Days on the Earth are getting longer, thanks to the movement of the Moon away from the planet, according to a study which found that 1.4 billion years ago a day lasted just over 18 hours.
The study, published in the journal Proceedings of the National Academy of Sciences, reconstructs the deep history of our planet's relationship to the Moon. It shows that 1.4 billion years ago, the Moon was closer and changed the way the Earth spun around its axis.
"As the Moon moves away, the Earth is like a spinning figure skater who slows down as they stretch their arms out," said Stephen Meyers, a professor at the University of Wisconsin-Madison in the US.
It describes a tool, a statistical method, that links astronomical theory with geological observation (called astrochronology) to look back on Earth's geologic past, reconstruct the history of the solar system and understand ancient climate change as captured in the rock record.
"One of our ambitions was to use astrochronology to tell time in the most distant past, to develop very ancient geological time scales," Meyers said.
"We want to be able to study rocks that are billions of years old in a way that is comparable to how we study modern geologic processes," he said.
Earth's movement in space is influenced by the other astronomical bodies that exert force on it, like other planets and the Moon.
This helps determine variations in the Earth's rotation around and wobble on its axis, and in the orbit the Earth traces around the Sun.
These variations are collectively known as Milankovitch cycles and they determine where sunlight is distributed on Earth, which also means they determine Earth's climate rhythms.
Scientists have observed this climate rhythm in the rock record, spanning hundreds of millions of years.
However, going back further, on the scale of billions of years, has proved challenging because typical geologic means, like radioisotope dating, do not provide the precision needed to identify the cycles.
The solar system has many moving parts, including the other planets orbiting the sun. Small, initial variations in these moving parts can propagate into big changes millions of years later; this is solar system chaos, and trying to account for it can be like trying to trace the butterfly effect in reverse.
Researchers combined a statistical method that Meyers developed in 2015 to deal with uncertainty across time - called TimeOpt - with astronomical theory, geologic data and a sophisticated statistical approach called Bayesian inversion that allows them to get a better handle on the uncertainty of a study system.
They then tested the approach, which they call TimeOptMCMC, on two stratigraphic rock layers: the 1.4 billion-year-old Xiamaling Formation from Northern China and a 55 million-year-old record from Walvis Ridge, in the southern Atlantic Ocean.
With the approach, they could reliably assess from layers of rock in the geologic record variations in the direction of the axis of rotation of Earth and the shape of its orbit both in more recent time and in deep time, while also addressing uncertainty.
They were also able to determine the length of day and the distance between the Earth and the Moon.