THE EARTH’S WATER; WHERE DID IT COME FROM?

By T.Frank Lee, geologist, MAppSc. BSc., etc., 102 Mill Street, Ballarat, 3350,Victoria, Australia.

Any hypothesis developed to explain the origin and development of the Solar System must be able to give a satisfactory explanation of why Earth has such a high percentage of water compared to the other “silicate” planets and satellites. The Single Body Breakup Hypothesis must therefore be able to give one. The following description, taken from my 1994 book, gives an outline of how I attacked the problem and the conclusions that were reached. Here and there throughout what follows I add brief comments on later work done on the problem.

In Section 3, subsection 3(e), and beginning on p.177. Let us now turn to the atmospheres of Venus, Earth, and Mars. It has been proposed above (e.g. p145) that the atmospheres were captured (or largely captured) by the planets after stripping of the planets and immediately before ejection. If this is true then it is not valid to compare abundances of the various gases of the planets using gramme of atmosphere per gramme of planet. Instead it is required to compare atmosphere percentages of one planet to another. (Note that this mirrors the argument of Shukolyukov for the noble gases.) I shall now do this using the three major gases N₂, CO₂, and H₂O. These make up almost the whole of the atmospheres.

In the paper of Oyama et al (1979), in Table 3, is given the measured mixing ratios of the various gases in the three planetary atmospheres as now exists. This table gives in part:

Gas Venus Earth Mars

N₂ 0.034 0.78 0.027

CO₂ 0.96 0.00033 0.953

H₂O 0.014* 1x10^-2 1x10^-3 * should read 0.0014

If only N₂ and CO₂ are considered, the inclination is to suggest a relationship between Venus and Mars. Earth is quite different. If the hypothesis is correct, and as it suggests that the three planets obtained their atmospheres from near locations, then the Earth’s great difference must be due to some later event. This will be investigated below. But before doing so consider adjustments to the gases as given by Oyama et al. These adjustments were made to account for possible/probable gases in near-surface reservoirs such as Earth’s oceans and limestone, and they listed the results as the ratios of the respective gas per planetary mass. The values for the three gases being considered in gm per gm are:

Gas Venus Earth Mars

Minimum Maximum

N₂ 2.1x10^-6 2x10^-6 1.9x10^-8 to 1.2x10^-7

CO₂ 9.5x10^-5 7x10^-5 7.0x 10^-7 to 4.9x10^-6

H₂O 5.7x10^-8 1.6x10^-4 4.5x10^-6 to 3.2x10^-5

These ratios have been taken and multiplied by planet mass to give the individual gas masses as follows (in kg):

N₂ 1. 0227x10¹⁹ 1.196x10¹⁹ 1.216x10¹⁶ 7.680x10¹⁶

CO₂ 4.6265x10²⁰ 4.186x10²⁰ 4.480x10¹⁷ 3.136x10¹⁸

H₂O 2.7759x10¹⁷ 9.568x10²⁰ 2.88x10¹⁸ 6.40x10¹⁸

Making the assumption that the three gases summed to 100% for each planet (closely true) then the gas percentages obtained are:

Percentages

Gas Venus Earth Mars

Minimum case Maximum case Average

N₂ 2.16 0.86 0.36 0.80 0.58

CO₂ 97.78 30.17 13.41 32.62 23.02

H₂O 0.09 68.97 86.22 66.58 76.40

These values are much more random than the raw atmosphere values; and if they suggest any sort of relationship it is between Earth and Mars. However, if H₂O is deleted, and only N₂ and CO₂ are compared, then a totally different picture emerges.

Venus CO₂/(CO₂ + N₂) = 97.837%

Earth CO₂/(CO₂ + N₂) = 97.222%

Mars CO₂/(CO₂ + N₂) = 97.357% minimum case

97.610% maximum case. Average 97.484%

The arguments given in the next five paragraphs are no longer valid and the formula given has been typed incorrectly and so is wrong. In its place I give here:

Of course the data must be considered too approximate to permit a definite quantitative relationship of the values between the three planets but quite clearly it does give a qualitative relationship: Venus ejection position (e.p.) nearest to the centre of protoJupiter 10748 km; Mars e.p. 11309 km; Earth e.p. 23176 km have the same sequence as their CO²/(CO₂ + N₂) values. The hypothesis thus gives an explanation for the variation.

