetary formation in general, and the formation of the solar system in particular. 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