The length of a day 900 million years ago was only about 18 hours, according to a study in the July 5, 1996, edition of the journal Science. The study, authored by planetary scientists and geologists from the University of Arizona in Tucson, the Indiana Geological Survey in Bloomington, the University of Utah in Salt Lake City, and Colorado State University in Fort Collins, inferred from the geologic record that the moon has receded from the earth at an approximately constant rate over millions of years. The study results were based on records of ancient tidal patterns left in sedimentary rock in the United States and Australia.

Astronomers have known for many years that the moon and earth are moving apart. The United States Apollo 11 mission to the moon in 1969 provided the means to collect direct evidence of this recession by placing a laser-beam reflector on the moon. By sending a laser beam from earth to the reflector on the moon, scientists could measure precisely how long it took for the laser beam to travel and thereby measure the precise distance between the earth and the moon, knowing that the laser beam traveled at the rate of 300,000 km/sec (186,000 mi/sec), the speed of light.

The reflector measurements indicated that the earth and moon are moving apart at a rate of about 3.82 cm (about 1.5 in) per year. Astronomers had previously deduced from the dates of lunar eclipses that the distance between the earth and moon has changed over time.

A geologic record of the changing relationship between the earth and moon has been more difficult to find, however. In the recent study, the investigators examined deposits known as tidal rhythmites or tidalites (rock formed from the sand and mud deposits of ocean tides) in four rock formations of various ages. The rock deposits studied included the Big Cottonwood Formation in Utah (900 million years old); the Elatina Formation in Australia (650 million years old); the Pottsville Formation in Alabama (312 million years old); and the Mansfield Formation in Indiana (305 million years old). A rock formation is a grouping or layering of rock deposits similar enough to be considered as a unit.

The very thin layers found in tidalites are records of daily tides. The two strong tides and two weak tides of each lunar month—the time it takes for the moon to revolve once around the earth—are called spring tides and neap tides, respectively, and show up as distinct bands. These bands in tidalites are typically spaced a few millimeters apart. These patterns provide information about the interaction between the earth and moon because tides are caused by the moon's gravitational pull on the earth (and to a lesser extent the sun's), particularly on the earth's oceans.

The gravitational pull on the earth's oceans and the outward centrifugal force generated by the rotation of the earth and moon system combine to form high tides on the sides of the earth closest to and farthest from the moon. As the earth turns on its axis, the tides move across the surface of the planet, creating two high tides each day at any given location on the earth's oceans. The weaker neap tides and stronger spring tides each lunar month are a result of the moon's changing alignment with the sun as the moon orbits the earth.

The researchers, led by planetary scientist Charles P. Sonett, a professor emeritus at the University of Arizona, examined the rock samples to determine seasonal patterns within the tide cycles that would indicate the passage of a year. The researchers could then count the number of lunar cycles each year, giving the speed at which the moon was orbiting the earth. As expected, the moon was found to revolve around the earth more quickly millions of years ago than it does at the present time.

The lengthening of the lunar cycle on earth and the moon's recession are directly related: As the earth and moon rotate more slowly, the moon moves farther from the earth. In mechanical terms, the total momentum of the two bodies remains nearly the same (some energy is lost to friction through the tides), but potential energy—energy based on position in a mechanical system rather than movement—is being transferred to the moon.

Based on the changing length of the lunar cycle over time, the scientists calculated the rate of lunar retreat over hundreds of millions of years. They found this rate to be comparable to the contemporary rate found by the Apollo program experiment, suggesting that the retreat of the moon has progressed steadily over time.

Based on this rate of lunar retreat and the orbital mechanics of the earth-moon system, the study authors found that a day on earth about 900 million years ago, near the end of the Proterozoic Eon, lasted about 18 hours. The study indicated that in the late Proterozoic, one year—one complete circuit of the earth around the sun—equaled 481 days.