1

. Scott A. Sandford et al., “Organics Captured from Comet 81P/Wild 2 by the Stardust Spacecraft,” Science, Vol. 314, 15 December 2006, pp. 1720–1724.

2

. “We know that it is hard to find a comet without the spectral features of C₂, C₃, and CN in their comas. Huggins was struck by the fact that the material in the comets was similar to organic matter of unquestioned biological origin on Earth. Many scientists cautiously concluded that the carbon compounds found by Huggins [in 1868] in the comas of comets were, as one of his contemporaries wrote, ‘the result of the decomposition of organic bodies.’ ” [emphasis in original] Carl Sagan and Ann Druyan, Comet (New York: Ballantine Books, 1997), p. 148.

“Recent observations of comet celebrities Halley, Hale-Bopp and Hyakutake [Hyah-koo-tah-kay] revealed that these icy visitors are rife with organic compounds. In 1986 cameras on board the Giotto and Vega spacecrafts captured images of dark material on Halley’s surface that resembles the coallike kerogen in some meteorites, and mass spectrometers caught glimpses of carbon-rich molecules. More recently, ground-based telescopes inspecting the coma and tail of comets Hyakutake and Hale-Bopp distinguished a number of specific organic compounds, including methane and ethane.” Max P. Bernstein et al., “Life’s Far-Flung Raw Materials,” Scientific American, Vol. 281, July 1999, p. 45.

3

. If A and B have a similar and unusual characteristic, or they correlate, some might claim that A caused B. But maybe B caused A—or C caused A and B.  Perhaps no cause-and-effect link exists. Many humorous stories, scams, and even misguided scientific efforts are rooted in this logical fallacy—seeing a relationship and, with no other information, claiming a specific cause and effect.

Because (A) traces of organic molecules are found in comets, and (B) organic molecules are found in every living thing on Earth, did comets bring life to Earth (A caused B)? Maybe comets and organic molecules came from Earth (B caused A). We should consider all possibilities. Many who leap to conclude that comets explain life on Earth know how difficult it is to explain life originating by natural processes. Most authorities will privately admit that life is so complex that they can’t imagine how it could form anywhere. [See pages 14–21.] Desperation may force this poor logic—that comets brought life to Earth. But even if comets did, how did comets acquire life?  It takes more than time and distance.

Be aware that organic molecules—which simply means molecules containing hydrogen plus carbon rings or chains—are as far from becoming life as bricks are from becoming the Empire State Building. Yes, bricks might form naturally in a dried-up stream bed, but I cannot imagine the Empire State Building forming by natural processes. If you saw a large pile of bricks mixed with steel and glass, would you conclude that a building was evolving or had been destroyed?  Great intelligence is needed to produce life.

4

. The Deep Impact space mission found that the nucleus of comet Tempel 1 had a density of 0.62 gm/cm³ and was about 60% empty space. If the dirt’s density was 2.7 gm/cm³ and the ice’s density was 0.92 gm/cm³, it can be shown that about 38% of the comet, by mass, was water. [See M. F. A’Hearn et al., “Deep Impact: Excavating Comet Tempel 1,” Science, Vol. 310, 14 October 2005, p. 262, and Richard A. Kerr, “Deep Impact Finds a Flying Snowbank of a Comet,” Science, Vol. 309, 9 September 2005, p. 1667.]

5

. G. Gloeckler et al., “Interception of Comet Hyakutake’s Ion Tail at a Distance of 500 Million Kilometers,” Nature, Vol. 404, 6 April 2000, pp. 576–578.

6

. John Fleck, “Comets Showered Ice on Moon,” ABQ Journal of Science & Technology, 3 September 1998, p. C3.

7

. W. C. Feldman et al., “Fluxes of Fast and Epithermal Neutrons from Lunar Prospector: Evidence for Water Ice at the Lunar Poles,” Science, Vol. 281, 4 September 1998, p. 1496.

8

. David A. Paige, “Chance for Snowballs in Hell,” Nature, Vol. 369, 19 May 1994, p. 182.

“Radar images of Mercury show evidence of polar frost on that fiery planet.” Andrew Lawler, “Planetary Science’s Defining Moment,” Science, Vol. 295, 4 January 2002, p. 34.

9

. “But the association of comets with catastrophe remains curiously steady through the generations.” Sagan and Druyan, p. 279.

“Here, as indeed among all peoples generally, comets are regarded as omens of disaster.” Fred Hoyle and Chandra Wickramasinghe, Lifecloud (New York: Harper & Row, Publishers, 1978), p. 99.

10

. “For unclear reasons, deep moonquakes seem largely confined to the side of the moon facing Earth.” Elizabeth Svoboda, “New Computers Uncover Old Quakes on the Moon,” Discover, Vol. 27, January 2006, p. 38.

Seismometers left on the Moon during each Apollo landing recorded 12,500 seismic events. Then in 1977 NASA turned the seismometers off. The moonquakes have now been reanalyzed by more powerful methods. Conclusion: Even after making the most adverse assumptions, most deep moonquakes were on the near side of the Moon, and most of those cluster near the central portion of the near side. [See Yosio Nakamura, “Farside Deep Moonquakes and Deep Interior of the Moon,” Journal of Geophysical Research, Vol. 110, 18 January 2005, E01001.]

11

. “Astronomers were stunned by the first images of the moon’s farside, captured by the Soviet spacecraft Luna 3 in 1959. The two hemispheres seemed like different worlds. The face we see has fewer large craters and far greater areas of smooth, dark, frozen lava. Nobody really knows why.” Bob Berman, “Worlds Out of Balance,” Discover, Vol. 24, December 2003, p. 38.

Shadows in Figure 143 accentuate craters near the day-night boundary and minimize the appearance of craters on the near side. However, the Moon’s near side is smoother than the far side, for reasons given in Figure 143’s caption.

