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Meta Research Bulletin On-Line

2007 March 15 issue

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Meta Research Bulletin ©2007

The Violent History of Mars

Tom Van Flandern

Meta Research <>

Abstract. With overwhelming evidence now available for the basic correctness of the exploded planet hypothesis, questions arise about the details of the most recent such explosions responsible for shaping Mars and its orbit as we know them today. This study shows that the basic scenario suggested by the evidence and described previously stands up under rigorous scrutiny despite the improbability of passing these new tests by chance. And it allows us to derive specific information about the properties and history of the bodies involved that could only be guessed at heretofore. The solution we adopt is not unique, but satisfies all previous constraints and leads to the present day orbit and rotation period of Mars. “Planet V”, the original parent of Mars, was apparently of “helium class”, a proposed new class of planets. It had an estimated mass of 2.4 Earth masses, a circular solar orbit at about 1.5 au from the Sun, and two “twin” moons. The inner moon, which later became today’s planet Mars, originally had a circular satellite orbit with a period of 20 hours. Tidal locking made that its spin period as well. Outer moon “Body C” originally had a circular satellite orbit with a period of 40 hours and a mass of 86% of that of Mars. Following the explosion of Planet V 65 million years ago, Body C and Mars were left in a mutual, highly eccentric, prograde satellite orbit while continuing to orbit the Sun on an altered solar orbit. Tidal evolution continued until the explosion of Body C 3.2 million years ago, leaving Mars alone in its present solar orbit with relatively high eccentricity for a planet and a prograde rotation period of 1.026 days. Mars today shows the many scars that exhibit this violent history, seen dramatically in the accompanying video.


            A recent review article showed that evidence for the exploded planet hypothesis (EPH) scenario is pervasive and deep. [[1]] Especially telling are the many successful predictions of the hypothesis against all odds: satellites of asteroids; satellites of comets; salt water in meteorites; “roll marks” leading to boulders on asteroids; the time and peak rate of the 1999 Leonid meteor storm; explosion signatures for asteroids; strongly spiked energy parameter for new comets; distribution of black material on slowly rotating airless bodies; splitting velocities of comets; the asteroid-like nature of Deep Impact target Comet Tempel 1; and the presence of high-formation-temperature minerals in the Stardust comet dust sample return. This research report assumes the basic EPH is established and seeks to find out more about the now-exploded bodies involved in the two most recent events that have left behind the most surviving evidence.

            The table below, taken from the preceding reference, summarizes much of the evidence that Mars is a former moon of its now-exploded parent “Planet V”. This body should not be confused with hypothetical “Planet K” that exploded 250 million years ago in the outer main asteroid belt. In both cases, the outer (C-type) and inner (S-type) asteroids themselves probably came from the subsequent explosion of smaller, solid moons rather than these larger, probably gaseous parent bodies.


Evidence that Mars is a former moon

Much less massive than any planet not itself suspected of being a former moon

Orbit has eccentricity of near 10%, as would be expected for an escaped moon.

Spin is slower than larger planets, except where a massive moon has intervened (Mercury escaped from Venus; Moon robbed Earth of original 2-4 hour spin rate.)

Large offset of center of figure from center of mass – common for moons, not for planets

Shape not in equilibrium with spin, indicating reshaping by some cataclysm

South hemisphere is saturated with craters, the north has sparse cratering – indicates either a removal mechanism in the north or a massive cratering event in the south

The crustal dichotomy boundary is nearly a great circle – indicates that something nearby but external to Mars and short-lived devastated half the planet

North hemisphere has smooth, 1-km-thick crust; rough southern crust is up to 20-km thick – suggests massive bombardment of the south half from a planet-sized source

Crustal thickness in south decreases gradually toward hemisphere edges – consistent with external event, but not a local one

Lobate scarps occur near hemisphere divide, compressed perpendicular to boundary – indicates that impacts near the hemisphere boundary were extreme grazers

Huge volcanoes arose where uplift pressure from mass redistribution following pole change is maximal – consistent with present shape not being in equilibrium

Sudden 90° geographic pole shift occurred – as would happen if a great mass were added to one hemisphere centered on Mars equator, causing planet to tip over

Much of original atmosphere has been lost – as would result from a major cataclysm

A sudden, massive flood with no obvious source occurred – cataclysm may have brought the water from oceans on the source body

Xe129, a fission product of massive explosions, has an excess abundance on Mars

Crustal magnetization in southern highlands is weak to absent in northern lowlands

Table I

The specific goal of this treatise is to test the dynamical feasibility of the scenario for the history of Mars strongly indicated by many other lines of physical and circumstantial evidence; and while doing so, to perhaps learn some additional details about that history. The tests rest on three pillars with strong theoretical and observational foundations: fission theory, tidal theory, and the exploded planet hypothesis, in that order of applicability.

