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KRONOS Vol V, No. 1

THE SATELLITES OF NEPTUNE AND THE ORIGIN OF PLUTO

R. S. HARRINGTON AND T. C. VAN FLANDERN

Copyright (C) 1979 by Academic Press, Inc.

* Reprinted from Icarus by permission of the authors and Academic Press. The appearance of this article in KRONOS is not to be construed as endorsement by the authors or Academic Press of theories or ideas not specifically mentioned in the article.

Pluto and the chaotic satellite system of Neptune may have originated from a single encounter of Neptune with a massive solar system body. A series of numerical experiments has been carried out to try to set limits on the circumstances of such an encounter. These experiments show that orbits very much like those of Pluto, Triton, and Nereid can result from a single close encounter of such a body with Neptune. The implied mass range and encounter velocities limit the source of the encountering body to a former trans-Neptunian planet in the 2- to 5- Earth-mass range.

Editorial Preface: This paper is reprinted for KRONOS' readers because it is both an exciting speculation about the evolution of the Solar System and a model presentation of how catastrophic events can be investigated rigorously. Notwithstanding the obvious parallels between this paper and Worlds in Collision, the authors advise that they would not apply the same methodology to test the encounters deduced in Worlds in Collision because, in contrast to the visibly "chaotic satellite system of Neptune' the orbits of the inner planets today are not indicative of disruption within the last 3,500 years if all bodies are accounted for and if gravitation and tidal friction are the only forces that have operated. In discussions, the second author conscientiously invokes the "gravitation and tidal friction only " proviso in a manner that effectively keeps assumptions explicit while maintaining an openness towards entertaining heterodox alternatives. For example, in his recent article "A Former Asteroidal Planet as the Origin of Comets"[Icarus 36, 51-74 (1978)], Dr. Van Flandern concludes, based upon evidence comprising the orbital characteristics of first-return comets, that some five million years ago a planet exploded at the distance of the present asteroid belt despite the absence of any theory besides an ad hoc one to explain such an explosion. Similarly, in the present paper, the mechanism that would have brought the tenth planet into a Neptune-crossing situation is unspecified. However, an early draft suggested perturbation by a passing star or, alternatively, the passage of the Solar System through a cloud of dense interstellar dust or of rapidly-moving hydrogen gas ejected from the galactic center. Another interesting speculative paper by Harrington and Van Flandern is "A Dynamical Investigation of the Conjecture that Mercury is an Escaped Satellite of Venus " [Icarus 28, 435-440 (1976)]. They conclude that such a process is possible for Venus and Mercury, but observe that a similar fate does not await Earth's Moon.

INTRODUCTION

The idea that Pluto is an escaped satellite of Neptune has been suggested by the fact that the orbits of the two planets cross, and by the similarity in brightness of Pluto and Neptune's current satellite, Triton. However, the initial determination of the mass of Pluto from its perturbations on the orbits of Uranus and Neptune (Eckert et al., 1951) gave a value of 1/360,000 solar mass, just slightly less than the mass of the Earth. For such a massive body to exist as a planetary satellite would have been unprecedented, but more recent studies have considerably lowered the estimate of the mass of Pluto. The apparent detection of frozen methane in the infrared spectrum of Pluto (Cruikshank et al., 1976) implied a reflection albedo of about 0.5 and therefore a diameter of about 3000 km, which in turn implied a mass of only perhaps 1/70,000,000 for estimated specific gravities of around 2. The detection of a satellite of Pluto has further lowered the mass estimate to 1/200,000,000 (Christy and Harrington, 1978), which is in the middle of the mass range of solar system satellites (e.g., Triton is estimated to be 1/10,000,000) and most unusually low for a principal planet. Nor is the presence of a satellite necessarily an indicator of planetary status, since satellites have now been discovered around other minor solar system bodies (Science News 114, 36; l 978). We are therefore led to look more closely at the circumstances under which Pluto could have escaped from Neptune in its present orbit.