How then to explain the water contents of Earth and Mars by use of the hypothesis?

p.180 In the literature accepting the planetesimal (nebula) theory a terrestrial planet’s present atmosphere “—must have been produced almost entirely by outgassing –“ (Wood, 1979 p.82) or “--, because materials added later (as planetesimals and/or comets) came as solid ices, which H₂O, CO₂, NH₃ could be, --“ (Hoyle, 1978, p.37. See also Owen et al, 1992) or as mass fractionation and differential escape of an originally solar composition gas envelope (Hunten et al, 1987) or preferably by a combination of methods as one alone does not fully explain known data. The hypothesis offered in this paper allows a similar mechanism as planetesimal collision but requiring limiting conditions.

According to the hypothesis the satellites would have initially formed three rings (a better term would be annulus. F.L) (Section 1, p.61). The outer ring consisted of a limited number of fairly large, medium density bodies, the middle ring consisted of three (perhaps four) “silicate” bodies, and the inner ring consisted of many, mostly small, low density bodies. Ejection of these groups of bodies was inner ring, outer ring and silicate ring. (The sequence has since been shown to be inner ring, then the silicate and outer rings simultaneously. F.L.,2009) Saturn captured many of the low density satellites while it still remained near protoJupiter. (That is why its satellites have a low density compared with those of Uranus) Mars, as it passed outwards through the rings, had the highest chance of colliding with or of capturing a satellite in the inner ring but its relatively small size would have required small bodies and optimum conditions e.g. very near passing). Its two satellites may be the cores of two satellites, their volatiles (as “ices” having been lost (to Mars) after capture. The chance of capturing one of the larger, heavier bodies in the middle and outer rings would be small, and collision even smaller.

Uranus and Earth were the next ejected. Immediately before ejection Uranus would have formed a bulge on the side of protJupiter so that as Uranus began moving outwards the satellites would possibly have initially moved along paths of dumbbell outline. At first thought it might be assumed there would have been a very large number of collisions but distortion of the satellite paths would more likely mean few collisions but common captures. Uranus being massive, and not travelling at a great speed relative to protoJupiter, would be expected to have captured a number of the now less numerous inner satellites and would have had a high possibility of picking up one or two of the far fewer satellites in the middle and outer rings.

Earth, travelling nearly three times as fast as Uranus, and being smaller would have been much less likely to capture or collide with a satellite. However it would not have distorted the satellite path as Uranus would have but tended to pass through, increasing the chance of collision; and at an orbit of 2R_J, the satellites would have been moving at nearly the same speed as Earth and so have increased the possibility of collision and capture. (The satellite speeds would have been greater.)

After Uranus and Earth came Neptune and at the same time Venus followed by Mercury. Neptune is a little more massive than Uranus but was ejected at a greater velocity. It would also have passed through rings containing less satellites than existed previous to it, many already having been captured. It should be expected, then, that Neptune would have captured less satellites than Uranus.

Venus moved outwards faster than Earth and Mercury even faster. Its speed, together with there being less satellites present, would have meant Venus would have had a lower chance of collision or capture, even though its mass is approximately that of Earth. Mercury’s very high speed and its very small mass would have made capture or collision very unlikely.

If a collision were to take place as the terrestrial planets were being ejected the most likely one to be involved would have been Earth because of mass, ejection speed, and number of satellites present at the time. Let us assume that a collision of a satellite did take place with the Earth and that the collision occurred in the most likely ring, the inner ring. The body in this case would have been dominantly H₂O with a silicate (probably hydrous silicate) core and would have been of a mass to place it within the inner ring. Assume that all Earth’s water is due to collision and retention of the satellite. (This assumption allows for the mass of the water probably present in Earth before the collision to offset the mass of the silicate core of the satellite.) Then the mass of the satellite would have been 9.568x10²⁰ kg. This is a little less than the mass of Dione, a satellite of Saturn. Dione is a low density (1.430 S.G.) “icy” satellite having a mass of 10.5x10²⁰ kg and a radius of 560 km; and in Section 1 has been placed in the inner ring. That is, if such a collision occurred the body would have been approximately 1/6250^th the mass of the Earth, approximately 1/12^th the Earth’s radius, and travelling at about 2½x the Earth’s speed (about 43 kmsec^-1). It would have been an incompetent body striking a probably plastic body (but the surface almost certainly had a skin of solid silicate. F.L). The collision could have been a source of comets (but not the only source). Of course it is possible that more than one collision occurred but the one body lies within the necessary parameters. Thus only one collision is required for the hypothesis to account for the atmospheres of the three terrestrial planets Venus, Earth, and Mars. (See the sub-section “The Probability of Collision or Capture of a protoJupiter satellite by a Terrestrial Planet for a continuation of this argument.)

p.231 THE PROBABILITY OF COLLISION OR CAPTURE OF A PROTOJUPITER SATELLITE BY A TERRESTRIAL PLANET – ORIGIN OF THE EARTH-MOON COUPLE?

