The satellite Io in the Jupiter system of moons, shows evidence
of a substantial internal energy source. Speculation on the source of
that energy has offered many theories. Each seems to have major flaws.
A logical energy source can be present. Each time Io passes the three other
Galilean satellites in their paths around Jupiter, tidal forces
stretch and pull Io. These effects are great enough to explain the
heat source in Io. They resemble tidal forces but are somewhat different.|
The fact that Io is extremely close to Jupiter has led some scientists to speculate that that closeness somehow generates tides within Io that create frictional heating within it, and that resultant heat drives the geyser activity. There would appear to be an error in this logic. This paper will attempt to present a logical source for the forces that deform Io and thus create the internal frictional heating that drives the geyser activity.
The severe dynamics of such a situation rapidly had to synchronize the rotation and revolution long ago. Io must certainly have a permanently distorted shape due to the tidal forces created by Jupiter. The shape would resemble a prolate spheroid, with its long axis directed toward the center of Jupiter. My calculations suggest that the long axis should be approximately one mile greater than the dimension in either perpendicular axis. I am not aware if anyone ever tried to measure this prolateness of Io. But the shape would be relatively unchanging, since that long axis would stay closely directed at the center of Jupiter, and therefore not generating any dynamic differential tidal forces within Io. The shape might be measurable from the Earth. When Io is near conjunction or opposition, we should be viewing its minimum shape, which should be very nearly circular. A few hours later, when it is near greatest elongation, we should be looking at its profile, where the width of its image should be around 1 mile greater than its height. That's a difference from being circular of about 0.06%, which may be measurable from Earth or from the Hubble space telescope.
There are secondary effects, generally called perturbations, that CAN create dynamic changes in the forces, and therefore act to change the actual shape of Io, which creates the internal frictional heating needed to supply the geysers' energy source.
If Io's orbit had significant inclination to the equatorial plane of Jupiter, then the lobes along the prolate axis would alternately point above and then below the center-of-mass of Jupiter. This would induce continual torques so that Io would oscillate North and South (using Jupiter's reference frame) each orbit. Such oscillations would allow the differential dynamic forces necessary to produce tidal heating. As it turns out, however, Io is in an orbit that has quite small orbital inclination, about 0.04 degrees. The tidal heating that could result would appear to be insignificant. Io's orbit is very close to being equatorial.
If Io's orbit had significant eccentricity, then a different source of tidal forces could be developed. When Io was nearest Jupiter, the prolate axis dimension would be increased. By being closer to Jupiter, both the force attracting the nearest part of Io and the force attracting the farthest part of Io would be increased, but the attraction on the part nearest Jupiter would have incrementally greater attraction. This would induce force differentials that would tend to stretch Io along the prolate axis. THAT would be a tidal effect! Io has a rather circular orbit, but it DOES have some eccentricity, (0.004). Calculations suggest that this eccentricity would cause Io to change its prolate axis length, to stretch and recover, by about 40 feet once each orbit (42 hours). This is a very significant effect. (The Earth's solid-body tides due to the Moon's gravitation, are less than one foot.) The continuous stretching and rebounding of its long axis by a 40-foot differential every 42 hours would definitely create a lot of internal frictional heating. This seems like a very likely source of such energy.
There would appear to be another possible source of dynamic differential tidal energy generation. The next large satellite out, Europa, has an orbital period of approximately twice that of Io. That means that Io passes Europa (a conjunction, from Jupiter's point-of-view) each time around. Let's consider this carefully.
Remember that Io must be significantly prolate, along an axis radial from the center of Jupiter, by as much as a mile. As Io approaches Europa from behind, the gravitational forces due to Europa, on Io, will tend to pull it forward, obviously, but it will also act to rotate Io. This is much more similar to normal tidal analysis, where the differential forces present have component vectors along the surface of the satellite. Before the moment of opposition, the forces cause a torque that would slightly rotate (the outer portion of) Io forward. After opposition, a nearly precisely identical opposite torque acts to rotate it backward. (The fact that these two situations are infinitesimally different, a second-order effect, seems quite likely to be the explanation of the near synchronicity of the four large Galilean moons, but that's a different subject!)
There would be two effects of this interaction. First, the forces that first turn Io and then turn it back, represent dynamic differential forces acting on Io and its interior. Second, and probably more important, is that, once Io's prolate axis is no longer directed exactly at the center of Jupiter, the much larger effects due to Jupiter's gravity mentioned above (similar to the orbital inclination discussion) would come into play. This would act to dynamically keep distorting the shape of Io around the time of each opposition with Europa. Io would tend to "twist-flex", as the two short-range gravitational forces tend to try to rotate it in opposite directions.
The same argument can be applied to Ganymede, a much more massive satellite, but which Io passes at a greater distance. Occasionally, the effect of Europa and Ganymede add, as in spring tides on Earth. At other times, their total effect is reduced, as in neap tides on Earth.
Additional, precise study of the motions and mutual perturbations of the Galilean satellites should greatly increase our understanding of basic Gravitational Theory.
It seems particularly intriguing that the ratios of the orbital periods for the four large Galilean satellites of Jupiter are nearly exact multiples of each other. Is this merely an amazing coincidence? That seems doubtful. It seems much more likely that the perturbations of the satellites on one another have somehow acted to develop this synchronicity. A brief reference to this possibility is mentioned in the Io discussion above. Careful analysis of the existing empirical data may enable new insights. In addition, computer simulations of the differential dynamics of one satellite passing another, would seem to be especially promising.