12

. A uniform ball of mass M and radius R has a moment of inertia about any diameter of 0.4000 MR². The Moon’s polar moment of inertia is (0.3935 +/- 0.0011) MR²—almost the same. [See J. O. Dickey et al., “Lunar Laser Ranging: A Continuing Legacy of the Apollo Program,” Science, Vol. 265, 22 July 1994, p. 487.] Of course, pressure and density must increase with depth. This accounts for the Moon’s moment of inertia being slightly less than that of a uniform ball.  Little room is left over for a light crust.

13

. Nicholas M. Short, Planetary Geology (Englewood Cliffs, New Jersey: Prentice-Hall, 1975), p. 87.

14

. “In contrast, the far side [of the Moon] almost completely lacks maria.” Paul D. Spudis, “The New Moon,” Scientific American, Vol. 289, December 2003, p. 89.

15

. “A major surprise in the early days of lunar exploration was the discovery that the soft maria visible from earth were far more rare on the moon’s farside, presumably because of some one-sided influence of the earth.  Now refinements of Mariner 9 data show one hemisphere of Mars to be far rougher than the other, and Mariner 10 suggests the same asymmetry for Mercury. Data files grow, observes Bruce Murray of the California Institute of Technology, yet so does the mystery of hemispherical asymmetry. ‘We now know,’ he says, ‘a little less about the moon.’ ” Jonathan Eberhart, “The Mystery of the Hemispheres,” Science News, Vol. 105, 13 April 1974, p. 241.

16

. M. Ozima et al., “Terrestrial Nitrogen and Noble Gases in Lunar Soils,” Nature, Vol. 436, 4 August 2005, pp. 655–659.

17

. Isaac Newton, “Of the Attractive Forces of Spherical Bodies,” Proposition LXX, Theorem XXX, Section XII, Book I, The Principia (1687; reprint, Amherst, New York: Prometheus Books, 1995), p. 154. The shell must have uniform thickness and density.

18

. An oxygen tank that exploded soon after lift-off forced the Apollo 13 astronauts to abort their mission. Instead of landing on the Moon, they looped around the Moon and executed a tricky reentry back to Earth. Ground controllers had difficulty tracking the spacecraft by radar, because a cloud of urine orbited and partially hid the spacecraft. The astronauts were then told to hold all waste liquid in onboard containers. Today, astronauts avoid this problem by dumping waste material overboard just before igniting their rocket thrusters. Gravity, even that of a spacecraft, a rock, or a water droplet, acts on everything.

19

. Two spheres of influence (SoI) are sometimes confused. The first is used for navigating in space. The second, used here, is appropriate for understanding how captures occur in space. It can be shown that the radius of the SoI of a spherical rock of radius r is about

where R is the Earth’s radius and h is the rock’s height above the Earth.

When many particles (rocks, dirt, ice, and water molecules, all moving away from Earth) interact and exchange momentum, their velocities become more similar. The effective SoI of the combined mass increases greatly, and most of those particles will eventually merge.

20

. An extremely rare exception might occur if one body strikes the other with a very delicate glancing blow. Another exception would be if a third particle passing by had just the right mass, speed, direction, and position, so its gravitational attraction could slow the droplet enough to cause capture. However, impacts and interfering third bodies are much more apt to cause scattering than capture.

21

. Every body, even a dust particle or a star, has an escape velocity—that is, the slowest speed needed from a specified point to escape that body and go to infinity. For Earth, from its surface, that speed is 11.2 km/sec (7.0 mi/sec). For something at the surface of the Sun to escape the solar system, it is 617.2 km/sec (383.5 mi/sec). For something 1 AU from the Sun to escape the solar system requires 42.3 km/sec (26.3 mi/sec).

22

. “Capture” is the proper term. Those who say stars, planets, and moons formed through capture often use the misleading terms “accrete,” “condense,” and “gravitational collapse,” which imply a “pulling in” or “acquiring.” These words, while sounding scientific to a layman, betray a misunderstanding of the physics. While gravity would move two isolated particles in space toward each other if their relative velocity were initially zero, particles in space are not isolated and seldom travel with the same speed and direction. For a body to capture a particle, (a) the particle must be within the body’s sphere of influence, (b) the particle’s velocity relative to the body must never carry it outside the sphere of influence, and (c) the body’s gravitational grip on the particle must increase, so later perturbations do not strip the orbiting particle away. Requirement (c) is most easily satisfied if the body has an atmosphere—a surrounding gas.

23

. “It turns out to be surprisingly difficult for planetesimals to accrete mass during even the most gentle collisions.” Erik Asphaug, “The Small Planets,” Scientific American, Vol. 282, May 2000, p. 54.

In 1805, Laplace first explained the “sphere of influence” concept, or, as he called it, the “sphere of attraction.” He applied it to planets acting on comets, but did not use it to show why permanent capture to form larger bodies such as comets or planets is so difficult. [See Nathaniel Bowditch, Celestial Mechanics by the Marquis de Laplace, Vol. 4 (Bronx, New York: Chelsea Publishing Co., 1966), pp. 417–437.]

24

. Unfortunately, “short-period comets” have been arbitrarily defined as comets with periods less than 200 years. A more physically meaningful definition, used here, will be comets with periods less than 100 years, because there is a huge, recognized excess of such comets. Any acceptable theory of comet origins should explain this excess.

25

. All orbital information is from Brian G. Marsden and Gareth V. Williams, Catalogue of Cometary Orbits, 11th edition (Cambridge, Massachusetts: Minor Planet Center, 1996). This catalogue has been updated with recent comet discoveries and information from the Center’s web site.

26

. “Jupiter’s huge attractive mass has somehow collected two-thirds of all the short-period comets into a family. Saturn probably also plays a supporting role in the process.  Jupiter and Saturn appear to be much more important in the story of comets than was indicated by their slight disturbances of the motion of Halley’s comet. The existence of Jupiter’s comet family is one of our important clues to the origin of comets.” Fred L. Whipple, The Mystery of Comets (Washington, D.C.: Smithsonian Institution Press, 1985), p. 74.

