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Stability of Solid Core Cores in Gaseous Planets
ERIC W. CREW                                                 Fall 1977

If an imaginary planet made of uniform material has a diametrical hole through it and the weight of an object is measured at various points along the hole, the weight will decrease with distance below the surface of the planet until it becomes zero at the center.  This happens because the gravitational pull of the shell of material above any level inside the body sums to zero, and all the pull towards the center is due to the mass of the sphere of material below that level.  In this hypothetical model the mass of this inner sphere is proportional to the cube of its radius, while the gravitational pull at its “surface" is proportional to the inverse square of its radius; so the weight of any object will vary directly with its distance from the center.

It is of interest to note that this does not apply to a terrestrial mineshaft because the core of the Earth is much more dense than the outer layers, and weight actually increases slightly with depth at first.

When an object is exactly at the center of the imaginary planet, the smallest force will accelerate it in the direction of the force; then, as it moves, there will be a gradually increasing gravitational pull tending to return it to its central position.

Taking this a stage further, if the imaginary planet consisted of a solid shell and a solid core, all the rest of the interior space being a vacuum, the core could remain, in theory, at any location inside the shell, since the sum of the gravitational pull of the material of the shell acting on the core would be zero (like the zero electrical forces inside a Faraday cage).  If the shell and core in combination form a planet in orbit about a star, with the core initially in the center of the shell, as soon as the latter encounters some frictional resistance to its orbital motion, it will decelerate slightly, and the core will then move away from its central position due to the inertia of its mass, eventually colliding with the interior surface of the shell.  If the core and shell were in rotation about their common center, as with most planets, then there would be relative linear motion at the point of contact, and frictional heat energy would be produced.

The purpose of this simple theoretical model is to show that in the case of a large gaseous planet with a solid core, it should not be assumed that the core will always remain at the center of the planet.  The situation can be visualized by suspending a weight from a string in a bucket of water and mounting the whole of the apparatus on a turntable.  When it is rotated, the slightest displacement of the weight will cause it to behave like a conical pendulum in which the string makes an angle to the vertical given by cos θ=g/lw2, where 1 is the length of the string, w is the angular velocity, and g is the acceleration due to gravity.  The water surrounding the weight tends to reduce the speed and amount of the displacement, and if the weight is free to rotate independently about its vertical axis, it will eventually attain the same angular velocity as the apparatus, irrespective of its original value.

A solid core surrounded by fluid in a planet may therefore tend to drift away from the central location when the planet as a whole encounters some external resistance to its motion in stellar orbit.(1)  Certain other factors causing displacement of the core are probably far more important and will be discussed later.

As the core moves away from the center of the planet, matter will flow into the space it formerly occupied, and the mass of this material will produce a small gravitational force tending to restore the central position of the core.  Possibly such effects would be detectable in slight wobblings of the planet as a whole, since its center of mass would be disturbed.  Any displacement of the core will produce a centrifugal force away from the axis of the combined rotation, and unless the restoring force is greater than this the core will continue to travel outwards until the forces balance, if an equilibrium condition is to be attained.

This brief introduction is the basis for a closer look at a particular example, Jupiter, where there seems to be considerable evidence that its core, or a part of it, was ejected into an independent solar orbit, becoming the planet Venus.  There are many obvious problems arising from this claim, but these are negligible compared with the problems of devising alternative, satisfactory explanations for the vast mass of evidence about cosmic catastrophes in historical times which has been collected and published in the works of Velikovsky, who is now so well-known and respected by serious students of astronomy that there is no need to quote his books in detail.

If the solid core of Jupiter was, in fact, ejected, it probably emerged as an incandescent body and remained abnormally hot for a considerable time.  The present high temperature of Venus is claimed by some astronomers to be caused by the "greenhouse" effect of solar heating, but this is disputed by many others.  If the high temperature of Venus today is mainly due to remanent internal heat, then the rate of cooling to be expected, especially considering an originally much higher temperature, means that it must have been ejected from Jupiter comparatively recently - perhaps less than ten thousand years ago - as is supported by evidence from mythology.  It then follows that one might expect to see, even now, visible evidence on Jupiter of such a violent event.

