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KRONOS Vol VI, No. 2
THE GRAVITATIONAL-ELECTROMAGNETIC EFFECTS OF ULTRAMASSIVE OBJECTS ON THE SOLAR SYSTEM
MICHAEL SIMON BODNER AND MICHAEL E. BRANDT
For two and one-half centuries the orbital mechanics of Newton and Kepler has provided astronomers and astrophysicists with an almost perfect explanation of the motion of celestial bodies in the solar system. During this period, the precession of the orbital aphelion of Mercury was the only major phenomenon that could not be satisfactorily explained by Newtonian gravitation. After years of scientific speculation, this anomaly was finally incorporated into the Newtonian scheme by Einstein's general theory of relativity.(1) This situation is indicative of the paramount position the concept of gravitation has in astrophysics. Gravitation, after all, is presumed to be the molder of galaxies, and its influence extends to the deepest recesses of the universe. It contains within it the capacity to build star systems, or swallow all matter and energy in its vicinity, as in the case of a black hole.
In the past two decades, a cosmological influence not previously considered has arrived on the scene as a competitor to gravitation. The forces associated with electric and magnetic fields are now recognized as factors in the mechanics of the solar system, as well as in galaxy formation. Even though the electromagnetic force is 1039 times the gravitational force,(2) its short range had always precluded it from being accepted as having a serious influence on the motion of heavenly bodies. However, solar system phenomena such as the inferred huge electric charges of the Sun and Jupiter, the solar wind, geomagnetism, the radio frequency emissions and spectacular electromagnetic pyrotechnics of Jupiter,(3) have provided scientists with years of data for studying gravitational-electromagnetic interactions. Astrophysicists are also beginning to understand the effects of weak, extensive fields upon the geometry of galaxies, as well as their involvement with massive objects such as black holes, neutron stars, pulsars, and white dwarfs.(4) We will return to this topic briefly in the last section.
In this paper we shall speculate about the possibility of an object of this type travelling at high speed, in or near our solar system. We will also describe the possible effects that an interaction of this type may have upon a planet, or upon the solar system as a whole, depending on the trajectory of the object in question.
THE POSSIBILITY OF PLANETARY ENCOUNTERS WITH ULTRAMASSIVE OBJECTS
The physics and mathematics of objects that produce impact craters on the Moon, Earth and inner planets are thought to be fairly well understood by astronomers.(4a) These objects are debris, asteroids, and comets travelling in highly eccentric orbits. Utilizing simple collision physics, the mean free times between collisions can be calculated. This theory supposedly accounts for the number of craters on the Moon, Mercury, and Mars. It is also used to arrive at approximate collision probabilities. Thus, scientists have been able to estimate the ages of some recent Earth impact craters. Carl Sagan has used this approach, (5) along with some modifications based on the classic collision theory of Ernst Öpik,(6) to predict that an object the size of an average comet would impact the Earth once in 3 x 107 years - a very tiny probability indeed. This is as expected, when you consider that we are attempting to describe the odds that a ball, approximately the size of the Moon, would strike one of 30 objects stretched out over a 10 billion kilometer diameter circle.
According to Sagan, the probability of collision increases proportionately as the square of the number of Earth radii between the two objects under consideration. In this case, we are no longer referring to the physical interaction as a "collision", but rather an "encounter". For example, consider the probability of an encounter between the Earth and a massive object whose shortest distance of approach to the Earth is 25 million miles. Using Sagan's argument it is apparent that the probability of an encounter approaches one per year, but then we are talking about a very large class of "encountering" objects.
If we narrow this class to ultramassive objects such as neutron stars, black holes, pulsars, or white dwarfs, this probability will decrease. Appendix I discusses this topic speculatively. From these considerations, we believe that there is a "respectable" chance of such an encounter occurring over a period of several millennia. In the next section, we discuss the genesis of such encounters, and their possible effects on planets in the solar system.
PHYSICS OF ULTRAMASSIVE OBJECT ENCOUNTERS
Massive objects hurtling through space near our solar system could be produced by one of the many violent yet normal phenomena that occur regularly in our galaxy. The most likely candidates are star explosions (supernovae) that would generate enough momentum to cast a massive object outward at a reasonable fraction of the speed of light. The energy output of the average supernova is 105 ergs, the approximate amount of energy produced by the Sun in its lifetime of 10 billion years.(7) Thus, a typical supernova shines with the light of a billion Suns!
Supernovae are classified into two different types according to certain parameters of their energy outputs. It is believed that type II supernovae occur once in 70 years in the Milky Way, and that type I supernovae occur once every 360 years. Some astronomers argue that the true frequencies must be greater since we do not observe the occurrence of all supernovae.