We have also noted that the satellite system of Neptune is unusual and suggests possible disruption. Neptune has only two known satellites, as compared with five or more for other planets of comparable mass. The innermost (Triton) has a retrograde orbit with an inclination of 160 to the equator of Neptune, and a mean distance of 354,000 km. There is no other known case of a large, relatively close satellite being either retrograde or so appreciably inclined to its planet's equator. The low eccentricity presumably resulted from the action of tidal friction, which would cause the eventual decay of Triton's orbit into the atmosphere of Neptune (McCord, 1966). Note, however, that in the past 5 X 109 years the apocenter distance of Triton could never have been greater than 400,000 km under the action of tidal friction alone, except in the unlikely event that the tidal dissipation factor, Q, for Neptune is on the order of 103 or less.

The orbit of the outer satellite (Nereid) has a mean eccentricity of 0.75, which is twice as large as that of any other solar system planet or satellite (Jupiter VIII, probably a captured asteroid, is next with mean eccentricity of 0.38). Its apocenter distance from Neptune reaches 107 km, while its pericenter is 1.3 X 106 km (four times the distance of Triton). Its velocity at pericenter, 3 km/sec, is just 0.2 km/sec short of escape velocity. Its inclination is 27, and its mean magnitude implies that it is 100 times fainter than, or about one tenth the diameter of, Triton. An analytic theory of the long-term motion of Nereid (Mignard, 1975) shows that the inclination may vary by 3, but the eccentricity has a long-period variation of only 0.006. This is insufficient to permit the possibility that Triton and Nereid ever interacted in the past, based on gravitational and tidal forces alone, since the minimum pericenter distance of Nereid has always exceeded the maximum apocenter distance of Triton. Moreover, despite its high eccentricity, Nereid is too deep within the sphere of influence of Neptune to be a captured satellite, again unless some force other than known gravitational and tidal ones had acted.

The idea of an encounter between Pluto, as a satellite of Neptune, and Triton, as proposed by Lyttleton (1936) would also leave Nereid's orbit unexplained, or would require extreme energy exchanges. In addition, Pluto could not get into its present orbit by tidal escape because of its high inclination and eccentricity. It therefore seems more likely that any hypothetical disrupting body came from outside the Neptune system and was more massive than a single satellite.

THE MONTE CARLO EXPERIMENTS

To test the plausibility of the hypothesis that the Neptune satellite system was disrupted by a passing body of significant mass, we have carried out numerical experiments to study the effects of a planetary encounter on such a system. We assume that Neptune originally possessed a set of regular satellites in circular, equatorial orbits. Modelling these after the Galilean satellites of Jupiter, massless satellites with trial orbits having periods of 2, 4, 8, and 16 days about Neptune were chosen, with the initial phase angles of the satellites in various experiments taken in 45 increments around their orbits. This resulted in eight different initial positions for each satellite, or a total of 32 starting configurations.

The hypothetical disrupting body was given a trial mass and started on a two-body hyperbolic orbit around Neptune (thus ignoring perturbations by the Sun or the satellites). Direct, retrograde, planar, and inclined hyperbolic orbits were tried. The disrupting body was taken initially at the distance of a 25-day satellite orbit and run through the system until it reached that distance [approx. 900,000 km] again. Semi-major axes, eccentricities, and inclinations of the satellite orbits were monitored during the encounter. Afterward, approximate heliocentric orbits of the satellites that escaped from Neptune were calculated for each of six different phase angles for the Sun, assuming the heliocentric distance of each satellite to be the same as the present Neptune-Sun distance (30.1 AU), and with the velocity of the satellite added vectorially to the circular velocity at the present Neptune distance. The magnitudes of the satellite velocities with respect to Neptune were decreased to the corresponding velocity at an infinite distance from Neptune, but the directions were not changed.

Initial conditions for the encounter orbits were picked in ways to try to maximize the frequency of interesting results, as dictated by experience. Mass, velocity, orientation, and encounter distance were the variable parameters, with the interesting mass range turning out to be from 10-6 to 10-5 solar masses (0.02-0.2 Neptune masses). Masses in the lower end of this range turned out to be too small to disrupt the satellites sufficiently, while masses above the range produced catastrophic results that usually destroyed the entire satellite system. Note that the present very low eccentricity (0.01) and inclination (2) orbit of Neptune argues against a mass for the encountering object large enough to have disrupted that planet's orbit, which also sets an upper limit on the encounter mass at a fraction of the mass of Neptune. Encounters were "hard" (heliocentric hyperbolic) or "soft" (heliocentric elliptic), and in plane (inclinations of 0 and 180) or out of plane (inclinations of 30, 90, and 150). A total of 10,368 satellite orbits was examined in the above mass range.