There would have been extensive chemical reactions with the gaseous outer regions of the planet as the core emerged, and there would have been a trail of residues of various kinds, polluting the atmosphere and leaving a scar which may still be visible.  A significant comment in relation to this view was made recently by an authority on planetary atmospheres(2) who wrote that "on Jupiter, a steady-state storm is possible. . . . The Great Red Spot may also fit into this picture.  It is difficult at this stage to account for its uniqueness, which may be associated with some unseen surface irregularity or the result of a chance capture of a planetary body."  This is evidently a wild guess, in keeping with the many other unsatisfactory explanations offered by astronomers when they do not conform to the usual view that the Great Red Spot is a complete mystery.

It seems much more likely that the Great Red Spot is the site, not of the capture of some unknown planetary body, but of the ejection of an incandescent core to become a planet, especially as it happens that Venus would fit comfortably into the width of the Great Red Spot.(3)  There are other much smaller Red Spots as well, and perhaps

Venus 12,100 km diameter
Great Red Spot of Jupiter
40,000 km x 13,000 km

these are the sites of falling debris from the ejected core, or secondary ejection sites.  It has been suggested that some comets may have been formed by electrical discharges in the extensive atmosphere of Jupiter, (4) but these would be relatively small and largely gaseous objects, and only the ejection of core materials could account for a body the size and weight of Venus.  The suggestion that some kind of vast explosion of the core took place(s) is as difficult to substantiate in detail as to account for the pieces subsequently coming together again and forming a planet such as Venus, travelling in an independent solar orbit.

Another factor supporting core-ejection is that the initial rotation of the Jovian core could have been reduced or stopped by frictional resistance on its long journey from the center of Jupiter, and the anomalous, low-speed rotation of Venus has not been satisfactorily explained in any other way.

There are widely differing views among astronomers about the existence and size of a solid core in Jupiter, but as the original matter from which the planet formed probably contained 2% or 3% of heavy elements, as in the case of the Sun and most other stars, these materials would be likely to have gradually accumulated at the center of Jupiter.  In addition, such a large planet would act as a cosmic vacuum cleaner, sweeping up dust and debris, which would also work its way into the interior and help to build the core.  The high pressure would liquefy and then solidify many gases, but the slowly increasing central temperatures may have limited this process.(6) An estimate that "Jupiter may have a solid core 40 times as massive as Earth" was recently quoted by a very sober astronomer-(7) and Juergens has estimated a rocky core of sufficient mean density to yield 100 planets the size of Venus, not even counting "wasted" matter. (8)

Of course, if Venus was ejected from Jupiter a few thousand years ago, Jupiter may now be in the process of building up a new massive core.  Many thousands or millions of years may elapse, however, before such a new core acquires sufficient energy to eject itself from the planet.

It may be of interest to note a further comment about the cores of gaseous planets from ref. 7. Mitton writes: "Although we can observe the atmosphere of the giant planets, the mysteries of their internal structure will yield only to theory and model making . . . Recently M. Podolak and A.G.W. Cameron, two planetary scientists working in New York, have assembled a new range of models to describe the structure of the outer planets.  One common feature is that each planet is thought to contain a rocky central core.  This has formed from metallic and silicate crystals that condensed in the interstellar cloud from which our solar system originally rose.  In the case of the terrestrial planets this rocky body is all that now remains, solar heating having driven away the lighter gases.  Jupiter may have a solid core 40 times as massive as Earth.  For Saturn, Uranus, and Neptune the cores are about 20, 4 and 3.7 times the Earth's mass."