Consider a supernova that causes an ejection of a piece of its high density neutron core. Even though the event has occurred many light years from the solar system, such an object could interact with our star group. Another example would be the massive explosion of one star of a binary group. Such an event would impart significant momentum to the other star and both the neutron core of the exploded star and the other star would recede from each other, possibly at velocities close to light speed. In this event we have two possible candidates that might enter or closely approach the solar system. There are many such combinations of these events and similar astronomical occurrences taking place regularly in our galaxy that could cause very massive, charged bodies to travel at extremely high speeds near the solar system.
This idea is not a new one.(7a) In 1974, Lynn E. Rose and Raymond C. Vaughan, in considering alternative solutions to the energy problem involved in a cataclysmic sequence of planetary orbits, noted that "much attention has been given recently to the possible existence of black holes in the universe; it would be worth investigating the effects of a black hole passing through the solar system - or even passing directly through Jupiter". And, again in 1974, within the
context of discussing the problem of orbital retrocalculation and projection, Lynn E. Rose had this to say: "The considerable success that modern astronomers have enjoyed in predicting planetary positions years in advance has eroded their caution. They forget that such predictions work out only if the present factors affecting the orbits are unchanged. If a black hole or other massive body passes through the solar system and near Earth, then to say the very least those calculations and predictions will have to be done over."
Eyewitnesses of the Tunguska Event that occurred in Siberia on June 30, 1908 described a hurtling object as a bright blue "tube" that levelled an entire forest, leaving behind it a fiery tail and thermal radiation. Speculation as to the cause of the event arose since no crater or meteoritic material could be found at the site. Due to the pattern of flash burning and searing of trees, and the throwdown path, several physicists have suggested that a small black hole travelling at low velocity caused the destruction.(8) This black hole is believed to have been molecular in diameter, with a mass of approximately 1020 to 1022 grams, the mass of a large asteroid. It has also been recently repostulated that a 10-kilometer wide asteroid travelling at 25 kilometers per second impacted the Earth, and cast enough meteoritic material into the atmosphere to cause the extinction of the dinosaurs 65 million years ago.(9)
From a physical point of view, the problem of collisions or encounters can be treated in a first approximation as a Rutherford scattering of neutral, nonmagnetic point masses.(10) In the Rutherford experiments, positively charged alpha particles were "shot" at a gold foil. These particles interacted with the positive nuclei in the foil and were deflected through it within some solid angle. The "missiles" and targets both have equal charge, and thus repel. In gravitational scattering, missiles and targets would attract each other. The deflection mathematics would therefore be similar to the Coulomb repulsion in Rutherford scattering.
In the gravitational case, where the bodies are assumed to have neither net charge nor significant magnetic fields, we must examine the so-called "tidal" effects of an encounter. Assume that the missile was a neutron star with a diameter in the 10 kilometer range, that its mass was approximately twice that of the Sun, and that the target was one of the planets of the solar system. Immense upheavals in the planet's physical structure and orbital path would result, depending on the distance of closest approach between the two objects and their relative velocities. Figure 1 is an illustration of the suggested scenario.
[*!* Image] Figure 1. New Orbital Path Resulting from Momentum/Energy Transfer (Schematic not to scale).
In the case of a rapidly moving massive object whose distance of closest approach is designated R2, the tidal force could be powerful enough to create a new planetary axis, extract a fragment that might later become a moon, fracture crusts, cause massive tidal waves, etc.
Notice that the tidal effects we are referring to are different from the tidal effect of the Moon upon the Earth. The latter results from the differential gravitational force exerted on the Earth at varying points by the Moon. The inverse-cubed relationship of this force results from the relative size of the Earth and Moon, and the distance between them . The Moon "pulls" more on the side of the Earth closest to it, producing the tidal bulges on opposite sides of the Earth.
To subject these events to a mathematical analysis,(10a) let us use the gravitational force exerted between the Moon and the Earth to define a standardized unit of lunar gravitational force. We shall refer to this as the "Lunar Gravitational Standard" (LGS). This force is defined by:
FG = (G Me Mm)/R2 = 1 LGS
where G is the gravitational constant, Me and Mm are the masses of the Earth and the Moon respectively, and R is the radius of the Moon's orbit about the Earth. Since the Earth's mass is constant. let us define GMe as the proportionality K, and redefine the symbol Mm to be simply M. Then we have:
1 LGS = KM/R2
For the sake of argument, let us consider a rapidly moving massive object that is one million times the lunar mass. This is an object approximately 12,280 times more massive than the Earth (the Sun is 329,390 times Earth mass for comparison). If the distance of the object from the Earth at a particular instant is 1000 R, that is, one thousand times the distance to the Moon, or roughly 400 million kilometers, the gravitational effect upon the Earth would be:
T = (K . 106M)/((103)2 R2)=KM/R2 = 1 LGS
equivalent to one lunar gravitational standard. If the object were 100 lunar orbital radii away from Earth, the gravitational effect would then be:
T =(K . 106M M2)/((102)2 R2) = K .100M/R2 = 100 LGS
or one hundred times the lunar gravitational standard.
