The distance to the Moon and the length of the day 2.46 billion years ago

At a slow pace, the Moon is moving away from the Earth and the Earth is rotating more slowly around its axis. To say something about these changes in the distant past, geologists use information stored in rocks and fossils. But the further back in time they look, the more difficult it becomes to retrieve this information. An international team of earth scientists has now managed to accurately determine the distance to the Moon 2.46 billion years ago, using so-called Milankovitch cycles. This is more than a billion years further back in time than was previously possible.

In their study, the team of scientists affiliated with Utrecht University, the University of Geneva and the University of Quebec in Montreal looked at a very ancient type of sedimentary rocks in Western Australia, which are known as ‘banded iron formations’. In these deposits, they found a regular pattern of iron-rich layers alternating with layers containing more clay. According to the researchers, this characteristic pattern is related to periodic changes in the shape of Earth’s orbit and the orientation of it spin axis. These past variations, in turn, influenced the distribution of solar radiation that Earth received (the Milankovitch cycles), and therefore also the climate. And it is these climate fluctuations that were subsequently recorded as cyclical patterns in the geological record. But what is important here is that this characteristic cycle pattern also changed gradually over time. This slower shift is the direct consequence of the ‘tidal evolution’ of the Earth-Moon system, and is thus also related to the distance between the Earth and the Moon in the past, explains earth scientist Margriet Lantink from Utrecht University.

  • Joffre Gorge, Karijini Nationaal Park, West-Australië
Click to enlarge image.

The Joffre Gorge in the Karijini National Park in Western Australia where Lantink and her team found evidence for the presence of Milankovitch cycles in 2.46-billion-year-old banded iron formations. Regular alternations between reddish-brown, harder rock layers and shadowy, softer clay layers on a scale of just below 1 meter are particularly well expressed in the cliff on the left of the picture. The researchers have linked these alternations to periodic changes in the eccentricity (ellipticity) of the Earth's orbit, at a scale of about 100,000 years. Photo: Greg Jack.


Through detailed analysis of the cycle patterns in the rock layers, the scientists were able to reconstruct the distance between the Earth and Moon at the time of deposition, 2.46 billion years ago. “Today, this distance is around 384,300 kilometres. On average, of course, because the Moon doesn’t make a perfect circle around the Earth; its orbit is an ellipse. During the time interval that we studied, the Earth-Moon distance was a lot shorter: around 321,800 kilometres.” This distance turns out to be consistent with an improved model for the Earth-Moon system history recently published by French astronomers. “It is also important to note that our interpretation of the patterns in the rock strata in terms of the Milankovitch cycles was confirmed by uranium–lead dating from volcanic minerals in the rock samples.” 

Gesteenteformatie in Joffre Gorge, Karijini Nationaal Park, West-Australië
Photo: Frits Hilgen

Regular alternations between white, reddish-brown and grey-blue layers on a scale of about 10 cm, which the researchers link to the precession cycle of the Earth's axis (a motion comparable to a spinning top), and which is visible in the foreground on left of the picture. 2.46 billion years ago, the precession cycle had a much shorter period - about 11,000 years - than today (about 21,000 years), due to the shorter Earth-Moon distance. The precise period of the small-scale cycles, and hence the Earth-Moon distance, could be determined from the thickness ratio with the larger-scale (100,000-year) cycles, visible in the background on the right and in Figure 1. Photo: Frits Hilgen.

Short day

Over time, the rotation of Earth around its axis has also slowed down. This was known since long, but Lantink has now found a way to establish how long a day lasted on the early Earth: 17 hours, rather than the current 24. In an earlier study she conducted together with colleagues from Switzerland, she already showed that the Earth’s climate underwent regular changes 2.5 billion years ago due to periodic changes in the shape of the Earth’s orbit. Lantink clarifies that today’s climate change does not have an astronomical cause: it is occurring at vastly shorter time scales, and we humans are responsible for it.


Margriet L. Lantink et al. (2022), ‘Milankovitch cycles in banded iron formations constrain the Earth-Moon system 2.46 billion years ago’, PNAS,