The problem of explaining how a body as large as Venus could change its path in a comparatively short time from an erratic and highly dangerous one to the present safe and almost circular orbit about the Sun was initially discussed in Worlds in Collision. (9) Since then, it has been dealt with in other serious studies,(10) one of which also casts doubt on the conventional views of the claimed stability for billions of years of the planets and satellites of the Solar System.(11)

The question of the energy required for the ejection of Venus from Jupiter has also been the subject of dispute, and Sagan estimated that as much as 1041 ergs would be required to attain escape velocity, using this high figure to "prove" that such an event would be impossible.(12)  The figure represents the kinetic energy of Venus travelling at 61 km/s, but it does not allow for the fact that the surface velocity due to the rotation of the periphery of Jupiter near its equator is presently about 13 km/s, and this may assist the ejection process in favorable circumstances.(13)  Also, as it is not necessary for an ejected body to attain the theoretical velocity of escape to infinity in order to achieve a solar orbit, a further reduction of about 25% of the theoretical velocity would be acceptable.  As described later, it is possible that one source of energy continued to propel the ejected core after it left the surface, and in addition some outward force may have been provided by electrical repulsion.

A reasonable estimate for the required velocity relative to the surface is 15-20 km/s, and the corresponding kinetic energy of a body of the mass of Venus would be 6 x 1039 to 1040 ergs.  Some additional energy would be required to propel the core to the surface and through the extensive atmosphere of Jupiter, so we must look for at least 1040 ergs of energy if the core-ejection hypothesis is to be sustained.

The core possesses several forms of energy which may help to propel it from the center.  It rotates with the planet, and if it is displaced from the center the rotation will produce frictional heat, adding to its own store of thermal and latent heat.  The pressure at the center of Jupiter is estimated as about 30 million atmospheres(14) or more(6) so that a considerable amount of energy, accumulated in the processes of compressing, liquefying, and solidifying hydrogen and other gases, would be released as the core travelled into regions of lower pressure.  The temperature of the core of a gaseous planet rises steadily because of gravitational consolidation energy release and the small amounts of nuclear fission energy available from radioactive elements.  It seems most unlikely that the temperature and pressure in the interior of Jupiter would rise high enough to produce nuclear fusion for many billions of years, or that a recent violent nuclear “explosion" with enough energy to have ejected the core of the planet has occurred.

The suggested start of the process of core-ejection is a sudden change in the core at a critical point of pressure and temperature, either of a physical or a chemical nature.  A large proportion of the substance of the core may shrink appreciably, the angular velocity of the core rapidly increasing, while surrounding fluids flow inward to prevent the formation of a void.  The disturbance and frictional heating eventually lead to a local eruption from the surface of the solid core, causing an initial displacement from the center.  The core moves erratically at first, as its rotation changes the position of the eruption on account of coriolis and gyroscopic effects, but it progresses steadily or spirally into the less dense, outer regions of the planet as long as the eruption continues; that is, it moves in directions offering least resistance to its movement.

The diminishing pressure of the surrounding fluid as the core travels away from the center enables the compressed gases in the core to continue to expand and sustain the eruption.

The high temperature of the core decreases as it gives up energy to the surrounding material and converts it into kinetic energy of the core, but the material remains hot enough to provide a powerful propulsive force like that of a rocket engine.  The continual ejection of material from the core steadily reduces its mass, tending to increase its acceleration.

It is most likely that frictional processes would also produce appreciable electrical charging, and that the charge would flow to the surface of the planet and leak away, leaving both core and surface with a charge of the same sign at the point of separation from the surface, causing subsequent repulsion and aiding the ejection.  Discharges of current might also take place to equalize potentials; evidence from mythology suggests such spectacular events on Jupiter in the past, as well as during near-encounters of Venus with other planets.

Estimates can be made of the energy values of some of these items.  If the core is assumed to have been originally about twice the diameter of Venus, and therefore 8 or more times its present mass (a much lower estimate than that in ref. 7), and was rotating at the present angular velocity of Jupiter, [1] its rotational energy would have been 3.5 x 1038 ergs - an insignificant amount compared with the total required for ejection, but more than adequate for a triggering effect.  The amount of heat energy liberated if the temperature of the core fell by 10,000K would be 3.3 x 1039 ergs, assuming a specific heat of 0.2. The most recent estimate(15) of Jupiter's temperature, however, is 300,000K, giving a value for the heat energy of about 1041 ergs, which is several times the amount estimated for ejection.