Notice that 100 lunar orbital radii is a little over one-quarter the distance separating the Earth and the Sun, and can hardly be considered a "near encounter". However, the effects of such an approach would cause massive tidal waves and earthquakes, and serious damage to the Earth's crust. Table I provides calculations of the gravitational effects at distances of 400 million kilometers (1000 R), and 40 million kilometers (100 R), for four different supermassive objects. Note that there are many different kinds of each object in the table, with different masses. It is readily apparent that if a neutron star came anywhere near the solar system, it would have extremely profound effects. We shall elaborate further upon this paper
Figure 2 illustrates a possible geometry of interaction between the Earth and a rapidly moving massive object. In this configuration the object would produce its effects in the upper half of the circle which represents a cross-section of the Earth in the plane of the object's trajectory. We have constructed a normal line from the center of the circle to a point on the object's straight line path (length referred to as rm ). We have chosen this trajectory for simplicity of calculations. Two other lines have been drawn on either side of the normal, extending from the circle's center to the object's trajectory line, each 2rm in length. The angle formed between these two lines is 120 degrees and the portion of the Earth's circumference that is subtended by this angle is one-third of its entire circumference, or approximately 13,363 kilometers. As the object traverses the distance between the chosen points A and C, the gravitational force that it exerts will affect the Earth between points D and E. For an object of any mass, the time that it takes for the effect to pass from D to E depends on the velocity of the object and its closest distance of approach to the Earth (rm). The distance between A and C is:
2 . sqrt([ (2rm)2-rm2])
If we choose rm to be equal to 100 R (40 million kilometers, or 100 times the distance between Earth and the Moon), then AC is:
2 R . sqrt((200)2 - (100)2) = 346.41 R = 138,550,000 km
If we then set the object's velocity at one-tenth the speed of light (30,000 km per second), the time for the object to travel the distance AC is:
1.3855 x 108/(3 x 104) =~ 4618 seconds
This is also the time it would take for the effect to travel from point D to point E on the Earth. The effect could be highly variable depending on the rigidity of the Earth, on the object's mass, and the exerted forces.
[*!* Image] Figure 2. Earth Effect Geometry (Schematic, not to scale)
If we assume the Earth to be a non-rigid body comprised of concentric shells of varying density, the atmosphere, hydrosphere, and crust will bulge along the line of centers between the ultramassive object and the Earth. This gravitational effect will dominate substantially over the tidal effects caused by the Moon, and the bulge formed may "roll" across the Earth as it "tracks" the ultramassive object across the heavens. If we consider the Earth a rigid, uniform density object, the gravitational effect of an ultramassive object would most probably cause either orbital path alteration, momentum transfer, or flipping effects, and not shape distortion. The bulging/ flipping possibilities are schematized in Figure 3.
[*!* Image] Figure 3. Bulging/Flipping Effect (Schematic, not to scale)
Table 2 provides calculations of the time of the effect for variable rm and fixed velocity (30,000 km per second). Note that if the object's closest distance of approach to the Earth is 20 million kilometers (50 R) its presence would affect one third of the Earth's circumference in about 38.5 minutes (2309 seconds). Tables 3 and 4 provide calculations for two fixed values of rm with variable object velocity. Note that in Table 3 for object velocities very near, but less than the speed of light, the effect over one third of the circumference would occur in approximately 7.5 minutes (less than 461 seconds). Thus, if the object was very massive and the forces therefore very great, the Earth would probably be destroyed somewhere in that range of minutes.
In this paper we have speculated about the possibility of a very massive object such as a neutron star, black hole, or white dwarf passing through or near the solar system. We have also performed several simple calculations to show the possible physical effects a near planetary encounter might have. One of the most important results obtained is indicated in Table 1. If a neutron star of radius 10 km and twice the solar mass passes within 400 million kilometers of the Earth, the relative force exerted is 53.6 times the force exerted on the Earth by the Moon (which we are referring to as the "Lunar Gravitational Standard"), and if the object's closest distance of approach is 40 million kilometers ( 100 times the distance between the Earth and the Moon) the force exerted by it upon the Earth is 5360 times the force exerted by the Moon upon the Earth (one LGS).