“What is the chance that Jupiter could catch them [comets falling from an Oort cloud] by its gravity and tame them into short-period, prograde orbits?  He [H. A. Newton] found that the chance is very small. Only about one in a million would have its period reduced to less than Jupiter’s period of 11.86 years.”  Ibid., p. 75.

27

. “By comparing the orbital element distribution of JFCs [Jupiter’s family of comets] to that produced by our simulations we deduce that JFCs are statistically most likely to have physical lifetimes of about 12,000 years.” Harold F. Levison and Martin J. Duncan, “From the Kuiper Belt to Jupiter-Family Comets,” Icarus, Vol. 127, May 1997, p. 13.

“But once so deflected [into short-period orbits], these comets must have comparatively short lifetimes, astronomically speaking, and probably no short-period comet can survive more than about 10,000 years.” R. A. Lyttleton, Mysteries of the Solar System (Oxford, England: Clarendon Press, 1968), p. 110.

28

. Disregarding the effects of wind resistance, fired bullets and thrown balls are very briefly in elliptical orbits about Earth’s center of mass. Once they strike the Earth’s surface, the orbit ends.

29

. “Many scientific papers are written each year about the Oort Cloud, its properties, its origin, its evolution. Yet there is not a shred of direct observational evidence for its existence.” Sagan and Druyan, p. 210.

However, Sagan and Druyan believed that the Oort cloud exists, and went on to predict (p. 211) that “with the refinement of our scientific instruments, and the development of space missions to go far beyond Pluto,” the cloud will be seen, measured, and studied.

Mathematical errors led to the belief that a cloud of cometary material, called the Oort cloud, surrounds the solar system. [See Raymond A. Lyttleton, “The Non-Existence of the Oort Cometary Shell,” Astrophysics and Space Science, Vol. 31, December 1974, pp. 385–401.] Assuming that the Oort cloud exists helps preserve arguments for a multibillion-year age of the solar system.

“Recently, Lyttleton (1974) confirmed our conclusion of 1954: the Oort’s hypothetical cloud of comets cannot exist.”  S. K. Vsekhsvyatsky, “Comets and the Cosmogony of the Solar System,” Comets, Asteroids, Meteorites, editor A. H. Delsemme (Toledo, Ohio: The University of Toledo, 1977), p. 470.

Vsekhsvyatsky estimated (p. 470) that considerably more than 10²⁰ gm/yr of cometary matter are lost from the solar system. Over the supposed age of the solar system (4.5 billion years), lost comet mass would “nearly correspond to the total present mass of the planets.” He believed this was unreasonable.

“... many people would be happier if there were more objective evidence for the reality of the Oort Cloud.” John Maddox, “Halley’s Comet Is Quite Young,” Nature, Vol. 339, 11 May 1989, p. 95.

30

. “Using current standard models for the formation of comets, a significant number of [hyperbolic] comets should have been observed. This lack of detections of extrasolar comets is becoming an embarrassment to the theories of solar system and cometary formation and may drive the parameters of these models.” Thomas A. McGlynn and Robert D. Chapman, “On the Nondetection of Extrasolar Comets,” Astrophysical Journal, Vol. 346, 15 November 1989, p. L105.

Paul R. Weissman, “Dynamical History of the Oort Cloud,” Comets in the Post-Halley Era, Vol. 1, editors R. L. Newburn et al. (Boston: Kluwer Academic Publishers, 1991), pp. 463–486.

“No comet has ever been observed on a trajectory originating outside the gravitational influence of the Sun. And yet, sooner or later, such comets should be seen.” Sagan and Druyan, p. 350.

31

. “A flaw in our understanding of the orbital evolution of comets is that the number of short-period comets—those with orbital periods less than 200 years, such as comet Halley—is much greater than theory predicts. The discrepancy is enormous; the observed number is two orders of magnitude larger than expected.” Julia Heisler, “Orbital Evolution of Comets,” Nature, Vol. 324, 27 November 1986, p. 306.

32

. This expected distribution of comets, first shown mathematically by van Woerkom in 1948, has frequently been verified by powerful computer simulations. [See A. J. J. van Woerkom, “On the Origin of Comets,” Bulletin of the Astronomical Institutes of the Netherlands, Vol. 10, No. 399, 8 December 1948, pp. 445–472.]

A few researchers once believed that second-pass comets were not visible, because they dimmed after losing volatile gases on their first pass. This early loss of volatiles happens, but the effect is not strong. Comets moving away from the Sun are not appreciably dimmer than when they approached the Sun. [See M. C. Festou, “The Derivation of OH Gas Production Rates from Visual Magnitudes of Comets,” Asteroids Comets Meteors II, editors C. I. Lagerkvist et al. (Uppsala, Sweden: Uppsala University Press, 1986), pp. 299–303.]

Wiegert simulated 125,495 artificial comets in orbits 10,000–50,000 AU from the Sun. For 5 billion simulated years, the giant planets and the galactic tide perturbed the comets. Even when artificially simulating comets that rapidly fade in visibility, Wiegert found that neither fading nor many other effects could explain the lack of observed long-period comets that have completed more than one orbit. [Paul Arnold Wiegert, The Evolution of Long-Period Comets (Ph.D. dissertation, University of Toronto, 1996).]

Thomas D. Nicholson, “Comets, Studied for Many Years, Remain an Enigma to Scientists,” Natural History, Vol. 75, March 1966, pp. 44–46.

Lyttleton, Mysteries, p. 110.

Hannes Alfven and Gustaf Arrhenius, Evolution of the Solar System (Washington, D.C.: NASA, 1976), p. 234.