  • Fission theory for the origin of planets and moons indicates that, as forming bodies condense and heat up (stars) or cool (planets), their spin increases to conserve angular momentum. Each time that spin reaches an overspin condition, solid bodies fission to form singlet moons; whereas liquid or gaseous bodies (such as the Sun or gas giant planets) fission to form twin companions. [[2]] Examples of the former are (1) Earth’s Moon, and (2) Mercury as an escaped moon of Venus. Simple examples of the latter are (1) Venus and Earth, (2) Uranus and Neptune, (3) the four major moons of Jupiter, and (4) the four major moons of Uranus. Such twin pairs then evolve under the influence of tidal forces into or near to synchronous orbits with a 2-to-1 period ratio.
  • Tidal theory indicates that orbits and rotation periods evolve when bodies interact. [[3]] Although small for planets in today’s solar system, the strength of tidal forces between a primary and secondary body is inversely proportional to the cube of their mutual distance in units of the primary body’s diameter. And the effect on an orbit varies roughly with the inverse seventh power of the same ratio. These tidal forces are primarily longitudinal when acting on Earth-like bodies with liquid oceans and solid land; but are primarily latitudinal or radial when acting on gaseous bodies with differential rotation. So tidal forces were of major importance in the early solar system when both Sun and planets were much larger during their formative stages, with correspondingly much larger tides. Moreover, when tidal stresses reach a maximum and internal conditions are otherwise suitable, they can act as a trigger for a sudden planetary core collapse, blocking a planet’s normal heat flow and leading directly to an explosion.
  • The exploded planet hypothesis (as originally developed) indicates that six of the solar system’s original planets and several more of its moons have since exploded into asteroidal fragments and comets. [[4]] In particular, hypothetical “Planet V”, the former parent of its moons Mars and “Body C”, exploded 65 million years ago, leaving Mars and Body C in mutual orbit. Then almost 62 million years later, Body C exploded 3.2 million years ago, leaving Mars as the sole major body at that distance from the Sun. It is this history we intend to test using dynamical constraints in this report.


In this study, we wish to focus our attention on hypothetical original Planet V, which occupied the position in the solar system now held by Mars; and on its original twin-moon companions, Mars and Body C. The evidence that Mars was a moon of an exploded planet is extensive and summarized in Table I. The existence of a “twin” is required by fission theory if the parent body was liquid or gaseous, and by evidence suggestive of a second explosion affecting Mars. [[5]] This twin is the body most likely to have held life, as suggested by findings of water and organic molecules and evidence for weathering in meteorites dated close to Body C’s indicated explosion date of 3.2 million years ago. (See also remarks in Appendix VII.)

Of those two moons of Planet V, Mars was apparently closer to Planet V than Body C was. This is because Body C most likely took less damage than Mars did when Planet V exploded 65 million years ago. Had it been the other way around, life of any kind might not have survived or evolved to an advanced stage on Body C. [[6]] However, we tried developing the dynamical tests in this article assuming the opposite order (Body C as the innermost moon) and found no solutions compatible with the applicable theories and available evidence, Of course, both moons would have been badly damaged by the Planet V explosion. But both managed to survive for the next 62 million years in mutual orbit around each other, which indicates that damage done by the Planet V explosion was not the sole cause of the much later Body C explosion, or of its timing.

Following the explosion of their parent, the two moons of Planet V are initially captured into elongated mutual elliptical orbits around each other. Tidal forces rob a little angular momentum from these mutual orbits, and take away all their spin angular momentum. As this happened, tidal stresses on each body would have risen progressively. But because the original inner moon (Mars) must be the more massive of the two bodies, the tidal stresses would be greater on Body C. This explains why Body C, rather than Mars, was the next to explode after surviving for 62 million years and taking less damage than Mars. The mutual tidal forces finally produced too much tidal pumping and stress on Body C’s interior. Formulas for the effect of tidal friction on orbits are available [[7]], but will not be used directly in this analysis because they require knowledge of the strength of materials in each body, which determines the strength of tidal forces.

The end result of tidal evolution was the explosion of Body C at 3.2 Mya, leaving Mars in its present solar orbit. Free from tidal stresses, Mars then cooled and relaxed, ceasing volcanism and returning to internal stability. There is therefore no longer a reason to expect that Mars is in danger of exploding.[8]

            Our goal here is to determine if we can go from plausible initial conditions through a dynamical and tidal analysis, setting constraints as we go for what can work and what cannot work, and still arrive at the spin and orbit of the Mars we see today. Finally, we will adopt the following symbols and formulas for our initial calculations. Programmers are encouraged to develop code of their own to test the solution shown here and to look for any flaws in the development or analysis.

Symbols and notation: Subscripts restrict a symbol to a single body or point with subscript zero indicating the center of mass. a = radius for a circular orbit, or mean distance (also called semi-major axis) for an elliptical orbit, of a satellite relative to its primary; P = orbital period (sometimes equal to rotational period); m = total mass (primary + satellite); w = speed for a circular orbit, or speed at mean distance for an ellipse; q = apsidal axis distance (pericenter or apocenter) for an ellipse; e = eccentricity for an ellipse (negative values indicate  is apocenter); r = distance and v = orbital speed relative to primary for an arbitrary point on an ellipse; h = angular momentum. A bold symbol with an arrow over it, as in, represents a vector with (x, y, z) components along the three unit vectors , respectively. (This scenario is planar, so the z-component is mostly not used.) The same symbol without bold and arrow, as in , is the magnitude of that vector; i.e., .  and  are cross-product and dot-product for vectors, respectively.[9]

Equations [Constants are set for units of km for a, q, r (except for solar orbits, where they are astronomical units (au); days for P; Earth masses (Å) for m; km/s for w and v; km3/s2 for ; and Åkm2/s for h.] “Parameter” in the formula column of Table II indicates a quantity tested with a variety of values to determine what values lead to acceptable end conditions for Mars. The “Value” column contains the particular value in the final solution adopted here.