This hypothesis could serve as an explanation of several "inexplicable" phenomena of the solar system. Why does the Sun rotate so slowly? With the existing mass and radius of the solar system, the Sun's angular momentum should be such that it rotates in several hours as opposed to its present rotation of 24.6 days. The Sun contains over 99 percent of the mass of the solar system, yet it has less than 3 percent of its angular momentum. Two possible explanations have been advanced for the apparent lack of conservation of angular momentum in the solar system. One theory is that the solar system lost a large percentage of its original mass. The other theory asserts that a large force slowed the Sun's rotation to the present rate. An ultramassive object with mass comparable to that of the Sun would be a likely candidate for the latter theory.(11)
Consider the rotation of Uranus. This planet is tilted so that the axis of rotation is almost in the plane of its orbit about the Sun.
Uranus therefore rolls like a barrel with its five moons circling above. This is a highly unusual planetary motion since most planets have rotational axes approximately perpendicular to the plane of their orbits about the Sun. It is possible that a rapidly moving massive object whizzed by Uranus at some time and transferred momentum to the planet causing it to flip on its side.(12)
There has been much speculation concerning the origin of Pluto. Astronomers have difficulty understanding why such a tiny planet is near the outer giants of the solar system. Noting that Pluto is approximately the same size as Neptune's moon Triton, it is conceivable that the gravitational force of one of our proposed objects extracted Pluto from a moon-like orbit about Neptune, or perhaps from Neptune itself, which caused Pluto to travel away from the Sun until it fell into the Sun's gravitational well and established its own orbit.(12a) Our theory can also be used to explain the origin of our Moon, since it could have been a moon of one of the outer planets that was sent sprawling by a massive object inward toward the Sun where the Earth captured it. The theory could also account for retrograde motions, the asteroid belt, and the origin of planetary rings. Also, if the ultramassive object were charged it could transfer some of its charge to a planet, and thus account for the inferred very large charge distributions of Jupiter and the Sun. In fact, if a large tidal bulge was jarred loose from one of the outer giants by an ultramassive object, and possessed a trailing tail of debris and gases, it might appear as a comet to an Earth observer. It is most interesting that speculation concerning the occurrence of such an event could account for many of the phenomena of the solar system that have been longstanding mysteries to us. If the universe is as violent and dynamic as modern astronomers propose, then the possibility of the occurrence of this and similar type events should serve to invite additional speculation and more serious study of these matters.
. . . to be continued.
This Appendix serves as speculation on the possibility of a rapidly moving massive object entering a volume sphere of solar system radius, utilizing physical and geometrical arguments.
The Milky Way has a volume of approximately 2.4 x 1013 cubic light years with an average of one star per 200 cubic light years (refer to Appendix 2 for calculations).(13) There are therefore about (2.4 x 1013 / 2 x 102) = 1.2 x 1011 stars in the Milky Way. An appreciable percentage of these are second generation stars arising from large numbers of supernovae of the first generation stars. The supernovae remnants probably formed three major types of objects: binary stars, stars that would eventually have planetary systems, and stellar debris. Let us assume that 75 percent of the stars in our galaxy are second generation objects. Thus, there are approximately 90 billion of these altogether. It is estimated that half of these are binary stars; while the other half, for the sake of argument, are mostly single stars like the Sun (thus ignoring the small proportion of triple or larger star systems). Can we infer that since the supernovae of first generation stars produced three different major classifications of objects, that there are approximately 45 billion binary stars, 45 billion single stars, and 45 billion pieces of debris in the Milky Way? Assuming that these numbers are approximately correct, we now wish to estimate the percentage of the debris objects that are supermassive.
For the sake of argument, let us assume that 10 percent of this debris is supermassive.(14) These numbers would then suggest there are approximately 4.5 billion massive objects distributed throughout the Milky Way all travelling in random directions at reasonably high velocities. If we then assume a homogeneous distribution of these objects, there are (4.5 x 109 / 2.4 x 1013) = about one massive object in 5000 cubic light years. This figure needs to be modified since there are probably a higher number of massive objects in a dense volume of stars at the center of the galaxy.
We could treat the distribution as if it were an ideal gas in a certain large volume, with the velocities of the objects distributed in a Gaussian fashion,and use statistical thermodynamics to compute the probabilities of finding objects in a certain velocity range, or in some tiny volume, but these methods would be extremely tedious for this application, and probably not very reliable. Let us suggest that additional research in these areas is indicated, and that on an intuitive basis we believe there exists some appreciable probability of a rapidly moving massive object coming within a volume sphere containing our solar system with radius 5 billion kilometers in some fixed time frame, i.e., several millennia. We intend to develop this in some detail in a forthcoming paper.