The energy stored as latent heat and in the highly compressed core materials, largely representing stored gravitational energy from the enormous mass of the whole planet, is also very considerable at the levels of pressure and temperature involved.  No attempt has been made to assess these values, nor the equally difficult problem of the possible values of electrical forces and energy.  However, there seems little doubt that there would be enough energy in total to make it extremely probable that the core of Jupiter was ejected, and the same applies to the cores of Saturn and other gaseous planets.

The suggestion that the solid cores of gaseous planets may be ejected periodically, sometimes achieving independent orbits about the parent star, may solve a very important, long-standing problem in Solar System astronomy: that of the origin of the dense, "terrestrial" planets and satellites.  The large gaseous planets would have the volumes and masses to attract and retain enough heavy cosmic materials to form large cores in much shorter times than would be required for the same masses of solid material to accumulate without this assistance.  It seems likely that many cores may have been ejected from gaseous planets in the Solar System into orbits in which some were destroyed by too-near approaches to the Sun, and that at least one may have collided with a former dense planet to produce the asteroid belt.(16)

NOTES AND REFERENCES

1.         Normally this resistance is negligible, but it is possible that at a certain time the presence of cosmic dust, excessive numbers of meteorites, powerful electrical and magnetic forces, or other external interference may have changed this stable position.  Velikovsky has suggested that an explosion in Saturn may have been the cause of the later ejection of Venus from Jupiter, but the detailed discussion of this is outside the scope of this paper.

2.         G.E. Hunt, "Jupiter," New Science in the Solar System, P. Stubbs, ed., (IPC Magazines, London, 1975, pp. 42-50).  Cp.  Pensee I (May, 1972), p. 23.

3.         See Pensee II (Fall, 1972), p. 46 - letter to the Editor from Ragnar Forshufvud.

4.         E.W. Crew, "Problems of Electricity in Astronomy," SIS Review (Jan., 1976), pp. 8-9.

5.         R. Forshufvud, "The Jupiter Puzzle," SIS Review (Spring, 1976), pp. 21-24.

6.         Z. Kopal, in The Solar System (Oxford Univ.  Press, 1972, p. 1 1), states: "the pressure at the centre of Jupiter would be expected to exceed 1013N/m2,, (100 minion atmospheres - over 3 times the value given in ref. 14).  He continues: "Under the pressures prevailing in the Jovian or Saturnian interiors, hydrogen Can remain in the solid (metallic) state up to temperatures near 7500K, but no higher; this is probably the limit which their external temperature cannot exceed." Kopal does not say what would happen when heat continues to be generated in the interior of the planet, as it would, but he seems to imply the possibility of an explosive or disturbed condition.

7.         S. Mitton, "Saturn and Beyond," New Science in the Solar System, pp. 50-51.

8.         R.E. Juergens, "The 'Bulk Chemistries' of Venus and Jupiter," KRONOS II, 1 (August, 1976), p. 12 - "In the 1920's, Harold Jeffreys calculated that Jupiter might have a rocky core of some 400 Venus-masses." - Ibid.

9.         I. Velikovsky, Worlds in Collision (N.Y., 1950), pp. 384-385, 371; also Yale Scientific Magazine (April, 1967), p. 15.

10.       See the articles authored and co-authored by Chris S. Sherrerd, Lynn E. Rose, Raymond

C. Vaughan, C.J. Ransom, and L.H. Hoffee in Velikovsky Reconsidered (N.Y. and London, 1976), Part 111.  See also A. Hamilton, "The Circularisation of Planetary Orbits," SIS Review 1:4 (Spring, 19 77), pp.  I 1-1 3.