33

. “Since planetary perturbations typically change 1/a [a quantity proportional to energy per unit mass] by several hundred units during one revolution about the Sun, we were forced to conclude, following Oort, that the great majority of these comets [the near-parabolic comets] were making their first passage through the inner part of the solar system.” Brian G. Marsden et al., “New Osculating Orbits for 110 Comets and Analysis of Original Orbits for 200 Comets,” The Astronomical Journal, Vol. 83, No. 1, January 1978, p. 64.

34

. “There is no example of a known short-period comet evolving into a long-period comet of small enough perihelion to be visible.” Edgar Everhart, “Examination of Several Ideas of Comet Origins,” The Astronomical Journal, Vol. 78, No. 4, May 1973, p. 332.

35

. Harold F. Levison and Martin J. Duncan, “The Long-Term Dynamical Behavior of Short-Period Comets,” Icarus, Vol. 108, March 1994, Figure 5, p. 25.

36

. “Hence, if comets like Hale-Bopp brought in the Earth’s water, they would have brought in a factor of 40,000 times more argon than is presently in the atmosphere.”  T. D. Swindle and D. A. Kring, “Implications of Noble Gas Budgets for the Origin of Water on Earth and Mars,” Eleventh Annual V. M. Goldschmidt Conference, Abstract No. 3785 (Houston: Lunar and Planetary Institute, 20–24 May 2001).

How did comets collect argon? Argon was probably produced by solar wind (which consists of 95% protons) striking chlorine in the frozen salt water that comprises much of a comet. Protons (p) bombarding chlorine (Cl) produce argon (Ar) and a gamma ray (g), a process called proton capture. For example:

p + ³⁵Cl ³⁶Ar + g    or in shorthand:    ³⁵Cl(p,g)³⁶Ar

Only the comet’s outer shell would have this argon, which accumulated after comets were launched. Argon was measured in the gases that vaporized from Hale-Bopp’s outer shell. Failure to recognize proton capture and the presence of 4% chlorine (by mass) in comets will lead to a false conclusion that the entire comet contains large amounts of argon.

Sodium, which few would expect to find in outer space, was one of the first chemical elements identified in comets. [See Donald K. Yeomans, Comets (New York: John Wiley & Sons, Inc., 1991), p. 217.]

37

. “Comet investigators found levels of ethane in Comet Hyakutake that are about 1,000 times greater than can be explained if the molecules were formed by normal physical processes within the gases of the primordial solar nebula, the birth cloud of the Solar System.” Douglas Isbell and Jim Sahli, “Chemical Measurements of Comet Hyakutake Suggest a New Class of Comets,” NASA Press Release 96–108, 31 May 1996.

38

. “Krasnopolsky’s team calculates that comets striking Mars couldn’t deliver enough methane to replace what’s lost.”  Ron Cowen, “Martian Methane: Carbon Compound Hints at Life,” Science News, Vol. 165. 10 April 2004, p. 228.

39

. “But in late March, researchers analyzing data from the European Mars Express satellite reported the planet’s atmosphere contains traces of methane, a by-product of bacteria here on Earth. Could this be the long-awaited sign of Martian life?” Maia Weinstock, “Our Favorite Martians,” Discover, Vol. 25, August 2004, p. 16.

40

. “... there is no reasonable astronomical scenario in which mineral grains can condense [in space].” Fred Hoyle and Chandra Wickramasinghe, “Where Microbes Boldly Went,” New Scientist, Vol. 91, 13 August 1981, p. 413.

“Although very little is known about how the [dust] grains are formed, observations of interstellar matter indicate that the process must be very efficient; otherwise, how could the striking depletion of the refractory elements [such as silicon and magnesium] in the interstellar gas be explained?” Hubert Reeves, “Comets, Solar Wind and the D/H Ratio,” Nature, Vol. 248, 29 March 1974, p. 398.

My Translation: No one knows how dust could form in space, but dust formation must be very efficient, because practically none of the chemical elements needed to form dust are there. (We know that dust formed in space, because dust is in space. )

My Response: Maybe comet dust came not from almost-empty space, but from Earth.

41

. “As in the interstellar medium, much of the dust from comets consists of silicate minerals, but despite the similarities, there are puzzling differences. For example, interstellar dust shows the absorption signature of amorphous particles with a silicate composition, whereas Hale-Bopp and other comets have crystalline silicate, probably in the form of magnesium-rich olivine.” Dale P. Cruikshank, “Stardust Memories,” Science, Vol. 275, 28 March 1997, p. 1896. [See also pp. 1904–1909.]

Humberto Campins and Eileen V. Ryan, “The Identification of Crystalline Olivine in Cometary Silicates,” The Astrophysical  Journal, Vol. 341, 15 June 1989, pp. 1059–1066.

“In particular, the resonance peak seen at 11.2 mm [in the impact debris from comet Tempel 1] is indicative of Mg-rich crystalline olivine.”  K. J. Meech et al., “Deep Impact: Observations from a Worldwide Earth-Based Campaign,” Science, Vol. 310, 14 October 2005, p. 267.

42

. Could interstellar dust, which has no crystalline pattern, have melted (or almost melted), cooled, crystallized, and then acted as condensation sites for water ice that formed comets? Probably not. Had nonspherical dust particles melted, or almost melted, they would be spherical due to their surface tension. (Surface tension is what causes drops of water to be nearly spherical.) Interstellar dust particles polarize starlight, so they must be elongated. Therefore, cometary dust is probably not derived from heated interstellar dust.

43

. M. F. A’Hearn et al., pp. 258–264.

44

. “The existence of hydrated [containing liquid water] silicates in comets is provocative, because it would suggest the presence of abundant amounts of reactive water in the formation region of the comet or in the cometary parent body.” Carey M. Lisse et al., “Spitzer Spectral Observations of the Deep Impact Ejecta,” Science, Vol. 313, 4 August 2006, p. 637.