Strictly speaking this small sub-section should not appear in Section 2 of this paper. It is not a presentation of data, or other people’s opinions, which support the hypothesis, as it should by rights be. However, it seems appropriate to present it after the material dealing with the suggested origin of the terrestrial planets atmospheres. What follows is an attempt with the crudest of mathematics, first to show that the probability of collision of a light density satellite of protoJupiter with Earth was sufficiently high for it to be accepted that such an event could have and probably did take place, second to show that a similar event could and possibly does account for the Earth having a satellite.

The calculations are crude, probably so greatly so as to cause amusement and contempt by those knowledgeable in celestial mechanics. May they have the tolerance towards one who does not have the knowledge and at the same time sees no necessity to learn it and spend the great amounts of time required for accurate calculations at a point when probably not yet needed. After all, the intention of this paper is to direct the attention of others to data which suggests a quite different origin of the Solar System than currently accepted in the variants of the Planetesimal (Nebula) theory, and to present data from a large number of fields that appear to support the hypothesis offered. To attempt a detailed proof in any particular branch would defeat the aim of this paper, so I consider it sufficient in this really small, immediate matter to merely point out in the crudest way that probability of collision and capture was high. Just how high I leave to others to determine, should they think the hypothesis has sufficient merit to warrant such calculations.

It has been suggested in Section 1 (p.58) and sub-section 6 that the satellites formed before the planets and that they originally formed three broad rings (annuli) of objects about protoJupiter. The inner ring consisted of small, light density satellites, the first bodies (other than comets) to be ejected. Assuming only one collided with a larger body, the Earth, - and this is a conservative assumption – then there were originally 14 objects with a mean orbital radius about protoJupiter of about 2.5x the radius of Jupiter. The middle ring consisted of the three heaviest satellites – Io, Moon, and Europa – and had a mean orbital radius of about 7.746x the radius of Jupiter (Dimensions from Section 1.). Finally, the outer ring consisted of five satellites of large to medium size, of medium density, and had a mean orbital radius of about 21.313x the radius of Jupiter. The outer and inner ring satellites consisted dominantly of “ice”, while the middle ring satellites consisted mainly of silicates. (Increasing silicate content: Europa to Moon to Io?).

Using these dimensions and the approximate formula v = (GM/a)^1/2 for determining the orbital speeds of the satellites we obtain:

Rad. Orbit Circum. Orbit Orbit speed Time of revolⁿ

km. km. kmsec^-1 sec.

Inner ring 179750 1129403 27.23 41476

Middle ring 556937 3499338 15.47 226202

Outer ring 1532405 9628385 9.33 1031981

The mass of protoJupiter was different for each case of ejection – Mars, Earth, Venus – being 2199.78x10²⁴, 2107.2x10²⁴, and 1999x10²⁴ kg respectively. (The three figures are incorrect by +100. The value for Jupiter given by Cole (1990) was being used at the time of writing. The difference on subtracting 100 leads to little alteration and, considering the approximations used throughout, does not change the argument presented.)

The probability of collision and capture of a satellite by each of the terrestrial satellites (read planets) (Mercury is ignored) will be carried out first for Mars, then Earth, and finally Venus.

Inner Ring of Satellites.

Mars: Diameter of planet 6796 km. Say width of contact (without changing the trajectory of the satellite) is 7000 km. Time taken for Mars to travel 7000 km = 7000/(24.1 – 12.9) = 625 sec. Time of revolution of one satellite about protoJupiter (average) = 41476 sec. Chance of impact therefore is 1 in 41476/625 = 1 in 66.36.

But at the time of Mars’ ejection there were a minimum of seven satellites in this ring, possibly nine if Mars’ present moons were captured here, and as many as sixteen if Saturn had not yet captured its low density satellites. That is, the chance of colliding with a satellite of the inner ring was approximately 1 in 9.48 or 1 in 7.37 or 1 in 4.15. Actually, the odds would be somewhat better than these.

Now consider the force law. As an approximation assume that for Mars and protoJupiter at the Mars ejection stage GM_pJm/a_pJ² = GM_Mm/a_M², where m is the mass of the satellite, a_pJ the distance of the satellite from the centre of protoJupiter, and a_M the distance of the satellite from the centre of Mars.