The results may be briefly summarized as follows. For 10-5-solarmass projectiles, high eccentricity elliptic or hyperbolic orbits were commonly produced, including some with a reversed sense of revolution (only with retrograde projectiles). Only rarely did these interesting orbits result from projectiles with masses of 10-6 . The resulting satellite orbits which became hyperbolic with respect to Neptune were classified as "soft" (heliocentric orbit close to that of Neptune), "hard" (heliocentric orbit probably or certainly hyperbolic), and "firm" (heliocentric orbits with intermediate eccentricity, generally between 0.2 and about 0.6). Firm orbits were further classified as "inclined" if there were a good probability that their inclination to the plane of the orbit of Neptune exceeded 10 (produced only by out-of-plane projectiles). In this system, Pluto has a firm, inclined orbit at present.

Only 0.005 of the postencounter orbits escaped Neptune for the 10-6-mass encounters, whereas 0.080 of the 10-5-mass case with the same initial conditions escaped. Therefore masses approaching the latter value are necessary to have a reasonable chance of producing an escaped satellite. Soft encounters generally produced an escaping orbit about twice as often as hard encounters, but this breaks down to about equally likely for in-plane encounters and three times as likely for out-of-plane encounters. In-plane encounters generally produced more escapes than out-of-plane, being four times more likely for hard encounters and twice as likely for soft ones. Thus, to produce the required firm, inclined orbit for an escaping satellite, a soft, out-of-plane projectile (heliocentric elliptic, slightly inclined) is much more likely to succeed.

Hard escape orbits were approximately twice as frequent as firm escapes, while there was an almost negligible number of soft escape orbits. For the 10-5-mass out-of-plane cases, somewhat more than 0.02 of all encounters lead to firm escape orbits, approximately 20% of which were inclined. Therefore, for an appropriate encounter orbit with an object having a mass intermediate between that of Neptune and the Earth, the a priori odds are about 1:200 that a satellite will escape on an orbit with the same classification as that of Pluto, but the odds quickly become negligible if the encounter mass is much less.

TABLE I
Results from Monte Carlo Trajectories 1705-1712
Sat. Initial Final Suggested identification

Period Phase
()
Neptunocentric Heliocentric



Period e i
()
a e i
()

l 2.0 45 Escape 4.1 88 70-500 0.6-0.9 40
2 4.0 225 Escape 1.4 29 18 - 0.5-l.0 9-20 Pluto
Triton
Nereid
3 8.0 315 41.1 0.9 124


4 16.0 45 133.6 0.8 9


DISCUSSION

One particular set of trajectories is of interest to illustrate what is possible from such an encounter. For a 10-5 -solar-mass projectile with starting eccentricity of 1.2, inclination of 30, argument of pericenter of 90, and pericenter at the distance of a 2.6-day satellite orbit, pre- and post-encounter elements of the four hypothetical regular Neptune satellites are given in Table I, and the paths during the encounter are shown in Fig. 1. Satellites 3 and 4 wind up in Neptune orbits reminiscent of Triton (retrograde) and Nereid (highly elliptical), respectively. (Recall that the orbit of Triton would be rapidly reduced to circular by tidal friction following the encounter.) Satellite 1 is transferred, and becomes a satellite of the projectile. The escape orbit of satellite 2 is strikingly like that of Pluto for certain phase angles. It should be noted that the 3- to 2- resonance between Neptune and Pluto is easy to get into in this way, and, once established, very difficult to get out of [see Van Flandern and Harrington (1976)]. It is often objected that if Pluto had a close approach with Neptune in the past, then such approaches must remain possible for all time. While in principle quite true, this reasoning ignores probabilities. Just as escape is enormously easier than capture, getting into a resonance is enormously easier than getting back out.

As to the source of the massive projectile, there are no known candidates except Pluto itself. However, Pluto has much too small a mass to have significant impact, even with repeated encounters. Moreover, Pluto seems more likely to be an escaped satellite, and it could not have escaped into its present orbit without such an encounter by some other body. Further, an interstellar body can be ruled out, since the encounter orbit would have been intensely hyperbolic with respect to the Sun (the local rms velocity of the Sun is approximately 25 km/sec), reducing the probabilities of obtaining the observed results to negligible. Moreover, such a random encounter would be no more probable for Neptune than for the other planets. Our experiments show that the observed situation is more likely to have resulted for a low-relative-velocity encounter by an approximately 10-5 -solar-mass body. This is the description of a trans-Neptunian planet.