                                                    Kelper’s law:                                          [1]

                                             virial law (for circle):                                   [2]

                                       distance = velocity * time formula:                            [3]

                                              combining [1] and [3]:                                    [4]

                                            escape speed = 1.41421 * circular speed w                                [5]

                                          virial law (for ellipse):                                [6]

                                    center-of-mass speed:                        [7]

                                 angular momentum:                      [8]

                         orbital angular momentum parameter:              [9]

                                                    pericenter distance:                                        [10]

Figure 1. Configuration of Sun, Planet V, Mars, and Body C, respectively, when tidal stresses on Planet V are a maximum. This is the most probable configuration for tidally triggering the explosion of Planet V at 65 Mya.

First Stage: Mars & Body C orbiting Planet V

In what follows, we will follow the scenario just outlined and use the same theme, that bodies are most vulnerable to explosion (from whatever cause) when tidal stresses are at a maximum, with the tidal stresses serving as the final “spark” to ignite the blast. We can then make some inferences about orbital conditions under which the two explosions considered here occurred. Recall that the nature of tidal forces is to cause a body to become prolate (American football or rugby ball shaped), bulging in both directions along the line of forces. Correspondingly, tides have two maxima and two minima for every rotation of the affected body relative to the tide-raising body.

The maximum tidal stress on Planet V would have occurred when the Sun, Planet V, Mars, and Body C, in that sequence, were all aligned. See Figure 1. This configuration has slightly more stress than the alignment Sun-Body C-Mars-Planet V because solar perturbations on satellite orbits cause satellites to be slightly closer to their primary body, on average, when they are opposite the Sun than when they are closer to the Sun. This configuration also places the primary itself closer to the Sun than at any other time.

According to fission theory, the outer moon of any pair of twin moons should have less mass than the inner moon. See Appendix I for the derivation of the particular percentage adopted here. From the known mass of Mars, that relation determines the likely mass of Body C as 86% of the mass of Mars. See Table II, lines 6-8.[10] We will use this table to record all parameters in this scenario and their adopted final values after many trials.

            Lines 1-2 in Table II are the important gravitational constants for the Sun and Earth, the latter because masses in the V-C-Mars system are expressed in Earth-masses. Lines 3-5 are the adopted starting solar orbit parameters for Planet V, where the Sun is the central mass and distance units are in au.

Table II. Relationships and values (See text.)






(link to Table II)


The entry “parameter” in the Table under the heading “Formula” means the value is determined by trial-and-error trying all values (using some small interval) in the range that produces viable solutions. The value shown is the one that led to the “best” solution. “Parameter” differs from “estimate” on line 4, the adopted initial mean distance of Planet V from the Sun. An estimate has a more limited choice of possible values. In particular, for line 4, we first noted that the mean distance of hypothetical “Planet K”, the parent of the C-type asteroids in the outer main asteroid belt, was measured as 2.82 au based on the explosion signature it produced in asteroid orbital elements. The same technique applied to Planet V suggests a mean distance of ~1.5 au, but with so few asteroids defining it as to generate little confidence in the estimate. The competing choice would be the 2-to-1 period resonance orbit with Planet K, which occurs at 1.78 au. Fortunately, the choice of this parameter, the starting mean distance for Planet V, has relatively little effect on the rest of the solution except for the final value of the mean distance of Mars. Because of that insensitivity, because only one of the twin-planet pairs in the solar system has retained its presumed original 2-to-1 period ratio today, and because the “explosion signature” test is distinctly more consistent with ~ 1.5 au than ~ 1.8 au, we will skip the choice of 1.78 au and stick with the 1.5 au starting value here. Pleasantly, the end of the scenario happens to evolve that initial choice into excellent agreement with today’s observed value of 1.524 au. That agreement with today’s value would be difficult to achieve with any starting value over ~1.6 au without including solutions with questionable physical plausibility on other grounds.

            This tendency for the solutions to “home in” on values supportable by other theoretical and observational considerations was manifest in several places as the analysis developed. It is a type of positive feedback that, when experienced, is grounds to gain confidence in the underlying assumptions, including the entire scenario. The opportunities for the analysis to fail or reach an impasse were numerous; and the fact that it succeeded stands as a source of amazement to this author in a way that is best appreciated by coding the algorithms and trying all the possible adjustments for oneself.

            For example, I initially made the “obvious”-but-wrong assumption that the tidal forces on Planet V would be a maximum when Sun, Mars, and Body C were all aligned on the same side. That led to a failed scenario with too high an eccentricity for the final orbit of Mars around the Sun after the Body C explosion because the residual speed of Mars was in the same direction for both explosions, contradicting the present status of Mars. So I re-examined all assumptions and found this one to be in error for the reason stated: The tidal forces depend most strongly on distances, and the distances of the two moons from their parent planet are a minimum when they are in alignment on the opposite side from the Sun. Surprisingly, this necessary correction of a mistaken assumption led to a successful scenario.

To continue the scenario, we next assume (as expected from fission theory) that the relevant initial orbits are approximately circular and in the ecliptic plane. Specifically, this applies to Planet V’s orbit around the Sun and the satellite orbits of Mars and Body C around Planet V. Moreover, the original Mars and Body C orbits around Planet V are assumed to have had a 2-to-1 period resonance. This resonance exists for many solar system pairs, but especially the major moons. And fission theory indicates this is the most probable configuration.[11]

            To the preceding conditions we can add a few tentative assumptions (parameters) that will be adjusted as needed later. We adopt our guess for the mass of Planet V on line 10 in the table using a value appropriate for a predominantly gaseous or liquid planet from which much of its original hydrogen has escaped. See Appendix II. (If Planet V were not liquid or gaseous, it would fission a singlet moon, not a twin pair.) We will also guess the initial orbital period of Mars around Planet V (table line 13), using a value comparable to the rotation periods of the innermost major moons of the solar system’s other gaseous planets. The values in the Table for both of these guesses were refined by trial-and-error to be consistent with constraints that arise deeper in the scenario. We then note that tidal forces would have synchronized the rotation of Mars to be the same as its orbital period around Planet V so that it keeps the same face toward its parent, just as Earth’s Moon and all major satellites in the solar system do. Fission theory then fixes the orbital and rotational periods of Body C at double that value. With these preliminary estimates, we use the standard orbital equations [1]-[10] (for circular orbits, modified here to accommodate the physical units we are using). The “Formula” column in the Table indicates which equation is used for each step in deriving the quantities in Table II lines 17-23.