To specify this premise a little more, as the satellites orbit Jupiter, it often happens that they pass each other, which can be called oppositions. There are subtle, second-order modifications to the orbits of each as a result. This effectively is an example of "forced vibration", a standard Physics and Engineering analysis concept. The force vectors that exist as an opposition is approaching, might seem to be exactly mirror-opposites of those that exist as they separate after opposition. They are not. The satellites are slightly affected (moved and given slightly different velocities) from the situation they would have had if they had not had to approach one another. This makes the opposition encounter slightly asymmetric. This results in a second-order effect of the opposition episode. If computer simulations were invoked to track these tiny variations for the equivalent of millions of years, better understanding of the nearly synchronized orbits may result.
The forced vibration approach to analysis actually results in a requirement for a NEAR synchronicity, and essentially suggests that a pure synchronous situation would be unstable.
This effect is vaguely similar to the Regression of the Nodes of our Moon, or about the process that causes Precession of the Earth. As the Moon approaches a Node, its path is curved slightly toward the Ecliptic. After it passes the Node, that effect is reversed, leaving no residual effect except for the fact that the location of the Node passage had very slightly regressed along the orbit.
In the case of an opposition passage of Io and Europa, the initial acceleration of Io and the deceleration of Europa are exactly reversed after the opposition, allowing each to leave with the same velocity it would have had if no opposition had occurred. However, the second-order effect is that Io gained a few feet along its orbit, while Europa lost a few feet. Exactly how this might result in the near synchronization of the orbits of the four Galilean satellites is not clear. The forced vibration approach seems to offer some intriguing possibilities. A separate essay on that is linked below.
Hopefully, another quirk of the Galilean satellite system will also be explained as well. All four of the Galilean satellites can NEVER be on the same side of Jupiter at the same time! This fact has been long recognized. It's just that no present theory can explain why it's true!
As an aside on this topic, even a much simpler system has many behaviors that are not fully understood. Our own Earth-Moon system is VERY complex. When President Kennedy first announced that the United States was going to put a man on the Moon, scientists were concerned, because they couldn't predict precisely enough exactly where the Moon would be! A HUGE effort was put forth to accomplish that goal. By 1969, when the moon landings actually occurred, the calculations were not yet complete! (They still aren't!) (But they were accurate to within a few inches, which was good enough) The calculations which presently best describe the motion of the Moon involves hundreds of thousands of terms. Theory is FAR behind in actually understanding the sources of many of those terms.
It would be nice to think that there was some elegantly simple way of presenting all this so that the empirically observed results could be predicted from theory. There doesn't presently seem any traditional way to accomplish this. The resolution may require some entirely new insight, such as Newton realizing that he needed to invent Calculus to solve the problems he faced three centuries ago.
A possible area to investigate more precisely and thoroughly, is the behavior of the Trojan asteroids. Our present Gravitational theory is pretty good at describing and understanding TWO-BODY gravitational interactions, but THREE-BODY (or more) are presently generally beyond our theoretical expertise. One of the few exceptions is the behavior of those Trojan asteroids. They orbit the Sun in meta-stable orbits which have effectively the same radius as Jupiter's orbit, but they permanently remain 60 degrees ahead of or behind that planet as they orbit the Sun. There are several large Trojan asteroids in each of these two groups. Several questions come to mind. How do they move within their little groups? Do the orbit each other? Do they sometimes crash into each other? What is the path of the center of mass of each of the two groups? Does that point orbit the Sun at EXACTLY the same radius as Jupiter does? Does that point experience any oscillation or resonance (or ringing) phenomena? I have some preliminary thoughts where there should be small resonances that occur with periods of odd-fraction integers (1/7, 1/9 etc) of Jupiter's period. Much more research is necessary in these areas, and they might contribute toward a more complete theory for Gravitation.
An event like that early that Summer was when Jupiter was not very near opposition, from our viewpoint on Earth. In other words, the Earth was a little off to the side of the sunlight that was getting to Jupiter and its satellites.
This seemed to me to offer a unique opportunity for gaining some data. If we aimed a spectrograph at Europa at any normal time, we should get a pretty normal spectrum of reflected sunlight. (The eclipse I had predicted for 1997 would have a duration of about 17 seconds.) If we took a spectrogram of Europa 0.5 second before totality began, we should be able to collect some useful information. The sunlight that would have arrived at Europa at that moment had to have earlier passed within about 60 miles of the surface of Io on its path from the Sun to Europa. If there was sulphur or ionized sulphur or ionized sulphur dioxide (or anything else) in an atmosphere surrounding Io, the sunlight that would later arrive at Europa would have had to pass through those atmospheric materials near Io, and we should get evidence of absorption lines in the spectrum taken of Europa at that moment.
NOTE: In the repeating series of these mutual Galilean eclipses, another series of them occurred during the year 2003. There were bound to again be some Io eclipses of Europa, early or late in the string of such events, such that the Earth is off to the side. This last is necessary such that the image of Europa would be as separated as possible from the brilliant image of Jupiter, so a spectrogram of Europa was not contaminated with light from Jupiter. As in 1997, it seems like an ideal way of confirming the specific atmospheric components of Io.
I haven't done any calculations for the Saturnian system, but if Titan ever eclipses any of the other Saturnian satellites, a similar spectrogram of that satellite might give evidence of the chemical composition of the atmosphere around Titan.
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C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago