The Days are Getting Longer.

 

Although the Moon  is less massive than the Earth its gravitational field still has significant effects on the Earth. The most noticeable of these are tides, the periodic rise and fall of sea levels.

The principle cause of tides is that the pull of the Moon’s gravity is stronger at the area of the Earth closest to the Moon and weaker at the area facing away.

 

This causes a tidal bulge in the area closest to the Moon, shown as A in the diagram below. Another tidal bulge also occurs in the area of the Earth farthest away from the Moon, where the Moon’s gravity is weaker than its average value. This is shown as C in the diagram.

Tidal Friction

The Earth rotates on its axis in around 24 hours, whereas the Moon takes 27.5 days to complete an orbit of the Earth.  Because the Earth rotates on its axis faster than the Moon revolves around the Earth, the tidal bulge is always a little bit ahead of the moon. This is shown in the diagram below.

 The diagram above shows that the tidal bulge is always ahead of the Moon

This causes two separate effects: one on the Moon and one on the Earth.

• The pull of the tidal bulge ahead of the Moon causes the Moon to accelerate very slightly.  In effect the Moon saps the Earth’s rotational energy, causing it to gradually spiral away from the Earth.
• As the Earth’s rotational energy is sapped, it rotates more slowly. This causes the length of the day to get very slightly longer, at the rate of approximately 0.0023 seconds per century.

The sapping of the Earth’s rotational energy by the Moon is not 100% efficient. Rather than all of the extracted energy going to accelerate the Moon away from the Earth, some of it is dissipated as heat – warming up the oceans slightly.

How fast is the moon moving away from the Earth?

Experimental equipment left on the Moon by the Apollo astronauts has confirmed that the average distance from the Earth to the Moon is increasing at the rate of about 3.8 cm a year. So, the Moon is now nearly 2 metres farther away from the Earth than it was at the time of the Apollo 11 landing in 1969.

The Origins of Life?

Because the Moon has been getting farther away from the Earth, in the distant past the Moon was much closer than it is today. When the Moon was first formed about 4.5 billion years ago it was only 25 000 km away. The Moon’s proximity to Earth meant tidal forces were much stronger and when the first primitive single celled life forms emerged, about four billion years ago, the Moon was already around 138,000 km away from Earth, 36% of its current value. At this time, the Earth rotated faster and a day was around 18 hours in length. It would have taken only eight of these 18-hour days for the Moon to complete one orbit around the Earth.

Four billion years ago the tidal forces would have been 22 times larger than they are today. There would have been a difference of hundreds of metres between the water levels at low and high tides and a large number of tidal pools  These would have filled and evaporated on a regular basis to produce higher concentrations of amino acids than found in the seas and oceans, which facilitated their combination into large complex molecules.  These complex molecules could well have been the origin of the first single celled lifeforms.

 

 

The Lengthening of the Day

In the year 1900 a mean solar day (the term astronomers use for the day measured by the rising and setting of the Sun) was exactly 24 hours in length. However, analysis of astronomical observations over the last few hundred years has shown that, due to tidal friction, the days are getting longer at a rate of 0.0017 seconds per century. A day, in the early part of the twenty first century, lasts 24 hours 0.002 seconds.

Because the day, defined by the Earth’s rotation, is slightly longer than 24 hours, every so often an extra second, known as a leap second,  needs to be added to ensure that the time we use on a day to day basis lines up with the real time defined by the Earth’s rotation and does not gradually drift away. Leap seconds are always added just before midnight on 30 June or 31 December.  They were first introduced on 30 June 1972 and since then there have been 27 leap seconds. At the time of writing the most recent leap second was on 31 December 2016

Leap Second June 30 2012

In the Future

In the future, as the Earth’s rotation continues to slow down, the days will continue to get longer. As this happens, we will have to add leap seconds more often to ensure that the day that we use still aligns with the day defined by the Earth’s rotation.

This table assumes that the length of a mean solar day increases due to tidal friction at a rate of 0.0023 seconds per hundred years.

 

 

As you can see, assuming that humanity is still around (;-) ), in 10,000 years’ time in the year 12020, we would have to add a leap second every 4.3 days. It is possible that, instead of having frequent leap seconds, we might choose in the future to redefine how long a second is.  We could have a ‘new second’ which would be slightly longer than the second we currently use, 60 of these new seconds would make a ‘new minute’, and 60 new minutes would make a ‘new hour’. With these new units then a day would be exactly 24 hours again – but not quite the hours as we now know them.

 

Other factors affecting the speed of the Earth’s rotation

Like many things in science, there are multiple causes of a single phenomenon (in this case the change in the Earth’s rotation speed). If tidal friction were the only cause, the day length would increase at a rate of 0.0023 seconds per century. However, the Earth’s rotation is erratic and events such as a large earthquake can temporarily speed it up. Also, since the end of the last ice age the Earth has been changing shape to become less flattened at the poles. This has caused a temporary speeding up of the Earth’s rotation – shortening the day by 0.0006 seconds per century. This is why we observe an average increase of only 0.0017 seconds per century.

Updated 28 May 2020