“The presence of carbonates is provocative because, like the phyllosilicates, liquid water was thought to be required to form carbonates from CO2 in the presence of silicates.”  Ibid.

These results are “provocative” only if you didn’t realize that comets came from the earth—the water planet.

45

. “[Comet Tempel 1 is] the size of a mountain held together with the strength of the meringue in a lemon meringue pie.” Carey M. Lisse as quoted by Ron Cowen, “Deep Impact,” Science News, Vol. 168, 10 September 2005, p. 169.

“[The comet’s] structure is more fragile than that of a soufflé ....”  Jay Melosh as quoted by Ron Cowen, Ibid., p. 168.

46

. “The most abundant minerals are the crystalline silicate minerals, olivine and pyroxene, along with troilite (FeS). These are very stable phases, common in planetary materials; however, finding them here is somewhat surprising because many expected that cometary material would be similar to interstellar material, in which most silicates are believed to be amorphous. In contrast, cometary amorphous material in the returned samples is rare or nonexistent.” Don S. Burnett, “NASA Returns Rocks from a Comet,” Science, Vol. 314, 15 December 2006, p. 1710.

47

. Hoyle and Wickramasinghe, Lifecloud, pp. 87–113.

For two decades, these authors have led a growing belief among scientists that comets brought cellulose, bacteria, and other organic matter to Earth. To understand the faulty logic that led to this conclusion, see Endnote 2 on page 282.

Hoyle and Wickramasinghe, “Where Microbes Boldly Went,” pp. 412–415.

48

. Hoyle and Wickramasinghe, Lifecloud, p. 91.

49

. “The cellulose strand is a complex structure, and one can wonder how a giant molecule of such a highly organized form could be present in interstellar space.” Ibid., p. 94.

50

. Roland Meier et al., “A Determination of the HDO/H₂O Ratio in Comet C/1995 O1 (Hale-Bopp),” Science, Vol. 279, 6 February 1998, pp. 842–844. [Similar and consistent measurements also have been made of comets Halley and Hyakutake.]

Roland Meier and Tobias C. Owen, “Cometary Deuterium,” Space Science Review, Vol. 90, Nos. 1–2, 1999, pp. 33–43.

51

. A. Vidal-Madjar, “Interstellar Helium and Deuterium,” Diffuse Matter in Galaxies, editors J. Audouze et al. (Boston: D. Reidel Publishing Co., 1983), pp. 57–94.

52

. Of the hundred or so important publications on this topic, the following is most recommended: Louis A. Frank with Patrick Huyghe, The Big Splash (New York: Carol Publishing Group, 1990). [See also related endnotes on page 96.]

53

. “We found that there were ten times as many small comets in early November as there were in mid-January.”  Frank and Huyghe, p. 187.

54

. These arguments are effectively rebutted by Louis A. Frank and J. B. Sigwarth in “Atmospheric Holes: Instrumental and Geophysical Effects,” Journal of Geophysical Research, Vol. 104, No. A1, 1 January 1999, pp. 115–141.

55

. “In view of the connection of comets, meteors, and meteorites, the absence of meteorites in old deposits in the crust of the earth is very significant.  It has been estimated that at least 500 meteorites should have been found in already worked coal seams, whereas none have been identified in strata older than the Quaternary epoch (about 1 million years ago). This suggests a very recent origin [of meteors] and, by inference, of comets.” N. T. Bobrovnikoff, “Comets,” Astrophysics, editor J. A. Hynek (New York: McGraw-Hill Book Co., 1951), p. 352.

56

. Thomas C. Van Flandern, “A Former Asteroid as the Origin of Comets,” Icarus, Vol. 36, October 1978, pp. 51–74.

Tom C. Van Flandern, Dark Matter, Missing Planets and New Comets (Berkeley, California: North Atlantic Books, 1993), pp. 185–190.

Van Flandern built on earlier proposals by Olbers (1796) and Ovenden (1972) that a planetary breakup produced the asteroids. Van Flandern has altered his earlier paper in several ways. For example, the exploded planet was initially 90 Earth masses. Since then, his number of exploded planets has increased and their total mass has decreased.

57

. Bode’s law is a simple formula which gives the approximate distance of most planets from the Sun. While Bode’s law has no theoretical justification, it correctly predicted the existence and approximate orbital radius of Uranus (1781), but not Neptune (1846) and Pluto (1930). Also predicted is a planet 2.8 AU from the Sun, which closely corresponds to the average position of most asteroids. This led to the early belief that asteroids are the remains of an exploded planet that once orbited 2.8 AU from the Sun. [For reasons given on page 292, most experts now reject this.] Bode’s formula is

Consider how many thousands of other equally simple-looking formulas with arbitrary numbers (corresponding to 0.4, 0.3, 2, and the values for n ) could be constructed. It should not be surprising that one of these formulas could approximate 7 of the 9 planet-Sun distances.

Bode’s law, a mathematical curiosity rather than a true law, was formulated by Johann Daniel Titius in 1766 but popularized by Johann Bode in 1772. Thus, it is often called the Bode-Titius law or the Titius-Bode law.

58

. In 1668, Johannes Hevelius wrote that comets formed in the atmospheres of the giant outer planets and were flung into space by the planets’ rotation. In 1814, French mathematician Joseph Louis Lagrange proposed a more modern version of this theory. Since then, others have refined the theory, especially S. K. Vsekhsvyatsky.

S. K. Vsekhsvyatsky, “New Evidence for the Eruptive Origin of Comets and Meteoritic Matter,” Soviet Astronomy, Vol. 2, No. 3, November–December 1967, pp. 473–484.

S. K. Vsekhsvyatsky, “The Origin and Evolution of the Comets and Other Small Bodies in the Solar System,” The Motion, Evolution of Orbits, and Origin of Comets, editors G. A. Chebotarev and E. I. Kazimirchak-Polonskaya (New York: Springer-Verlag, 1972), pp. 413–418.