Then substituting values gives: Gx2199.78x10²⁴/179750² = Gx0.64x10²⁴/a_M²

So a_M = (0.64x179750²/2199.780)^1/2 = 3065.98, say 3066 km.

Without taking into account prograde or retrograde motions of the present Mars satellites, satellite capture would probably have taken place over a total distance of nearly 2x3066 = 6132 km.

Note that 6132 km is less than the collision width. This suggests that a satellite would need to virtually touch Mars to be captured. (Remember, no account has been made of satellite trajectory change due to the nearness of the planet.) The chances of collision or capture are then about 1 in 9.5 (1:8.5) 1 in 7.5 (1:6.5) or 1 in 4.25 (1:3.25).

Mars would then have passed through the middle and outer rings of satellites of protoJupiter, but Mars’s small mass and the scarcity of satellites in the two rings makes capture or collision unlikely to have happened (about 1 in 44 for the middle ring). The chance of collision or capture at the inner ring was, however, quite high.

Earth

After Mars, of the terrestrial planets came Earth.

The diameter of the Earth = 12756 km. The possible collided satellite diameter = 1120 km. The possible width therefore = 13876 km. Time taken for Earth to travel 13900 km = 13876/(29.8 – 12.9) = 821.07 say 821 sec.

Again, collision, here, does not take into account the changing of the trajectory of a near satellite, i.e. the following calculation is conservative.

Time of revolution of one satellite about protoJupiter = 41476 sec. Chance of impact therefore = 1 in 41476/821 or 1 in 50.52.

But at the time of Earth’s ejection there were 7 satellites (assuming one collided) and so the chance of it colliding with a satellite of the inner ring was 1 in 7.2.

Venus

In a like way as for Earth (above) the width of the contact zone for a Venus collision = 13220 km. Time taken for Venus to travel 13220 km = 13220/(35.0 – 12.9) = 598.2, say 598 sec. i.e. chance of impact 41476/598 or 1in 69.36.

But if it is assumed that Earth did not collide with an inner ring satellite, and Uranus had captured its five low density satellites from the ring, then only two satellites remained and the chance of collision was 1 in 34.68.

In total, assuming nine satellites were present for Mars, seven present for Earth, and one present for Venus, there would be about a 1 in 3.5 chance (i.e. 1:2.5) chance of a collision of one of the terrestrial planets with a satellite of the inner ring – and this is a conservative estimate. A better than 28% chance.

Now consider the force law for Earth and Venus, as applied for Mars, on the three rings of satellites.

Inner ring

Earth GM_pJm/a_pJ² = GM_E/a_E² Substituting values: 2107.2/179750² 5.98/a_E² and a_E = 9575.6, say 9576 km.

Again not taking into account prograde or retrograde motion of a captured satellite, the total effective distance would be approximately 2x9576 = say 19150 km.

The Earth moved across the ring at (29.8 – 12.9) kmsec^-1 and so was capable of capturing a satellite for 19150/(29.8-12.9) = 1133.14, say 1133 sec. And as the satellite average speed in this ring was 27.23 kmsec-1 and a satellite at this speed takes 41476 sec for one revolution about protoJupiter then the opportunity for capture of one satellite was 1 in 41476/1133 or 1 in 36.61. For the seven satellites then present the chance of capture of one was 1 in 5.23.

Venus In a similar way, a_V = (4.87x179750²/1999)^1/2 = 8872.1 say 8872 km. and effective capture distance would have been 17744 km.

Venus moved across the ring at (35.0 – 12.9) kmsec^-1 and so was capable of capturing a satellite for 17744/(35.0-12.9) = 802.90 say 803 sec., so the opportunity for the capture of only one satellite was 1 in 41476/803 or 1 in 51.65. If it is assumed that Earth did not capture a satellite from this ring then there would have been two satellites remaining and the chance of capture of a satellite by Venus would have been 1 in 25.8.

Middle ring

Consider only capture.

Earth Applying the force equation 2107.2/556937² = 5.98/a_E² so a_E = 29669.1, say 29670 km.

Again, not taking into account whether the satellite has prograde or retrograde motion the total effective distance would have been 59340 km.

The Earth took 59340/(29.8-12.9) = 3511.24, say 3511 sec. To cross the ring and as the average satellite speed in this ring was 15.47 kmsec^-1 and at this speed took 226202 sec for one revolution about protoJupiter then the opportunity for capture of one satellite was 1 in 226202/3511 or 1 in 64.43. But if three satellites existed in this ring then there was a 1 in 21.5 chance of capture of a satellite.