Second Stage: Explosion of Planet V, leaving Body C orbiting Mars

            This leads us to examining the orbital conditions of Mars and Body C relative to each other at the time of the Planet V explosion, when the twin moons transition from satellite orbits around Planet V to mutual orbits around each other. This explosion is triggered when tidal stresses are a maximum, which occurs when the Sun, Planet V, Mars, and Body C are lined up in that sequence. Given the parameters already set, the two moons have a known separation and relative transverse speed with zero relative radial and normal speeds. That makes the motions of the two moons parallel when they are first freed, which would seem to place the initial post-explosion locations of Mars and Body C on or near the line of apsides of their new mutual orbit, either at its pericenter (closest) or its apocenter (farthest) separation depending on their relative speed. The standard orbit equations and known masses and initial separation (Table II lines 19-20) should then allow us to derive the initial Mars-Body C mean distance, orbital period, and eccentricity.

However, at this point we encounter a major problem that potentially falsifies the whole scenario. If the two moons are set free at a time when their relative motion is entirely perpendicular to the line between them, then the faster motion of Mars will assure that the new mutual orbital motion is in the opposite direction from the pre-explosion orbits. For example, if the moons started out prograde around Planet V, they would end up orbiting retrograde relative to one another. But in most scenarios, the tidal forces between the two bodies would then induce retrograde rotation for both bodies, which is contrary to the state that Mars is in today.

This problem is resilient against simple changes in assumptions made up to now. Reversing the initial sequence so that Mars is the outer moon does not change the problem. Letting the explosion happen when the moons are on the sunward side of Planet V does not change it. Letting the explosion happen when Mars and Body C are nowhere near conjunction and are far apart could yield direct post-explosion orbits. However, except for a narrow range of all such possible conditions, the relative velocities would exceed mutual escape velocity, and the two bodies could not end up orbiting one another, leaving no explanation for the second explosion event affecting Mars and dumping major masses of water onto it. (It should also be noted here that moons in similar solar orbits but not orbiting each other cannot collide, but are required by the laws of dynamics to librate and avoid collisions, much like the Trojan asteroids near the orbit of Jupiter do.)

So for a viable scenario, we seem to be left with the improbable coincidence that the moons happened by chance to be in just the right places in their initial orbits at the explosion to end up in mutual orbits, and the conclusion that tidal forces did not trigger the explosion. However, somewhat surprisingly, a satisfactory solution to this apparent scenario flaw exists that is not ad hoc. Once again, this solution came out of a careful re-examination of assumptions, and finding one that seemed obvious at first but cannot in fact be correct.

Our intuition readily thinks of explosions as more-or-less instantaneous events, or at least very rapid events, because this is the case for explosions on Earth. However, distances in space are vast, and entire planets are large bodies. For example, if Earth exploded, and the blast wave had a speed of 10 km/s, it would take ~ 11 minutes to travel from Earth’s center to its surface. Clearly, a real-time video of such an explosion would appear to us to be in super slow motion. Significantly for our purposes here, it would take the blast wave ~ 11 hours to reach the Moon. Closer artificial satellites would move through an even larger fraction of their orbit during the delay time for the blast to reach them because their orbital speeds are faster. So we cannot neglect to include explosion delay in our scenario because the satellites will move significantly away from conjunction during that delay. Moreover, an inner satellite will move through a greater angle along its orbit during the delay than an outer one because of its faster orbital speed and shorter period.

A further consideration is that it is not the blast wave itself that affects a satellite orbit by impacting the moon, but rather the disappearance of the central planet around which the satellite was orbiting. But that mass does not vanish quickly. It spreads out through space in a roughly spherical manner relative to the explosion site. During the time when most of that expanding mass is still interior to a moon, that moon continues to orbit just as it did before the explosion. The expansion of the mass has virtually no effect on the orbit until the mass starts to pass the moon’s orbit. Then as most of that mass becomes exterior to the moon, it is no longer in orbit at all. The net force on a body anywhere inside a uniform spherical shell of matter is exactly zero. So the de-orbiting of the moon occurs rapidly as the bulk of the exploded mass passes its orbit, rather than gradually as the debris wave from the explosion expands.

To model this effect, we need to adopt another parameter and use many trial debris wave expansion speed values to represent explosion delay in reaching the moons. This speed will be the mean speed of the most massive explosion fragments, because in an explosion (just as is true for the real asteroid belt), the mass in the largest pieces exceeds that of all others pieces put together. And the largest fragments (or blobs in the case of a gas giant) are generally the slowest, so we should not be too surprised to see that the adopted value in line 24 of the Table is slower even than escape speed from the surface of Mars (5 km/s), However, with very little mass left interior to the largest fragments, even relatively small debris wave speeds will escape and do so with minimal deceleration of the blast wave on its way out. Lines 25-26 show the calculated mean time delay for Mars and Body C to leave orbit, respectively. And lines 27-28 show the angular arcs for the continued orbits of the two moons before the main effect of the passing debris wave reaches each of them.

