Want to set your time machine to catch a solar eclipse with a group of curious Mesopotamians in the year 700 BCE? It's not as simple as you think. You need to adjust for the subtle slowing of Earth’s rotation over time and know the history of sea level change—and even those bits of knowledge might not be able to get you there on time. That's the conclusion that a team led by Harvard’s Carling Hay reached when they looked at what the ancient astronomical record tells us about our planet's timekeeping.

Tidal forces caused by the gravitational pull of the Sun and Moon act like a brake on the spinning Earth, gradually increasing the length of the day. It takes a long time for this to add up to anything meaningful, but the Earth has been around a long time: 400 million years ago, each year contained 400 days. At the current rate, days are growing just a couple milliseconds longer per century, so it would take more than 3.5 million years to add a minute.

This is not the answer to your plea for more time in the day to tackle your workload.

But if you were to compare two clocks, an atomic clock ticking away with perfect accuracy and another clock kept precisely in sync with the Sun, those milliseconds would accumulate faster than you might think. If the two clocks read the exact same time in 500 BCE, by the current day they would be 5 hours apart. So if your time machine works on the sort of time an atomic clock measures, you might not arrive at the time of day you intended.

The braking provided by tidal forces isn’t quite the whole story here. Researchers have taken advantage of careful observations made by astronomers over the ages of celestial events like eclipses to work out how our two clocks would actually have diverged over the last 3,000 years. By winding back a virtual Solar System, we can calculate the time and position in the sky those events should have occurred and use that to explore the Earth’s slowing rotation.

If we simulate the slowdown due to tidal forces alone, we get a greater difference between the clocks than these historical observations indicate—we're spinning faster than we should be. Some sort of acceleration of the Earth’s spin has counteracted part of that slowdown. What’s more, the change in the length of the day hasn’t been perfectly constant—there appear to have been some ups and downs along the way.

What could explain these discrepancies? To answer that question, we need to brush off the familiar example of the angular momentum of a spinning figure skater that is usually used to explain spin acceleration. The tighter a skater brings his or her arms to the body, the faster the skater spins. Push the arms out, and the rotation slows. The difference in spin speed is all about the distribution of mass, and this applies to the Earth just as well.

For example, a lower sea level near the equator resulting from the formation of high-latitude ice sheets can speed up the Earth’s rotation slightly. But those ice sheets also depress the bedrock beneath them, squishing the mantle around a bit and redistributing some mass in a different way. Melt away the ice, and that rock slowly bounces back. All of this shifting of mass has an effect on the speed of rotation.

So perhaps the small variations in global sea level (prior to modern climate change) over the past few thousand years can explain the variations in the lengthening of the day. That’s the idea that the team set out to test.

The researchers used a precise reconstruction of global sea level over the past 3,000 years and a complex model that accounts for variations in regional sea level caused by a myriad of factors. For an extreme test, all of the changes in global sea level are assigned to losses (or gains) of glacial ice rather than warming or cooling of the oceans, which shouldn’t change the Earth’s distribution of mass.

The results of these simulations were used to calculate changes in the Earth’s rate of rotation, which the team compared to our records from historical eclipse observations.

The simulated effect was apparent but not overwhelming. The influence of sea level could explain part of the most recent wiggle in the rotation trend around 1200 CE, but it didn’t really get close to explaining the earlier wiggles around 500 CE and 700 BCE. Those earlier wiggles are based on only a couple of eclipse observations, though, so we're less certain about the exact timing of things there.

Sea level probably has played a role in the story of time over the last millennium, but other factors must have been involved as well—particularly prior to that. Factors could include shifting exchanges of angular momentum between the Earth’s liquid outer core and the mantle. Tracking down the cause of a few extra milliseconds added to the length of the day is no simple task.

We tend to be most interested in studies that present confident explanations, but results that quantify subtler relationships—or rule out certain explanations—push science forward just as well. In this case, the crazy fact that we’re very precisely working out how the Earth’s spin rate changes over time only gets more interesting as it gets more complex.

Earth and Planetary Science Letters, 2016. DOI: 10.1016/j.epsl.2016.05.020 (About DOIs).