(An important point in the possible Earth capture of a middle ring satellite is that Uranus did not capture one. This suggests, if the hypothesis is correct, that the satellites were on the Earth-side of protoJupiter as Uranus crossed the ring. This could raise the chance of Earth capture to 1 in 7 or even better. And again, this is a conservative figure.) (See other more recent papers in this website discussing the capture of Moon by Earth and Titan by Saturn.

Venus In a similar way, a_V = (4.87x556937²/1999)^1/2 = 27489.3, say 27490 km. To cross the ring Venus took 54980/35.0-12.9) = 2487.78, say 2488 sec. And as a satellite took 226202 sec. for one revolution about protoJupiter then the opportunity for capture of a satellite was 1 in 226202/2488 or 1 in 90.92. If it is assumed that Earth did not capture a satellite from this ring then there would have been a 1 in 30.3 chance of capture of a satellite by Venus.

Outer ring

Earth The force equation becomes 2107.2/1532405² = 5.98/a_E², so a_E = 81634.0 km.

Again not taking into account prograde or retrograde motion of a captured satellite the total effective distance would be 163268 km.

As for the middle ring the time for Earth to move across the ring was 163268/(29.8-12.9) = 9660.83, say 9661 sec., and as a satellite in this ring took 1031981 sec to complete one revolution about protoJupiter then the opportunity for capture of one satellite in the ring was 1 in 1031981/9661 or 1 in 106.82.

But in the outer ring at that time there were 4 satellites so the chance of capture was 1 in 26.7.

Venus In a similar way, a_V = (4.98x1532405²)^1/2 = 76486.0 km, or an effective distance of 152972 km.

The time for Venus to move across the ring was 152972/(35.0-12.9) = 6921.81. say 6922 sec. and so the opportunity for capture of one satellite was 1 in 1031981/7922 or 1 in 149.09. Assuming that 4 satellites were still present in the ring, the chance of capture of one of them by Venus was 1 in 37.3. But if 3 satellites existed, i.e. Neptune had already captured Triton, then the chance was 1 in 49.7.

(It has since been shown that Triton did not form at the same time as the “medium” density satellites. However, the time between the two events was small and it has been given in a more recent paper in the website what almost certainly did occur. F.L.)

From the above figures we can say that the chance of collision or capture of an inner ring satellite by one of the terrestrial planets (Mercury ignored) was 1 in 2.74 (This figure assumes that Mars captured two satellites.); for a satellite in the middle ring 1 in 12.6; and for a satellite in the outer ring 1 in 15.6.

From the above calculations the possibility of one satellite in the whole system being captured by one of the terrestrial planets was about 1 in 2, at least, and probably much better. The probability of four collisions or captures, i.e. two for Mars and two for Earth, at the periods of densest satellite populations is therefore quite high. And no account has been made in the calculations for possible satellites that collided with the giant planets, or were ejected from the Solar System, or for the effect of ring widths, or as mentioned above concerning the middle ring the satellites being possibly clustered on the terrestrial side of protoJupiter at the time of Earth passing, etc.

It appears to the writer viewing the calculations that it was highly probable that the Earth suffered a collision by an inner ring satellite, so that the explanation for the Earth’s high water content given in sub-section 3(e) is perfectly feasible.

A last comment. In the above attempted explanation for the abundance of water on the Earth I made the assumption and accepted that the colliding “icy” satellite had a S.G. of about 1.715. And in my determination at a later time of the S.G .of Planet X (or satellite X) I calculated its S.G. of about 1.529. I was not happy with the order of the values. I believed, without proof, that the figures should be reversed and in my latest paper on Planet X came to the conclusion that it was Planet X that had the higher figure of 1.715 or there abouts. This is more consonant with the order of ejection for if the “medium icy” sequence of bodies was Ganymede, Titan, Callisto, and Satellite X then the n values sequence in the formula 2x0.981⁺ⁿ should be +2, +4, +6, and for Body X +8 so the S.G. of Planet X should be about 1.715. See the latest Planet X paper in this web site.

Also, for a small, dominantly H₂O-containing “icy” satellite it appears to me that its S.G. should be moderately low; a value below 1.7 would be more likely to be expected; a value nearer, say, S.G.1.5. That is, the missing value of n = 14 (= 1.529). I am not inclined to study the matter further but am certain that both events took place closely as described. F.L., 2009.