Obviously, it was a serious mistake to neglect this continued orbital motion, different for each moon, before each body ceased to orbit around Planet V. The scenario could not have been realistic without taking this delay into account. And amazingly, adding this required element to the model places the moons in or near the parts of their relative orbits where escape from each other is less likely than capture, and where the resulting mutual orbit is more likely to be prograde. In short, making the test model more realistic takes us into the domain of solutions that lead ultimately to the present-day spin and orbit of Mars, something that several of the more naïve models did not allow to happen for any parameter values.

Of course, in the new mutual orbit following the explosion, both bodies actually move on ellipses with their center of mass at the focus. But in Newtonian mechanics, we are free to describe the orbit of Body C relative to Mars as if the latter were fixed in space. So we use the formulas specified in Figure 2 and its accompanying equation box for the quantities in Table lines 29-42 to compute the relative orbit parameters. The fact that the starting values adopted here, appropriate for this analysis for reasons that have nothing to do with the outcome, happen to lead to mutual capture rather than escape and to prograde rotation for Mars rather than retrograde, argues for the general correctness of the scenario because the right end result is difficult to impossible to reach by chance.

The length of the present day rotation period of Mars (line 78) is another constraint on the whole analysis. For Earth’s Moon, tidal friction has evolved its orbit from very close to Earth out to its present distance of 60 Earth radii while Earth’s spin slowed from a few hours to its present 24 hours. But there is much less spin angular momentum in this scenario. As Mars and Body C assume a mutual elliptical orbit, tidal forces will quickly evolve the rotations of both bodies to eventually be locked facing one another during the pericenter part of their orbits, where tidal forces are by far the strongest. Near pericenter, the heavy side of each body will face the other body. All other original spin angular momentum (lines 17-18) is converted into orbital angular momentum (line 23), which does not change the orbit very much. Later we can use Mars’s present rotation period to infer constraints on its previous orbit around Body C.

Another consideration is the motion of the center of mass of this mutually orbiting pair relative to the Sun, which we calculate on lines 44-46. Our goal here is to meet the constraint that, at the end of our analysis when Mars is alone, the calculated orbit of Mars around the Sun (lines 47-51 for this stage of the analysis) should ultimately resemble the orbit we observe today Lines 76-78). (Exact agreement is not critical because of long-term variations; but rough agreement is important.) When Planet V explodes, the motion of both co-orbiting bodies is propelled forward when the exploded parent releases its hold on them (Figure 2). The initial location on the pair’s new, elliptical solar orbit is at perihelion, the point on the solar orbit closest to the Sun. That will ultimately be where the next explosion occurs because that is where solar tidal forces are a maximum. Solar perturbations on the mutual eccentricity may change the orbit significantly over the next 62 million years until the Body C explosion at 3.2 million years ago.

But those effects should be periodic, not cumulative, and have amplitude about 0.1 in eccentricity with maximum eccentricity at a Sun-Mars-C-pericenter alignment.



Figure 3. Mars and Body C continue to orbit Planet V after it explodes until the debris wave passes the orbit of Mars (M1). Then Mars continues linearly (except for the attraction of Body C) to M2, and Body C still orbits Planet V until the debris wave reaches its own orbit. Thereafter, both former moons orbit each other.
Figure 2. Mars pseudo-orbit relative to “fixed” Body C.


            Note in the equations with Figure 2, subscript 1 indicates the time when the debris wave arrives at Mars; subscript 1.5 denotes the mid-time between times 1 and 2; and subscript 2 denotes the time when the debris wave arrives at Body C. The specific results to this stage of calculation depend strongly on the explosion fragment speed parameter in Table line 24. A fuller discussion of that parameter’s meaning and significance appears in Appendix III. General equations to go from an initial position vector and velocity vector to the corresponding orbital parameters appear in Appendix IV.


“It is trial that proves one thing weak and another strong. A house built on the sand is in fair weather just as good as if built on a rock. A cobweb is as good as the mightiest cable when there is no strain upon it.” – Henry Ward Beecher (19th century motivational speaker and author)

Third Stage: Tidal evolution for Body C orbiting Mars

Because the mutual orbit of Mars and Body C is highly elliptical, gravitational interactions cause considerable internal stress from tidal pumping to both bodies. For Mars, this produced massive volcanism, the remnants of which remain in the Tharsis region today following 3.2 million years of cooling. But the stresses would have been greater on Body C because the mass of Mars stressing Body C was greater than the mass of Body C stressing Mars, and the amplitude of the forced librations in the spin of Body C would have been correspondingly larger, too. This is why it is Body C that eventually explodes, allowing Mars to relax, cool, and stabilize.

            If either former moon has significant rotational angular momentum, tidal friction would feed that into the mean distance of the moons, which would then evolve just as Earth’s Moon is slowly evolving outward. However, that is not the case, so no important change in mean distance or orbital period occurs – a factor aiding the stability of the high-eccentricity mutual orbit. Although the matter of Mars-Body C orbital period was not considered as a hard boundary condition, Appendix VII discusses reasons for preferring solutions near a 7-day orbital period.

