1

. If you disagree, hold a rubber ball at arm’s length and release it. Of the many possible paths the ball could conceivably take (actually an infinite number), it will follow only one. As another example, compress the ball between two surfaces. Of the many possible ways the ball might deform, it will deform in a way that minimizes its stored energy. These are consequences of physical laws. Most things will not happen, even with an infinite amount of time.  Protons will not turn into planets, plants, or people.

2

. George Wald, “The Origin of Life,” Scientific American, Vol. 191, August 1954, p. 48.

3

. Two international conferences have tried to address this problem. [See P. Brosche and J. Sündermann, editors, Tidal Friction and the Earth’s Rotation (New York: Springer-Verlag, 1978) and P. Brosche and J. Sündermann, editors, Tidal Friction and the Earth’s Rotation II (New York: Springer-Verlag, 1982).] The studies presented were of mixed quality; none considered the effect described in equations 4–9, and all left this recognized problem somewhat “out of focus.”

4

. We will consider only the Earth-Moon interaction. The Sun’s tidal effect is about half that of the Moon.

5

. If a force (or a change in force) is sufficiently small, the displacement it produces is proportional to the small force provided all states passed through are equilibrium states. For example, a small displacement of an extension spring is proportional to the force causing the displacement. This doesn’t hold if the spring breaks or stretches beyond its elastic limit. Tidal forces and displacements at a particular location are quite small.

Once R is fixed, the tide’s height at a specific location depends on many other factors, especially the shape of the coastline and seafloor. When high tides arrive at a coastline with a narrow, funnel-shaped bay, tide heights increase. At the Bay of Fundy in eastern Canada, tides rise and fall up to 48 feet twice daily. The average tidal amplitude on the open ocean is about 30 inches. Inland lakes have practically no tides.  Lake Superior, for example, has 2-inch tides.

Tides also occur in the atmosphere and solid Earth. Relative to the center of the Earth, the foundation of your home (and everything around it) may rise and fall as much as 9 inches, depending on your latitude. Oceanic tides are the dominant cause of the Moon’s recession.

6

. Earth’s mountain ranges and equatorial bulge can be disregarded in this analysis, because their effects on the Moon’s recession cancel over many orbits.

7

. Laser beams have been bounced off arrays of corner reflectors left on the Moon by three teams of Apollo astronauts and the Russian Lunakhod 2 vehicle. Knowing today’s speed of light and the length of time for the beam to travel to the Moon and back gives the Moon’s distance. This has been successfully done more than 8,300 times since August 1986. Adjusting for many other parameters that affect the Moon’s orbit gives its recession rate: 3.82± 0.07 cm/yr.  [See J. O. Dickey et al., “Lunar Laser Ranging: A Continuing Legacy of the Apollo Program,” Science, Vol. 265, 22 July 1994, p. 486.] This recession was first recognized in 1754 by observing the Moon’s increasing orbital period. [For details see Walter H. Munk and Gordon J. F. MacDonald, The Rotation of the Earth (Cambridge, England: Cambridge University Press, 1975), p. 198.]

8

. How high would tides be if the Earth-Moon distance (R) were 15,000 km? (Whether or not the Moon would be pulled apart if it were ever that near Earth will be bypassed. It depends on many factors, including the Moon’s tensile strength, its rotation rate, and a subject called “Roche’s limit.”)

From equation 1b, the tidal height varies as 1/R³. The average height of tides on the open ocean today (with R = 384,400 km) is 30 inches or 0.76 meter. [See Endnote 5, above.] Therefore, if R were ever 15,000 km, the tidal height would be

Tides more than a mile high would occur if R < 30,000 km = 18,606 miles.

9

. In a much more detailed study that incorporated many more variables than I have, Touma and Wisdom arrived at a similar answer.

The evolution of the lunar semimajor axis presents the well-known time scale problem; the lunar orbit collapses only a little over a billion years ago.  Jihad Touma and Jack Wisdom, “Evolution of the Earth-Moon System,” The Astronomical Journal, Vol. 108, No. 5, November 1994, p. 1954.

They then disregarded the consequences of their work by saying, “Presumably, the tidal constants have changed as the continents have drifted.”

Another problem they uncovered, but also chose to ignore, is that as the Moon approaches the Earth, its orbit becomes highly inclined to Earth’s equator. All evolution theories for the Moon have it beginning in the plane of Earth’s equator.

We are presented with an unresolved mystery. All theories of lunar formation require that formation take place in the equator plane, yet models of tidal evolution do not place the Moon there. Touma and Wisdom, p. 1955.

The answer to both these mysteries is that the Moon did not evolve.

10

. The other evolutionary theories on the Moon’s origin require it to have an age of 4.5 billion years. Because we have seen that the Moon cannot be older than 1.2 billion years, and it may be much younger, these other theories can be rejected.

11

. Today, the Moon’s eccentricity is 0.0549. A perfect circle has zero eccentricity. An extremely elongated elliptical orbit has an eccentricity of slightly less than 1.000. The ellipse in Figure 148 on page 266 has an eccentricity of about 0.65.

12

. Most people, even scientists, do not appreciate the difficulty of placing a satellite in a nearly circular orbit. For an artificial satellite to achieve such an orbit, several “burns” are required at just the right time, in just the right direction, and with just the right thrust. Most planets and many moons have nearly circular orbits. How could this have happened?