*No definitive figure for the volume of the Milky Way presently exists.
An approximate volume of the Milky Way is computed in this appendix. Figure 4 is a schematized cross section of the galaxy which serves to represent the dimensions we are considering. We shall treat the inner portion of the galaxy as a sphere of radius 2500 light years. The entire galaxy is 100,000 light years in diameter, and we shall also assume the height of the disk portion to be 3000 light years. We will compute the volume of the entire disk as we would a flat cylinder. From this we subtract the cylindrical contribution in the sphere, then add the volume of the sphere:
For comparison let us calculate the volume in light years of a sphere of solar system radius. There are 9.5 x 1012 kilometers per light year, therefore 8.57 x 1038 cubic kilometers in a cubic light year. The volume of the solar system (5 x 109 kilometer radius) is therefore:
Therefore there are:
in a sphere of radius 5 x 109 km.
[*!* Image] Figure 4. Milky Way Schematic
REFERENCES1. C. M. Will, "The Confrontation Between Gravitational Theory and Experiment," in General Relativity - An Einstein Centenary Survey, edited by S. W. Hawking and W. Israel (Cambridge, 1979), pp. 55-57.
2. D. Halliday and R. Resnick, Fundamentals of Physics (N. Y., 1974, revised edition), p. 428.
3. E. C. Stone, et al., Science, 206 (Nov., 1979), pp. 925-996.
4. N. Calder, The Violent Universe (N.Y., 1979), pp. 41,51, 52.
4a. But cf. the remarks by Ralph E. Juergens in KRONOS V:2 (Jan., 1980), pp. 74-75.
5. C. Sagan, Broca's Brain (N. Y., 1979), pp. 320-324.
6. E J. Opik, "Collision Probabilities with the Planets and Distribution of Interplanetary Matter," Proceedings of the Royal Irish Academy, 54 (1951), pp. 165-199.
7. M. Zeilik, Astronomy, The Evolving Universe (N. Y., 1976), pp. 392-394.
7a. Lynn E. Rose and Raymond C. Vaughan, Pensee IVR Vlll (Summer, 1974), p. 33; Lynn E. Rose, KRONOS 11:4 (May, 1977), p. 59; [also see the letter by Justin M. Miller, Sr. in The Washington Star (Dec. 9, 1979) - LMG]
8. A.A. Jackson and M. P. Ryan, "Was the Tungus Event due to a Black Hole?", Nature, 245 (Sept., 1973), pp. 88-89; J. O. Burns, G. Greenstein, and K. L. Verosub, "The Tungus Event as a Small Black Hole," Monthly Notices, Royal Astronomical Society 175 (1976), pp. 355-357; J. Baxter and T. Atkins, The Fire Came By (N. Y., 1976), Chapter Nine; J. Stoneley, Cauldron of Hell: Tunguska (N. Y., 1977), Chapter 6.
9. R. Kerr, "Asteroid Theory of Extinctions Strengthened," Science, 210 (Oct. 31, 1980), pp.514-517, Cf.Science News, 115(6/2/79) p.356;Science News, 117(1/12/80) p. 22. According to The Washington Post (1 /6/80), p. A5 "Before embracing the asteroid collision theory, (Luis) Alvarez said, he tried out dozens of plausible theories that might also explain mass extinctions. He said his favorite explanation was that Jupiter suffered a partial explosion that bathed the earth in hydrogen, killing the animals by depriving them of oxygen." The date of the proposed dinosaur extinction may be subject to dispute on radiometric and paleontological grounds ~ see KRONOS 111: 1, pp. 3-17 and KRONOS 11:2, pp. 91-100.
10. H. Goldstein, Classical Mechanics (N. Y., 1965), pp. 81-92.
10a. Note that we are here discussing the classical Newtonian gravitational interaction. A discussion of the contribution of inverse-cubed "tidal" terms is left for a later paper.
11. R. T. Dixon, Dynamic Astronomy (N. Y., 1975), p. 203.
12. D. Goldsmith, The Universe (N. Y., 1976), pp. 325-327.
12a. Cf. R. S. Harrington and T. C. Van Flandern, "The Satellites of Neptune and the Origin of Pluto," KRONOS V 2 (Jan., 1980), pp. 48-56.
13. T. L. Wihart, Journey Through the Universe (N. Y., 1978), pp. 259-271.
14. The authors believe that almost all of these objects are ultramassive based on considerations from special and general relativity and the high energy outputs of supernovae.