Meanwhile, mutual tide-raising forces would tend to gradually lower the eccentricity of the mutual orbit, which would change the rotation period of Mars because it is synchronized with the mutual angular speeds at pericenter. Those speeds would gradually decrease as eccentricity decreased. And solar tide-raising forces might also cause significant evolution. These two parameters are shown on Table lines 52-53. Numerical estimates suggested that solar tides should be pretty small; and indeed, only values very close to unity for line 53 allowed solutions. So this parameter was set at unity and allowed no further influence. Its importance is in showing that adding arbitrary degrees of freedom to the scenario usually does little or nothing to add more acceptable solutions. By contrast, adding the mutual tidal parameter, which numerical estimates suggested was not negligible, allowed solutions with mutual orbital periods near one week because it allowed initially high-eccentricity orbits to relax to lower eccentricity orbits with slower rotation periods for Mars, making the overall solution more attractive.

            The tidal theory for lowering the eccentricity is easy to visualize. A bulge on Mars raised by Body C will tend to gravitationally speed up Body C on the inbound leg of its orbit, raising its pericenter distance. The same bulge tends to slow Body C on the outbound leg, lowering its apocenter distance by an equal amount. The effect of the application of this mutual tidal parameter on the mutual orbit is computed in lines 54-64.

Fourth Stage: Explosion of Body C, leaving Mars orbiting Sun

Tidal theory again dictates the orbital configuration at the time of the explosion of Body C. For reasons similar to that determining the configuration when Planet V exploded, the tidal stresses will again be a maximum when the Sun, Mars, and Body C are lined up in that order. And when such an alignment occurs with the pair of former moons at the perihelion of their solar orbit, and with the mutual orbital eccentricity near its maximum from solar perturbations, tidal stresses would be at their all-time peak.

In Sun-Mars-Body C alignments, the post-explosion residual motion of Mars would tend to decrease the eccentricity of the final solar orbit of Mars because Mars’s motion around Body C is opposed to its motion around the Sun. Based on our trial parameters, this is just what we need to get a Mars solar orbit close to that observed today. Therefore, the configuration at the Body C explosion would most likely be that shown in

Figure 4.

Figure 4. Configuration of Sun-Body C-Mars for maximum tidal stress at moment of Body C explosion. This is the most probable configuration for tidally triggering the explosion of Body C at 3.2 million years ago.

Table lines 65-75 show the corresponding parameters for the Body C explosion and the post-escape solar orbit of Mars for our adopted solution. These may then be compared with the observed values in lines 76-78. The solution shown is not unique, but has only a very narrow corridor of wiggle room. For example, note the main effect of the three main adjustable parameters. Adjusting the Mars initial period/spin affects mainly the escape speed and final Mars orbit. Adjusting Planet V’s mass affects the Mars-Body C period, and allows the solution to get close to today’s Mars rotation rate at pericenter. Adjusting the mean fragment speed for the largest fragments affects mainly the angular width of the arc leading to non-escape orbits.

            Near the high end of solutions, available only if we ignore the ~7-day estimate for the Mars-Body C orbital period, would be the following solution, which we compare here with the adopted solution: If it should turn out that helium planets cannot form with masses below 2.5 Earth masses, then a solution near the sample shown might be more appropriate. Some solutions allow Planet V masses up to roughly 5 Earth masses, but not more.







adopted solution





sample high-end solution






Generalizing this scenario’s methodology, we expect that something similar happened with former “Planet K” in the outer main asteroid belt. This leads to the expectation that Ceres was a former moon, and that its twin moon met the same kind of fate as Body C. So when close-up spacecraft views of Ceres become available, we expect they will show a hemispheric dichotomy and other explosion-related similarities to Mars. The lack of atmosphere would probably mean hard, melting or vaporizing impacts leaving lava-like deposits all over one hemisphere, but with no obvious source volcanoes for that hemisphere.

            Appendix VI notes other implications for fission theory’s reconstruction of the original solar system that were suggested by this analysis.

            Finally, a
4-minute video illustrates the scenario from start to finish, highlighting some of the points of evidence explained by the scenario, even though that evidence did not form part of the motivation for the scenario. It is 38 MB long and runs in Windows Media Player (for example). See A miniature or small screen version is also available at

Appendix I. Mass ratio for twin pairs

Twin pair

mass ratio
















            According to fission theory, three pairs of twin planets and four pairs of twin moons remain from the original solar system. Of those, Jupiter and Saturn might be the only major exception to the rule that the members of each pair are similar in mass. However, the Jupiter-Saturn exception has been substantially modified by the explosion of massive gas giants A & B from the early solar system (the cause of the “late heavy bombardment”), and it is not yet certain that Jupiter and Saturn should be paired with one another, or perhaps Jupiter with Planet A and Saturn with Planet B. So for present purposes, we omit these two planets from the comparison table.

            It is almost certainly not a coincidence that the four major moons of Jupiter are likewise a modest exception to the mass ratio that applies elsewhere. Indeed, Jupiter is almost certainly accreting mass even today faster than any other planet. So if its original mass was modified substantially by the Planet A & B explosions, it follows that its major moons would likewise accrete extra mass. If so, then the innermost of each moon pair would accrete more because it has faster orbital speed, is more massive to start with, and lies closer to Jupiter. And this is the direction in which the observed discrepancies lie for both Jovian pairs, with the discrepancy being larger for the inner pair as the same idea would predict.

