A study led by CU Boulder researchers provides new insight into the moon’s excessive equatorial bulge, a feature that solidified in place over four billion years ago as the moon gradually distanced itself from the Earth.

The research sets parameters on how quickly the moon could have receded from the Earth and suggests that the nascent planet’s hydrosphere was either non-existent or still frozen at the time, indirectly supporting the theory of a fainter, weaker sun that at the time radiated around 30 percent less energy than it does today.

The moon currently recedes from the Earth at a rate of about 4 cm per year according to lunar laser ranging observations from the Apollo missions. The recession is believed to result from gravitational or tidal interaction between the Earth and its moon. The same process also causes Earth’s rotation to slow down and the length of day to increase. However, the recession rate for the early moon is largely unconstrained.

“The moon’s fossil bulge may contain secrets of Earth’s early evolution that were not recorded anywhere else,” said Shijie Zhong, a professor in CU Boulder’s Department of Physics and the co-lead author of the new research. “Our model captures two time-dependent processes and this is the first time that anyone has been able to put timescale constraints on early lunar recession.”

The moon's rotation makes it flattened at its poles and bulge at its equator. About two hundred years ago, French mathematician and physicist Pierre-Simon Laplace determined that the moon’s equatorial bulge was too large (by twenty times) for its one-revolution-per-month rotational rate. Scientists have theorized that the moon, born hot, rotated fast after its formation and possessed an equatorial bulge much greater in size than it does today. The bulge tended to shrink in adjustment to reduced rotational force as the moon moved farther from the Earth and reduced its rotational rate, until the moon cooled and stiffened enough to have solidified a permanent bulge in its crust, creating the feature known as the fossil bulge.

The timing and necessary conditions of this fossil bulge formation, however, have remained largely unknown given that no physical models have ever been formulated for this process. Using a first-of-its-kind dynamic model, Zhong and his colleagues determined that the process was not sudden but rather quite slow, lasting several hundred million years as the moon moved away from the Earth during the Hadean time or around 4 billion years ago. But for that to have been the case, Earth’s energy dissipation in response to tidal forces—which for the present-day Earth and its recent past is largely controlled by the oceans—would have to have been greatly reduced at the time.

“Earth’s hydrosphere, if it even existed at the Hadean time, may have been frozen all the way down, which would have all but eliminated tidal dissipation or friction,” Zhong said, adding that a weaker, fainter young sun could have made such conditions possible in theory.

The “snowball Earth” hypothesis has been suggested previously for the Neoproterozoic around 600 million years ago based on geological record. Similar ideas were also hinted for the early Earth on the basis of the fainter young sun, but direct observational evidence in the geological record is currently lacking, making it the subject of debate among scientists.

The researchers plan to continue optimizing their model and will attempt to fill in other knowledge gaps about the moon and Earth’s early days between 3.8 and 4.5 billion years ago.

The study was recently published online in Geophysical Research Letters, a journal of the American Geophysical Union. Co-authors of the research include Chuan Qin (formerly of CU Boulder and now with Harvard University) and Roger Phillips of Washington University in St. Louis (formerly at the Southwest Research Institute in Boulder, Colorado). NASA and the National Science Foundation provided funding for the research.