[*!* Image] Figure 1. Case of a 3-Earth-mass body encountering a system of regular satellites of Neptune. Crosses mark locations of satellites at beginning of integration and at time of periapse of encounter object. Dotted portion of encounter orbit is below the plane. Sun is approximately toward bottom of page.

If the solar system originally had one additional 2- to 5-Earthmass planet in a roughly circular orbit beyond Neptune, the rest of the scenario would follow if something perturbed its orbit into a Neptune-crossing situation at some time in the history of the solar system. Whatever the mechanism for producing the encounter, an interesting prediction emerges from this investigation. The postencounter heliocentric orbit of the projectile would have a high probability of remaining elliptic, with a semimajor axis less than 100 AU and an eccentricity less than 0.6, suggesting there might still be another planet beyond the orbit of Neptune.

The existence of such a distant trans-Neptunian planet has often been conjectured on other grounds (e.g., Rawlins and Hammerton, 1972; Gunn, 1970), with the limits as to mass of the planet and size of the orbit being very similar to the ones suggested here. We also note that whatever circumstance perturbed the hypothetical planet's orbit into a Neptune-crossing situation may subsequently have also influenced the orbit of Pluto. For this reason, plus the probability argument already cited, these results do not conflict with recent results that suggest the present 3- to 2-resonance between Neptune and Pluto is a stable dynamical feature (Nacozy and Diehl, 1978).

The recent discovery of a satellite of Pluto does not necessarily detract from the suggestion that Pluto is itself a former satellite, especially in view of the discovery of satellites of minor planets. Cristy and Harrington (1978) suggest that our hypothetical encountering body was responsible for tidally splitting Pluto, making it a "double planet" with resonant rotation and revolution. Still another possibility is that Pluto and satellite are both former Neptunian satellites which ended up gravitationally bound together after receding far from Neptune and the disrupting body. Our numerical experiments failed to examine this possibility, since we used massless satellites.

CONCLUSION

The Neptune satellite system has probably been disrupted at some unknown time in the past. The most plausible cause of the disruption is an encounter with a massive body. Such an encounter could have produced the observed anomalous features of the orbits of Neptune's satellites, Triton and Nereid. The same event could have inserted a former Neptunian satellite into Pluto's orbit as well, suggesting that Pluto is not unlikely to be such an escaped satellite of Neptune. Constraints on the mass and orbit of the encountering body lead to the inference that the most likely candidate is a former trans-Neptunian planet of perhaps 2 to 5 Earth masses. Although this planetary body could have escaped the solar system following the encounter, it is more probable that it did not and today is an undiscovered planet at a large heliocentric distance.

REFERENCES

Christy, J. W., and Harrington, R. S. (1978), "The Satellite of Pluto," Astron. J. 83, 1005.
Cruikshank, D. P., Pilcher, C. B., and Morrison, D. (1976), "Pluto: Evidence for Methane Frost," Science 194, 835.
Eckert, W. J., Brouwer, D., and Clemence, G. M. (1951), "Coordinates of the Five Outer Planets, 1653-2060," Astr. Pap. Amer. Ephem. XII .
Gunn, E. J. (1970), "Another Planet?", New Sci. 48, 345.
Lyttleton, R. A. (1936), "On the Possible Results of an Encounter of Pluto with the Neptunian System," Mon. Not. Roy. Astron. Soc. 97, 108.
McCord, T. B. (1966), "Dynamical Evolution of the Neptunian System," Astron. J. 71, 585.
Mignard, F. (1975), "Satellite a forte Excentricite. Application a Nereide,"Astron. Astrophys. 43, 359.
Nacozy, P. E., and Diehl, R. E. (1978). "A Semi-analytical Theory for the Long-term Motion of Pluto," Astron. J. 83, 522.
Rawlins, D., and Hammerton, M. (1972), "Mass and Position Limits for a Hypothetical Tenth Planet of the Solar System," Mon. Not. Roy. Astron. Soc. 162, 261.
Van Flandern, T. C., and Harrington, R. S. (1976), "A Dynamical Investigation of the Conjecture that Mercury is an Escaped Satellite of Venus," Icarus 28, 435-440.

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