11.       C.J. Ransom, "How Stable is the Solar System?" Ibid.; also see Robert W. Bass, " 'Proofs' of the Stability of the Solar System," Pensee VIII (Summer, 1974), pp. 21-26; Idem, KRONOS II, 2 (Nov., 1976), pp. 27-45; R.W. Bass, "Did Worlds Collide?" Pensee VIII, pp. 9-20; R.W. Bass, "Can Worlds Collide?" KRONOS 1, 3 (Fall, 1975), pp. 59-71.

12.       Pensee VII (Spring, 1974), p. 37.  Sagan's statement was made at the San Francisco meeting of February 25, 1974, reported in Pensee.  He also argued that at least 10% of this energy would go into heating the ejected body.  No scientific reason for this statement was offered, and in fact energy almost certainly would have been obtained from the ejected body by cooling, as described in this paper.

13.       If Venus was ejected from Jupiter, then the rotational speed for the latter body was most likely even greater, prior to ejection, than it is today.  See YSM, op. cit, p. 14 and C.J. Ransom, The Age of Velikovsky (Fort Worth and Glassboro, 19 76), p. 108.

14.       This information is included in the comprehensive article on Jupiter in the Encyclopedia Britannica.  For example, the escape velocity is specified as 61 km/s (agreeing with other reference books), and the size of the Great Red Spot is given as 40,000 km x 13,000 km. (The diameter of Venus is 12,100 kin.) The article states that the interior pressure in Jupiter would cause matter to be ionized.  I take this to mean that outer electrons of atoms would be "squeezed out" and would then migrate to the surface of Jupiter, possibly aided by frictional charging effects.  Most of the free electrons would be neutralized by positively charged cosmic-ray particles, and some would leak away by attachment to small particles in the atmosphere, which would be repelled from the planet.  The core would thus acquire a massive positive charge, and in its subsequent near-encounters with other cosmic bodies extensive discharges would take place.

15.       This is based on a Tass report about a meeting of astronomers in Russia on June 9, 1977, which was briefly reported in some English newspapers the following day.  For instance, the Daily Telegraph of June 10 stated that "Jupiter is gradually turning into a second Sun and, barring human interference, will blaze out as a star in about 3,000 million years . . ." The report in the Guardian stated: "Far from dying, [Jupiter] is in a state of flaring up.  Temperature in the centre of the planet reaches probably 300,000 degrees on the Calvin scale and continues growing."  The Guardian published a letter the next day headed "Hot property" and stating: "I daresay Calvin did preach 'fire and brimstone' but you meant to express the temperature of Jupiter in degrees on the Kelvin scale."

16.       It is generally thought that the total mass of the asteroid belt is too small to support the idea that it arose from the breakup of a planet, but the following press report (No. 16178 dated June 23, 1975) from the Novosti Information Service disputes this: "Professor Elena Guskova of Leriingrad has calculated the dimensions and mass of the hypothetical planet Phaeton which once revolved round the Sun between Mars and Jupiter.  Basing herself on the study of the magnetic properties of meteorites, she proved that the 'lost' planet was somewhat smaller than the earth, but was hundreds of times bigger than the moon.

"Phaeton, as most astronomers believe, was destroyed in a space catastrophe.  It split as a result of an internal explosion or celestial collision and formed a belt of socalled small planets - asteroids and a multitude of meteorite flows.

"After studying over a thousand samples of meteorites from Soviet and foreign collections, Professor Guskova noted that among the multitude of insignificantly small magnetic fields, one always had the same magnitude and direction.  Professor Guskova considers this common magnetic, with a force of 0.2 oersteds, to be a residue of Phaeton's magnetic field."

[1].  The use of the present angular velocity figure is basically a calculation convenience.  "The conservation of angular momentum requires that Jupiter slowed in its rotation upon ejecting Venus; therefore.... it would be improper to calculate the conditions for escape on the basis of the present (resultant) angular momentum or speed of rotation of Jupiter." see Yale Scientific Magazine (April, 1967), p. 14. - The Ed.

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