Evolution of the Earth‐Moon System

The tidal stretching of Earth is not an instantaneous effect. The mechanical strength of Earth's rocks produces a time delay in the tidal rise and fall of the solid surface. Similarly, it takes time for water to flow; hence, the ocean tidal bulge is not perfectly aligned to the direction of the Moon or Sun (see Figure 1). The existence of the tidal bulge in turn results in additional gravitational forces that act opposite to the rotation of Earth, and in the direction of the motion of the Moon in its orbit. Earth's rotation, therefore, is slowing and the orbital distance to the Moon is slowly increasing with a proportional increase in its orbital period (the Earth‐Sun effect is negligible, and hence the length of the year is basically constant). Both effects are measurable. Growth patterns in 400 million‐year‐old fossils show daily, monthly, and annual cycles suggesting an Earth day of 22 hours at that time and a lunar synodic month of 28 present days (in comparison to the current value of 29.5 days). The study of the occurrence of historical eclipses also shows the slowing of Earth's rotation. This slowing is also responsible for the annual or semi‐annual addition of a second to our timekeeping in order to keep our clocks in synchronicity with Earth's rotation. Finally, direct measurement of the lunar distance over the last 25 years shows an annual increase in its orbital distance of about 2 centimeters per year.



Figure 1

The effects of the Moon's tidal force on Earth.


It is equivalent to consider the tidal evolution of the Earth‐Moon system in terms of energy. It takes energy to make Earth or the Moon stretch; thus rotational and orbital energy is expended or dissipated by tidal effects. This phenomenon is termed tidal friction. Bending a paper clip is analogous — mechanical energy must be used to bend the metal, which converts this energy into waste heat.

These tidal effects are mutual. The Moon acts on Earth, and Earth acts on the Moon. The Moon is the smaller object, and the effect of tidal friction has been to change the lunar rotation until its rotational period is equal to its orbital period about Earth — the Moon keeps the same face toward Earth. Ultimately, the Moon's action on Earth will produce a similar consequence. When Earth and the Moon achieve full synchronicity, with each rotation equal to their mutual orbital period, it is estimated that these periods will equal 55 present days and the Earth‐Moon separation will be 613,000 kilometers. The effects of tidal evolution also are seen elsewhere in the solar system.

Every moon in the solar system revolves with a period equal to its orbital period, thus keeping the same face to its primary planet. Both Pluto and its moon, Charon, have achieved synchronicity, each showing the same face to the other. And the planet Mercury, closest to the Sun, has a rotational period that matches its orbital motion about the Sun at perihelion, where the tidal forces are strongest.