59

. J. H. Oort, “The Structure of the Cloud of Comets Surrounding the Solar System, and a Hypothesis Concerning Its Origin,” Bulletin of the Astronomical Institutes of the Netherlands, Vol. 11, No. 408, 13 January 1950, pp. 91–110.

60

. Oort initially estimated that 10¹¹ comets formed 50,000–150,000 AU away. Later, others realized that at the more distant end of that range the Sun’s gravity is so weak that passing stars, galactic clouds, and the galaxy itself would have stripped too many comets from the Oort cloud long ago. [See, for example, Julio A. Fernández, “Dynamical Aspects of the Origin of Comets,” The Astronomical Journal, Vol. 87, No. 9, September 1982, pp. 1318–1332.] To solve this problem, more comets (10¹² comets) are usually assumed to be in the cloud initially, and the cloud is assumed to be concentrated nearer the 50,000 AU end of that distance range. Others have proposed that at least 10¹⁵ comets must initially populate the Oort cloud. Oort cloud theories have many variations; only the best known are described here.

61

. See “Is Pluto a Planet?” on page 25.

62

. H. D. P. Lee, Aristotle: Meteorologica (Cambridge, Massachusetts: Harvard University Press, 1952), p. 43.

63

. Thomas H. Corcoran, Seneca: Natural Quaestiones (Cambridge, Massachusetts: Harvard University Press, 1972), pp. 227–299.

64

. Previously, faulty logic (traceable to the time of Aristotle) went as follows: Because bodies (stars) beyond the Moon do not change their appearance, and a comet changes weekly, comets must not lie beyond the Moon.

65

. M. E. Bailey et al., “The Origin of Comets,” Vistas in Astronomy, Vol. 29, 1986, p. 61.

66

. Peter Lancaster-Brown, Halley’s Comet & the Principia (Aldeburgh, England: Aries Press, 1986), p. 17.

67

. On 1 March 1665, Samuel Pepys entered in his famous diary the following statement:

At noon I [went] to dinner at Trinity House, and thence to Gresham College, where Mr. Hooke read a second very curious lecture about the late Comet; among other things proving very probably that this is the very same Comet, that appeared before in the year 1618, and that in such a time probably it will appear again, which is a very new opinion; but all will be in print. Samuel Pepys, The Diary of Samuel Pepys, editor Henry B. Wheatley, Vol. 4, Part 2 (New York: Croscup & Sterling Co., 1946), p. 341.

Pepys later became the president of The Royal Society (of London), the prestigious scientific body that hosted the above lecture. The idea that some comets reappear was “a very new opinion” and deserves credit for originality. While no periodic comets were visible between 1609 and 1677, Robert Hooke may have suggested the possibility to later researchers, such as Edmond Halley. Halley’s correct prediction in 1705 of the return of the comet of 1682 (later called Halley’s comet) in 1758 was one of science’s classic achievements. However, Halley was criticized for making a prediction that would not be tested until after his death, “when he could no longer be embarrassed.”

68

. Newton, “That the Comets Are Higher Than the Moon, and in the Regions of the Planets,” Proposition XXXIX, Lemma IV, Book III, Principia, pp. 399–401.

69

. Fred L. Whipple, “Discovering the Nature of Comets,” Mercury, Vol. 15, January–February 1986, p. 5.

70

. Richard A. Proctor, “Comet Families of the Giant Planets,” Knowledge: A Monthly Record of Science, Vol. 6, 4 July 1884, p. 5.

Richard A. Proctor, “The Capture Theory of Comets,” Knowledge: A Monthly Record of Science, Vol. 6, 8 August 1884, pp. 111–112, 126–128.

71

. “Thus, cometary nuclei could not have condensed in situ at distances exceeding 100 AU ... Direct condensation of the comets in situ, at the great distances of their aphelia in Oort’s sphere, is not possible.”  Ernst J. Öpik, “Comets and the Formation of Planets,” Astrophysics and Space Science, Vol. 21, 1973, pp. 320, 394.

72

. Thomas M. Donahue, “Comment on the Paper ‘On the Influx of Small Comets into the Earth’s Upper Atmosphere II. Interpretation’ by L. A. Frank et al.,” Geophysical Research Letters, Vol. 13, No. 6, June 1986, pp. 555–557.

73

. Jack G. Hills, “Comet Showers and the Steady-State Infall of Comets from the Oort Cloud,” The Astronomical Journal, Vol. 86, No. 11, November 1981, pp. 1730–1740.

74

. This high improbability can be shown two ways. First, the “back-of-the-envelope” method. The Marsden-Williams Comet Catalogue lists 774 different sightings of nonperiodic comets. One can select two out of 774 different objects 299,151 ways, or . Five numbers (i, q, e, w, and W) specify an ellipse in space.  Let’s say that the chance that two randomly-selected comet sightings have “similar” values for the combination q and e is 0.25—at least as similar as those of the “strange pairs.” Two angles (W and w) have values ranging from 0 to 360 degrees and a third angle, i, ranges between 0 and 180 degrees. If each comet sighting in a “strange pair” had values for i, W , and w  within five degrees on either side of the corresponding angles of the other comet, one might expect about three “strange pairs” simply due to chance. 

This is a long way from the twelve “strange pairs” actually observed.

A more accurate approach involves a computer simulation. By examining the 30 recorded consecutive orbits of Halley’s comet, one can see that planetary perturbations change certain orbital elements less than others. (For example, i—the angle of inclination—changes very little from orbit to orbit.) Therefore, changes in each orbital element must be weighted properly when comparing two different orbits.

Next, for all 774 comet sightings, I swapped each true orbital element with the corresponding orbital element of a randomly chosen comet. Then a count was made of how many of the 299,151 random pairings were as similar as the “strange pairs.” Typically, there were three. In other words, chance can explain about three of the twelve “strange pairs” shown on page 273. That leaves about nine pairs—or nine comets that were seen on two consecutive orbits.

