The impact of climate change may appear to be overwhelmingly negative but there is a bright spot for those who struggle to find enough time in the day: melting glaciers are causing the rotation of the Earth to slow thereby lengthening our days, new research has found.

Harvard University researchers have provided an answer to a long-held conundrum over how shrinking glaciers are affecting the rotation and axis of the Earth, calculating that the duration of a day has lengthened by a millisecond over the past 100 years.

The brakes will be more sharply applied to the Earth’s rotation as glaciers melt at an ever faster rate, meaning that at least five milliseconds will be added to each day over the course of the 21st century. The axis of the Earth will shift too, with the north pole set to move position by about 1cm (o.4in) during this century.

The research, published in Science Advances, apparently solved a scientific puzzle known as “Munk’s enigma”, which came from a 2002 researcher paper by oceanographer Walter Munk, examining how the melting of glaciers had altered the Earth’s rotation and axis.

As land ice from the poles melts due to rising atmospheric temperatures, the shifting weight of water across the world should cause a change to the axis upon which the Earth spins, and a slight wobble in the rotation. Also, the added weight of water towards the equator will cause the Earth to slow, much in the way a spinning figure skater would slow if he or she reached their arms out away from their body.

Munk factored in the impact of the end of the Ice Age 5,000 years ago, when melting over the previous 15,000 years would have helped slow the Earth’s rotation. But, surprisingly, he found that even with average sea level rises of 2mm a year during the 20th century, there was no change to the Earth’s rotation or axis beyond that caused by the Ice Age ending.

“There should’ve been a whopping great signal and it would be immediate as it only takes days or weeks for that melted water from the poles to shift around the world,” said Jerry Mitrovica, professor of geophysics at Harvard University and leader of the research.

Mitrovica’s team went back to Munk’s research and applied the latest scientific understanding to it. They found that Munk had slightly overestimated the average sea level rise – it was around 1mm to 1.5mm each year over the 20th century rather than 2mm.

They also applied an updated model to the calculations. Munk assumed the Earth had rapidly adjusted to ice melting that occurred as the Ice Age ended. More recent understanding of this time, however, suggests that the Earth was not as spherical as it is now for a long time, as the huge ice sheets caused the poles to flatten and the equator to bulge out.

Once the team had factored in other influences such as the tides, they found that the glacier melting of the 20th century had indeed caused the Earth to slow and wobble. The speed of the planet’s rotation can be gauged from measurements of stars’ position in relation to Earth and also the orbit of satellites, which have to adjust slightly if the world’s rotation changes.

This slowdown is set to become more pronounced. The global average sea level rise is now over 3mm, according to the IPCC, with the volume of the world’s glaciers set to slump by between 15% and 85% by 2100, depending on how sharply nations reduce greenhouse gas emissions and reverse mass deforestation.

A recent study found that the current retreat of the world’s glaciers was “historically unprecedented”, with scientists warning that a huge glacier in Greenland that holds enough water to raise global sea levels by half a meter has begun to crumble into the North Atlantic Ocean. Sea level rise is also fuelled by thermal expansion, where the ocean grows as it warms up.

“The period of a day is now a millisecond longer than a century ago but that will accelerate as the melting increases,” Mitrovica said. “People won’t be running from their houses screaming about an extra millisecond but it adds yet further confirmation of what we are doing to our environment. It’s another fingerprint.”