            So if we overlook the two Jovian pairs, we find remarkably close agreement for the mass ratio of the remaining four pairs. And even there, we can make an a priori mandatory modification because fission theory tells us that our Moon originated as part of Earth’s mass, and Mercury originated as a moon of Venus. So if we examine the mass ratio of the two (planet + moon) pairs, we get a mass ratio that lies within 1% of the average of the other three pairs. This would make the mean of the four pairs 0.856
± 0.007, which we can round to 0.86 in light of the mean error so as not to overstate its accuracy.

            The mere fact that four pairs of adjacent planets or moons in the solar system have mass ratios so similar would by itself be an anomaly crying out for explanation if we did not have fission theory to explain it.

Appendix II. A new class of planets?

Tidal stresses trigger explosions, and the delays for the debris wave to reach the moons enables mutual capture into prograde orbits. But the window for both these things to happen is narrow. These essential post-explosion delays before the moons are free occur in a roughly equivalent way for any adopted initial Mars spin & orbit period. But they set an upper limit to the Planet V mass parameter. The smaller the mass we choose for Planet V, the wider is the window for satisfactory solutions. However, Planet V must be a predominantly liquid or gaseous planet to it can form twin moons in accord with fission theory. And there is a minimum mass for any planet to resist losing all its light volatiles (hydrogen and helium) and becoming a solid, terrestrial-type body such as the Earth and smaller planets and moons. But planetary formation theory is not yet advanced enough to tell us what that mass limit is.

Initially, when planets fission from a proto-Sun, they have essentially solar composition and consist mainly of hydrogen, perhaps 20% helium, and much smaller amounts of all other elements. If the protoplanet is massive enough, it retains most of that hydrogen, which assures that the planet will remain a gas giant. If the protoplanet does not have enough mass, most of the light hydrogen and helium will escape into space, leaving behind a relatively small-mass “terrestrial” planet comprised of heavier elements, which may then chemically differentiate. (For example, heavy elements may fall to the core and light elements may rise to the surface; or vice versa if the spin is fast enough.) The dividing line between one fate of the other depends on the planet’s size and mass, which determine its surface escape velocity; and the mean molecular speeds of the various elements. For example, the rms speed of N2 (atomic mass 14) at sea level on Earth is ~300m/s, which implies that the rms speed of H molecules would be ~4.2 km/s. That speed would have been higher for a much hotter early Earth. Escape speed from Earth’s surface today is 11 km/s, but that would have been much less for the original larger, gaseous proto-Earth. Even today, the Maxwellian tail of the speed distribution of H atoms (presumably from the breakup of water molecules) would be over escape speed, producing Earth’s faint hydrogen tail.

            To this point, this planetary formation model has much in common with mainstream models. However, it points up a major, neglected area in the transition zone between gas giants and rocky terrestrial planets. There must exist some proto-planet initial mass range allowing most of the hydrogen to escape, but not most of the heavier helium. The result will still be a gaseous planet, but a helium-dominated one, unlike any planets remaining in our solar system today. We know very little about the evolution or stability of such “helium planets”. But we do note with interest that, in both places in the solar system where intermediate-mass helium planets might have formed (between Mars and Jupiter, and beyond Neptune), we instead find asteroid belts. This suggests that helium planets might be less stable than other types.

So fission theory suggests that Planet V was a helium planet, somewhere in the mass range between Earth and Uranus (about15 Earth masses). The solutions here suggest masses near the lower end of that range, although solutions with masses up to about 5 Earth masses exist. It is also relevant that helium planets will be denser than hydrogen planets, and therefore tend to form relatively large and relatively close moons through the fission process. So that suggests an explanation for why Mars and Body C are larger than other solar system moons.

Appendix III. About the explosion-fragment-speed parameter

            If a planet undergoes a central explosion, most of its mass is vaporized because the blast wave has a speed faster than an intact mass can accommodate. The mechanism of vaporization is heating of all individual molecules, increasing their vibration speeds beyond what the forces of cohesion can resist.

            Most of the matter not vaporized lies near the planet’s surface, where it is under minimal pressure from the weight of overlaying layers, and where it can be accelerated to high speeds more gradually as the lower layers rise and push outward over the many minutes it takes even a very fast blast wave to travel from the center to the surface of a planet.

            The crust of the planet and parts of the upper mantle are then fractured into fragments of varying size and accelerated outward at high speeds. Next, the vaporized interior mass in the form of a blast wave passes that near-surface material, and is followed by additional vaporized or fragmented mass in the form of a debris wave. These produce the final acceleration of the larger fragments, which are the slowest. The passage of most of the interior mass in these two waves also drops the escape velocity to a much lower value. Indeed, escape velocity drops to zero for the largest, and hence slowest, fragment.

            One might think that mass speeding away in the opposite direction would still slow the last fragment and require some escape velocity. But that is not the case. The gravitational force outside any uniform, spherical shell of matter is the same as if that shell were concentrated at a single point at its center. And the gravitational force everywhere inside a uniform, spherical shell of matter is zero. The force from the small amount of nearby mass in the shell exactly compensates the larger mass in the far side of the shell. The slowest fragment this finds itself in a region of zero net force and therefore zero escape velocity.

            The high-speed blast wave contains only a small fraction of the total mass. The debris wave that follows is then well-sorted by fragment size, with the vaporized debris moving out fastest and the intact fragments moving slowest. Because we cannot model this wave in detail, we will conceptually approximate its action by assuming that the planet’s entire mass remains interior to any point in space until half of the mass has passed that point, at which time we assume that the planet’s mass is completely outside and the net force from the planet drops to zero.

