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ELECTROMAGNETIC-GRAVITATIONAL COUPLING PHENOMENA IN THE SATURN RING SYSTEM
MICHAEL E. BRANDT AND MICHAEL SIMON BODNER
The Voyager I encounter with Saturn provided space scientists with more data about the gas giant than that which was known for three hundred years.(1) Before the Voyager I mission, two main theories dominated scientific thought concerning the origin of the ring system. One theory held that a moon or other small body wandered too near to Saturn's surface, causing it to be ripped apart by tidal forces. This material consolidated into a large thin disk having bands and gaps. Four distinct bands were observed to exist: A, B, C, and D (in order of decreasing distance from Saturn). The largest gap (the Cassini Division) was believed to be about 3,000 miles wide and was located between the A and B rings.
The rings, consisting of ice particles ranging in size from fine dust to large boulders, lie within a specified radius from Saturn referred to as the Roche Limit.(2) According to classical orbital mechanics, if an object is in orbit about a larger body, whose density is approximately equal to that of the smaller body, it will be broken apart by tidal forces exerted upon it if the smaller body approaches to within 2.4 times the larger body's radius. This result assumes that electromagnetic forces holding the small body together are negligible, i.e., the tensile strength is negligible.
Another theory concerning the origin of the Saturnian ring system posits that they formed from the debris left over after the contraction of the protoplanet at the time of Saturn's formation. This debris collapsed into a thin disk about the equatorial plane due to gravitational forces.(3)
Before Voyager, gaps in the ring system, such as the Cassini and Encke Divisions, were believed to result from gravitational resonances with Saturn's known moons. This theory asserts that a ring object orbiting in one-half the period of a moon would be pulled out of that orbit into a higher one. For example, the Cassini Division is devoid of objects since Mimas' gravitational resonance has an orbital period twice as large as Cassini Division particles would have.
The gravitational resonance idea held up fairly well until Voyager's data began pouring in. Photos sent back from the robot spacecraft revealed that the three classic rings, A, B, and C, were actually divided into hundreds of ringlets. Also, the Cassini Division was not empty; rather it consisted of four broad rings bounded by two clearly delineated gaps. These discoveries struck a devastating blow to the belief that gravitational resonances are the sole cause of Saturn's rings.
One of the most exciting findings of the Voyager mission was the discovery of the structure of the (outermost) F ring. This is actually three separate rings, two of which are narrower than the third, and appear to be interwoven and at places kinked. Another interesting discovery was the baffling "spokes" within the rings. These are radial, fingerlike bands of darkness or brightness (depending on how they scatter sunlight, and the direction of observation) that sweep randomly across huge areas of the rings.
From the new data, it is apparent that Newtonian gravitational mechanisms are not sufficient to explain all of the observed phenomena. Even the most conservative orbital mechanician must now look to other forces, most likely electromagnetic, to explain the Voyager data.
In the remainder of this paper we wish to speculate upon the origins of the ring system, the F ring, and the radial spokes. We will do so from an electromagnetic/gravitational point of view. These speculations are tentative since all data from Voyager I have not been fully analyzed
II. SPECULATIONS ON THE ORIGIN OF THE RING SYSTEM
Why is Saturn's ring system a very thin circular disk about the planet's equatorial plane? If the ring resulted from the breakup of a satellite, followed by consolidation due to gravitational effects, it is likely that it would not be as flat and thin as present data reveal. Saturn, in this case, might resemble a miniature Milky Way Galaxy when viewed edge on. Thus, there would probably be appreciable amounts of matter above and below the equatorial plane of the planet.
Let us consider for the moment that all particles within the rings have either a positive or negative net charge. This could have resulted from electrostatic interactions among the objects after the breakup of a satellite that strayed too close to the planet. The magnetic force exerted upon each particle due to Saturn's earthlike magnetic field is greatest in the equatorial plane of the planet. The magnetic force on a charged particle is given by the vector cross product equation:(4)
F = QvxB = QvB sin[q] (1)
where Q is the net charge on the particle, v is the particle's velocity, B is the magnetic field, and q is the angle between the v and B vectors. Figure 1 is a schematic diagram illustrating the planet's field lines (only two shown for clarity) and ring system. Notice that the angle between the plane of the rings (which contains the v vector) and the field lines is 90 degrees. Thus, the magnetic force on each particle in the ring is a maximum:
F^ = QvB (2)
This holds true since the sine of 90 degrees is unity. F^ is the magnetic force at 90 degrees, and occurs when v and B are perpendicular to each other.
Any charged particles above the plane of the rings will be such that the angle between v and B will be something other than 90 degrees. This would introduce a vector component of force that would tend to "push" the particle toward the plane of the rings (the equatorial plane of Saturn). Thus it appears the flatness and thinness of the rings can be explained by assuming all particles inside the rings have net charge, and the magnetic force on each particle causes the rings to be in a minimum energy configuration.
[*!* Image] Figure 1. Saturn's Magnetic Field and Rings.
[*!* Image] Figure 2. Mass Spectrograph Apparatus.
A possible explanation for the circular structure of the rings utilizes an electromagnetic model similar to a mass spectrograph. Figure 2 illustrates this effect. Charged particles of net charge Q = nqe (qe is the elemental electronic charge) are injected into a vacuum chamber having a magnetic field going down (into the page). The magnetic field would exert a force at right angles to the direction of motion of each injected particle. The equation describing these forces is Newton's law in the form:
F^ = mv2/r = QvB (3)
where m is the mass of the particle, r is the radius of the particle's orbit, Q is the net charge, and v is the particle's velocity. From this equation we can solve for the radius:
r = mv/QB (4)
Thus, depending on the masses and charges of the particles we can have clearly defined orbital radii.