This is surprising, because the estimated periods for both members of each pair are too large for them to be the same comet. However, these comets spend most of their time far beyond the planets. Some very slight force, accelerating the comets for centuries, could greatly shorten their periods.

75

. Hannes Alfven and Gustaf Arrhenius, pp. 231–238.

76

. For example, billiard balls are very elastic (springlike), so collisions disperse the balls. However, if the balls were made of tar (inelastic), the balls would deform or even stick together on impact, so their paths would tend to merge.

77

. R. A. Lyttleton, The Comets and Their Origin (Cambridge, England: At the University Press, 1953), pp. 62–110.

78

. “Although ice has been detected [in interstellar space] by its 3.1 m   m absorption band, it is not nearly as abundant as expected.” P. G. Martin, McGraw-Hill Encyclopedia of Science & Technology, 6th edition (New York: McGraw-Hill Book Co., 1987), Vol. 9, p. 326.

79

. “... we have identified a compositional unit on Mars that contains a mineralogical component likely attributable to chloride salts. We initially identified these deposits because of their spectral distinctiveness ... The deposits range in area from ~1 km² to ~25 km² [at about 200 locations] and generally are topographically lower than the immediate surrounding terrain.” M. M. Osterloo et al., “Chloride-Bearing Materials in the Southern Highlands of Mars,” Science, Vol. 319, 21 March 2008, p. 1651.

“[The Mars Rover named Opportunity, operating in what appears to be a dried-up water channel,] has uncovered soil that is more than half salt, adding to the evidence for Mars’ wet past.” Guy Webster, “Mars Rovers Break Driving Records, Examine Salty Soil,” Jet Propulsion Laboratory News Release, 2 March 2005, p. 1.

“Some rocks may be as much as 40 percent salt, he notes. ‘That’s an astonishing amount’ and could result only from a briny solution soaking through rock and then evaporating, leaving the salt behind, Clark says.”  Benton Clark as quoted by Ron Cowen, “Red Planet Makes a Splash,” Science News, Vol. 165, 6 March 2004, p. 147.

80

. Many claim that comets had to begin outside the orbit of Mars where typically (a) temperatures are cold enough for frost to condense on dust particles in space, and (b) the Sun’s ultraviolet radiation is unlikely to break water molecules apart.  This belief overlooks two considerations.

First, if water vapor condensed as frost on dust particles beyond Mars, then frost should be commonly detected on asteroid surfaces.  Frost is not observed. Second, icy particles orbiting beyond Mars, will not, in general, form a comet. Long periods of time increase the chances of water vapor and ice particles disintegrating.

On the other hand, the fountains of the great deep would quickly form comets. Water molecules would not have to be brought together; they would start together. Dirt, ice, gases, and other unlikely chemicals in comets would not need to be found and mixed uniformly together; they also would start together.

81

. “Our next worry arose because the condensation of water-ice grains in interstellar clouds of low density presented severe conceptual problems. For ice crystals less than a micrometre in size to form in a pure gas, ‘condensation nuclei’, about which the crystals grow, must form at an adequate rate. ... Another early objection we had against the ice-grain theory was that calculations based on this model could not reproduce the way in which the fogging, or extinction, of starlight varied with wavelength: ... Secondly, attempts to find the strong absorption band at 3.1 m   m due to water ice in the spectra of heavily obscured stars consistently failed.” Hoyle and Wickramasinghe, “Where Microbes Boldly Went,” p. 412.

82

. Zdenek Sekanina, “Detection of a Satellite Orbiting the Nucleus of Comet Hale Bopp (C/1995 O1),” First International Conference on Comet Hale Bopp, Puerto de la Cruz, Tenerife, Canary Islands, Spain, 2–5 February 1998.

83

. The energy per unit mass (E) of a comet in a closed (i.e. elliptical) orbit can be written in two independent ways: 

where V is its velocity, R is its distance from the center of mass of the solar system, G is the gravitational constant, M is the mass of the solar system, and a is the comet’s semimajor axis.  Eliminating E and solving for V² gives

Knowing a comet’s velocity (V), position (R), and semimajor axis (a), we can calculate the mass of the solar system. Consider two possible values of the semimajor axis: a large value (a_L) which gives a mass M_L, and a small value (a_S) which gives a mass M_S.  This gives us two equations: 

Eliminating V² and solving for the ratio of the two corresponding masses of the solar system gives 

Let’s say R = 1 AU when a semimajor axis is calculated from trajectory estimates. Comets with an orbital period of 5,000 years have aphelions 585 AU. If 2a_L = 50,000 AU and 2a_S = 586 AU, then the mass ratio on the left side is only 1.0017. So, if the solar system’s mass is greater than usually assumed by only 17 parts in 10,000 and is concentrated at the center of the solar system, comets thought to be falling in for the first time from 50,000 AU with periods of about 4,000,000 years would have been launched only 5,000 years ago.

As explained on page 272, the extra mass is probably not concentrated at the center of the solar system. In November 2005, Jon Schoenfield analyzed the situations where the mass is spherically distributed 40 AU or more from the Sun. In those cases, the required extra mass would exceed 70 Jupiters.

84

. Actually, what is measured is not mass (M) but mass times the gravitational constant (G), or GM. Because the gravitational constant is known to only about one part in a thousand, mass is equally uncertain. However, only the GM of central bodies is of concern in calculating orbits, and those values for the Sun and planets are generally known to much higher precision.

85

. My computer simulations of the solar system during its last 350 years have shown that Herschel-Rigollet did not come near enough to any planet for that gravity boost. Therefore, its gravity boost probably came from mass beyond 40AU.

86

. John D. Anderson et al., “Indication, from Pioneer 10/11, Galileo, and Ulysses Data, of an Apparent Anomalous, Weak, Long-Range Acceleration,” Physical Review Letters, Vol. 81, No. 14, 5 October 1998, pp. 2858–2861.