            We do not know the speed of this imaginary expanding shell marking the “half-mass” boundary, and must model it as an adjustable parameter, . But we expect that  will generally be proportional to the square root of the mass of the exploding planet because escape velocity is. So we will define  as the limiting speed of an expanding half-mass boundary from an exploded one-Earth-mass parent at a distance of infinity. We then assume the speed is distance independent because most of the mass can all be considered as part of an expanding spherical shell that has minimal self-retarding force. That allows us to scale any adopted value for  to any other exploding planet or moon mass : .

            If there were a significant mass  remaining inside a given distance , then the time for the debris wave to reach  would not be a simple linear function of . Given  at infinity (which necessarily means a speed above the velocity of escape), to find the total time  (in seconds) for the half-mass boundary to travel from the exploding planet’s center, we would need the steps on the left below:


Because many programming languages and calculators do not offer hyperbolic functions as part of their standard commands, we might also need to code these in terms of the exponential and natural logarithm functions, as shown in the equation set on the right.

Appendix IV. Size and shape of an orbit derived from a single position and velocity vector

            Given a single position vector  and its velocity vector  of an orbiting body with mass  relative to a central body of mass, we first find the magnitude of each vector: . Then equation [6] (with ) can be used to solve for the semi-major axis (mean distance) of the elliptical orbit: . And equation [9] can be used to solve for the orbital eccentricity: .

Appendix V. The trajectory of Mars at escape from exploding Body C

            We use the same debris wave speed from the explosion of Planet V to model the escape of Mars when Body C explodes. This amounts to assuming the same kind of physical explosion mechanism, which seems reasonable. The main difference here from the Planet V explosion case is that the pre-escape orbit is a high-eccentricity ellipse instead of a circle. Because we are concerned only with a small portion of that ellipse near its pericenter, we will approximate the pre-escape orbit as a parabola (eccentricity = 1). Also, we only need to know the velocity vector of Mars relative to the former center of mass of Mars and Body C at the point when the debris wave passes Mars, because that is the only pre-escape orbit parameter that affects the eccentricity and mean distance of the final solar orbit of Mars.

            Here are the governing equations.

Appendix VI. Notes on fission theory

Why are twin planets Earth and Venus so far from the 2-to-1 resonance that fission theory suggests they started with? Fission theory indicates that Mercury escaped from Venus. The present circular orbital speed of Venus is 36 km/s, but needs to be ~38 km/s to place it in the 2-to-1 resonant orbit with Earth (orbital period 6 months). But when Mercury was still a moon of Venus, its tidal escape was through the L1 Lagrange point on the line from Venus to the Sun. As that happens, Mercury’s relative satellite orbital momentum is opposite its solar orbital motion. This means its escape causes a forward impulse to Venus, giving that planet more angular momentum but ultimately less orbital speed.

Analogously, as terrestrial planets shed their original H and He light gases, all that mass will likewise preferentially escape through L1. So most escaping mass has spin momentum opposite to orbital momentum, leaving terrestrial planets with a net gain in orbital momentum; i.e., they end up farther from the Sun. The same process, mass loss in Venus, would also have the effect of accelerating the tidal escape of Mercury. Such mass loss may interact with the Sun’s tidal forces to push proto-Venus or proto-Earth to faster or slower speeds than the 2-to-1 resonance orbit. But our Moon’s fission from Earth must have occurred before Earth shed much of its original gaseous mass.

This means that original Earth should be to present Earth as original Venus is to present Venus, except for the fact that our Moon is 4.5 times less massive than Mercury, and Venus is ~5/6 of Earth’s mass. Another factor this analysis has highlighted is that twin pairs will tend to evolve toward 2-to-1 period resonances, but there is no corresponding action pushing one twin pair into 2-to-1 period resonance with any pre-existing twin pair. So resonances are disturbed or never occur between twin pairs and within pairs of terrestrial planets that lost lots of mass and/or large moons.

So we now suggest the following original periods (in years) of the solar system’s original 12 major planets. New thinking is that the more massive planet (the outermost) of each pair of large gas giants would produce intense tidal stresses on the smaller (innermost) at times of closest approach shortly after fission from the enlarged proto-Sun. This means these giant twin planets would never get the chance to evolve into a 2-to-1 resonance before the smaller was induced to explode by the larger. It also means the outermost would absorb most of that exploded mass because there would not as yet be any planets further in, and it would be the closest and most massive body available for the purpose. Moreover, most such collisions would decrease the orbital angular momentum of the surviving planet, opposing its outward motion through solar tidal forces. This explains why the two surviving planets, Jupiter and Saturn, are closer in than a smooth sequence would suggest. The table reflects the implied fact that Planets A and B never reached their resonant position or evolved significantly before exploding.



























Appendix VII. Possible tie-in with Martian artifacts

Anomalies suggestive of artifacts are seen in recent high-resolution spacecraft imagery of Mars [[12]]. These have a character more like the kind of things that will be found someday on Earth’s Moon as a result of visiting human activities rather than the kind of things expected to be seen on a civilization’s primary world. Therefore, if either body was in fact a home world to a species capable of making artifacts, it would more likely have been Body C. Moreover, suggestions exist in the form of a distinctly terrestrial flavor to the possible artifacts, and in the dating “coincidence” of the Body C explosion (3.2 million years ago) and the dating of the oldest definitely hominid fossil found on Earth (“Lucy”, also dating to 3.2 million years ago). These suggestions of a connection between the demise of Body C and the rise of hominids on Earth led us to give mild preference to solutions where the orbital period of Body C around Mars was ~7 days, suggesting an origin for the special significance of that particular interval (“the week”) to modern humans.



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