A more unified approach to the problem of the structure of the rings must take into account electromagnetic as well as gravitational influences. Therefore, let us add the gravitational term to Equation (3):
mv2/r = QvB + GmMs /r2 (5)
where G is the gravitational constant, and Ms is the mass of Saturn. Notice that this is a coupled electromagnetic/gravitational equation which could be used to determine radii based on measurements of the mass and charge distributions of objects inside the Saturnian rings. Letting K = GMS (a constant) we arrive at the following equation, after performing some algebraic manipulation on Equation (5):
r2 – mv/QB . r + Km/QvB = O (6)
Equation (6) is a quadratic equation in r. Solving for r we get:
r = (mv/QB ± sqrt[(mv/QB)2 – 4Km/QvB])/2 (7)
Equation (7) simplifies to:
r = mv/2QB ± sqrt(p2/4Q2B2 – Km/QvB) (8)
where p is equal to mv (linear momentum), and m, v, Q, and B are all theoretically measurable quantities. Notice that, if K is equal to zero (thereby eliminating the gravitational term), Equation (8) reduces to:
r = mv/2QB ± sqrt((m2 v2)/(4Q2 B2)) (9)
Equation (9) reduces to Equation (4) when the positive square root is added to the first term on the right side of the equation. This provides a validition of Equation (5). From Equation (8) we accept only real positive roots (one cannot have an imaginary or negative radius). Thus, r is a function of the mass of the object, m, and the total charge upon it, Q, and depending on these two quantities it would not be unlikely to arrive at the Saturnian ring distribution as shown in the computer enhanced JPL photograph of Figure 3. The moons orbiting in the outer fringes of the rings in this figure may also be charged, and their orbital radii would therefore also conform to Equation (5).
[*!* Image] Figure 3. Computer-Enhanced Photo of Saturn's Rings taken by Voyager I.
III. THE "F" RING
The two intertwined components of the F ring resemble the phenomenon produced by injecting two oppositely charged particles travelling along parallel courses (and in the same direction) into a magnetic field. If both trajectories have a velocity vector component in the magnetic field direction, the particles may be observed to be travelling in intertwined helical paths. Figure 4 illustrates this effect for one such particle. In the F ring case, each strand has many
[*!* Image] Figure 4. Charged Particle in Magnetic Field (v vector component in B field Direction).
particles in it so that the net charge of one strand is opposite the net charge of the other strand. At various points along their path the two strands interact electromagnetically, probably causing the observed kinks. More data on the magnitudes and directions of Saturn's electric and magnetic fields, and the fields generated by the rings themselves, are needed in order to explain the precise mechanism of the F ring.
IV. THE "SPOKES"
The data from Voyager also suggest more activity on the planet's surface than was previously thought. Figure 5 is a photograph of what appears to be a swirling storm much like the atmospheric disturbances of Jupiter. If the swirling material on the planet's surface is composed of charged gases, a swirling current could develop. Circular currents have magnetic fields associated with them that travel radially outward from the plane of the circle as illustrated in Figure 6. This is a special application of Ampere's Law. If the storm on the planet's surface is strong enough, a powerful magnetic field will result, reaching into the ring system. Charged objects (or particles) in the rings will then tend to line up with this magnetic field similar to the way iron filings line up with the magnetic field of a bar magnet. This mechanism would produce the observed radial bands of darkness and light.*
[*!* Image] Figure 5. Storm on Saturn's Surface.
[*!* Image] Figure 6. Magnetic Field Resulting from Charged Gas Storm on Saturn's Surface.
In this paper we have speculated about the electromagnetic effects associated with various Saturnian phenomena. This summer, Voyager II will fly by Saturn furnishing us with new data and insights into the mysteries of our Solar System and universe. We have only begun to scratch the surface in learning how electromagnetic forces affect the motions and origins of Solar System objects. It is our hope that future space probes will provide us with enough data to answer some of our pressing questions on this subject.
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EDITORIAL POSTSCRIPT: The discussion of spoke dynamics in Astronomy and Star and Sky has been superseded by the latest information from Voyager investigators. "Encounter with Saturn: Voyager I Imaging Science Results" by B. A. Smith et al. [Science, Vol. 212, 10 April 1981, pp. 163-191 (188-190)] present observations suggesting "that the magnetic field is responsible for creation of the spokes and that Keplerian motion is responsible for their particle dynamics." Thus, it now appears the spokes rotate with the ring particles and not with the magnetic field. Also, without detracting from an electromagnetic explanation of the braids in the F-ring, it is noted that S. F. Dermott of Cornell shows "how gravitational perturbation of the ring particle orbits by [the newly-discovered satellites] S13 and S14 may not only account for the confinement of the ring particles but may also explain some of the 'braided' structure of the F-ring" [Nature, Vol. 290, 9 April 1981, pp. 454-7]. – CLE
REFERENCES AND NOTES1. "Voyager I at Saturn", Science, 210 (12/05/80), pp. 1107-1113.
2. D. Baker, The Larousse Guide to Astronomy (N. Y., 1978), pp. 202-204.
3. P. W. Hodge, Concepts of Contemporary Astronomy (N. Y., 1979), p. 103.
4. D. Halliday and R. Resnick, Fundamentals of Physics (N. Y., 1974, revised edition), pp.538, 549.
5. The authors wish to express their thanks to Steven Battista, and to Bernice Joy Blumenreich, M.D. for her illustrations, editorial help, and loving support.