John D. Anderson, personal communication, 25 September 1998.

87

. Lester Haar et al., NBS/NRC Steam Tables (New York: Hemisphere Publishing Corporation, 1984), p. 208.

88

. George E. Anderson, mechanical engineer, suggested that water hammers acted during the flood.

89

. K. J. Meech, and O. R. Hainaut, “HST Imaging of Distant Comet Nuclei,” Bulletin of the American Astronomical Society, Vol. 29, July 1997, p. 1021.

90

. Richard A. F. Grieve, “The Record of Impact on Earth,” Geological Society of America, Special Paper 190, 1982, pp. 25–37.

91

. The energy required just to “disperse” a planet of uniform density, mass M, and radius R can be shown to be 

where G is the gravitational constant. If the planet’s density is greater in its core, as it is for all planets, the energy requirement increases. “Disperse” here means to accelerate each of the planet’s particles to its escape velocity.

92

. W. McD. Napier and R. J. Dodd, “The Missing Planet,” Nature, Vol. 242, 23 March 1973, pp. 250–251.

A planet could explode if it contained enough fissionable material that suddenly became a critical mass. However, as Anders notes, “such an explosion 6 million years ago [or less] would have left large amounts of long-lived radioactivity, such as Be¹⁰ and Mn⁵³, on the Earth, Moon, and meteorites.”  These isotopes have not been detected. [See E. Anders, Discussions of “A Former Major Planet of the Solar System,” Comets, Asteroids, Meteorites, editor A. H. Delsemme (Toledo, Ohio: The University of Toledo, 1977), p. 479.]

93

. Jupiter generates tidal friction inside Io, which produces the heat. [See Ron Cowen, “Close Encounter: Galileo Eyes Io,” Science News, Vol. 156, 11 December 1999, pp. 382–383.]

94

. S. K. Vsekhsvyatsky, “Comets and the Cosmogony of the Solar System,” Comets, Asteroids, Meteorites, editor A. H. Delsemme (Toledo, Ohio: The University of Toledo, 1977), p. 470.

95

. Ariel A. Roth, “Some Questions about Geochronology,” Origins, Vol. 13, No. 2, 1986, p. 75.

96

. Marsden and Sekanina, p. 1123.

97

. Fernández, pp. 1318, 1324.

98

. Paul R. Weissman, “The Oort Cloud and the Galaxy: Dynamical Interactions,” The Galaxy and the Solar System, editors Roman Smoluchowski et al. (Tucson, Arizona: The University of Arizona Press, 1986), p. 212.

99

. Some researchers have suspected that one of two stars, Algol or Gliese 710, may have recently disturbed an Oort cloud. Actual measurements dispute this. “The new figures reveal that neither star comes close enough to shake up the Oort Cloud and generate a comet shower.” Ron Cowen, “Dino Death: A Stellar Weapon,” Science News, Vol. 153, 31 January 1998, p. 79.

Jeffrey Winters, “A Brief Tour of a Bad Cosmic Neighborhood,” Discover, Vol. 19, April 1998, p. 56.

100

. Julio A. Fernández, “The Formation of the Oort Cloud and the Primitive Galactic Environment,” Icarus, Vol. 129, September 1997, pp. 106–119.

Everhart, p. 329.

101

. Fernández, “Dynamical Aspects of the Origin of Comets,” p. 1318.

102

. Any giant planet would expend much of its energy in flinging 10,000 Earth masses of comets out toward an Oort cloud. Also, the gravity-assisted boosts needed to give so many comets their angular momentum would shrink the planet’s orbit, requiring it to have begun much farther from the Sun.

While this might help solve one aspect of the comet origin problem, it creates problems for the few astronomers trying to figure out how the giant planets evolved. These astronomers wonder how the giant planets could form where they are now, even if billions of years were available. That problem worsens for objects trying to form farther from the Sun, where matter is more spread out and moving even slower.  [See Öpik, pp. 307–398. Also see Richard Greenberg, “The Origin of Comets Among the Accreting Outer Planets,” Dynamics of Comets: Their Origin and Evolution, editors Andrea Carusi and Giovanni B. Valsecchi (Boston: D. Reidel Publishing Co., 1985), pp. 3–10.]

103

. S. Alan Stern and Paul R. Weissman, “Rapid Collisional Evolution of Comets during the Formation of the Oort Cloud,” Nature, Vol. 409, 1 February 2001, pp. 589–591.

104

. “No wastage would occur with Uranus or Neptune, but then the ejection time scale, 10¹¹ yr, is prohibitive.” Öpik, p. 395.

105

. Gerard P. Kuiper, “On the Origin of the Solar System,” Astrophysics, editor J. A. Hynek (New York: McGraw-Hill Book Co., 1951), pp. 357–424.

106

. Ron Cowen, “Second Look Finds No Comet Reservoir,” Science News, Vol. 149, 22 June 1996, p. 395.

107

. Weissman, p. 210.

108

. John F. Kerridge and James F. Vedder, “An Experimental Approach to Circumsolar Accretion,” Symposium on the Origin of the Solar System (Paris, France: Centre National de la Recherche Scientifique, 1972), pp. 282–283.

109

. Martin Harwit, Astrophysical Concepts (New York: John Wiley & Sons, 1973), pp. 394–395.

110

. Thomas S. Kuhn, The Structure of Scientific Revolutions (Chicago: The University of Chicago Press, 1970). [Both the National Review and the Modern Library (a division of Random House) listed this book among the hundred best nonfiction books written in English during the 20th century.]

111

. For example, recovered cometary material should contain minerals and isotope abundances that match those on Earth. If not, the theory that comets came from Earth will be severely weakened. However, if those minerals and isotopes are found, other theories are weakened. Resources of time and money can be more wisely spent by testing theories that better explain all the evidence.