Even though the Moon is far smaller and less massive than the Earth its gravitational field still has significant effects on our planet. The most noticeable of these are tides, the periodic rise and fall of sea levels. In this post I’ll give an overview of the causes of tides. This is something which many popular websites get wrong!!
High and low tides- Images from Wikimedia Commons
Why we have tides
The distance between the Earth and the Moon is on average 384 400 km. This is the distance of the centre of the Moon from the centre of the Earth and different locations on Earth will lie at different distances from the centre of the Moon. Every location on Earth in addition to the Earth’s gravity, which gives objects weight, is also subject to the gravitational field of the Moon. This is about 300 000 times weaker than the Earth’s gravitational field and varies as the inverse square of the distance from the centre of the Moon.
Therefore, the Moon’s gravitational field will vary significantly between individual locations on the Earth.
The average strength of the Moon’s gravitational field at the location on Earth closest to the Moon is 0.000 003 497g, where g is the acceleration due to gravity on the Earth’s surface. The strength of the Moon’s gravitational field at the location farthest from the Moon is significantly weaker at 0.000 003 272g.
Definition of tidal field (due to the Moon)
This is for any location, on the Earth, the difference between the Moon’s gravitational field at that location and its value at the centre of the Earth.
Tidal field (at location X) = Moon’s gravitational field (at X) – Moon’s gravitational field (at the Earth’s centre)
The tidal field has a magnitude and a direction. .The diagram below shows how the tidal field varies across the Earth. (The term tidal force is frequently used. The tidal force is the force acting on an object caused by the tidal field. )
In this diagram a two dimensional slice has been taken through the Earth.
- At the location on the Earth-Moon axis closest to the Moon -marked A, the tidal field is directed upwards away from the Earth’s centre in the direction towards the Moon.
- At the location on the Earth-Moon axis furthest from the Moon -marked B, the tidal field is directed upwards away from the Earth’s centre in the direction away from the Moon.
- At locations at right angles to the direction of the Moon -marked C, the tidal field is directed downwards towards the centre of the Earth.
- At other locations on the Earth, labelled D, the tidal field will be at an angle of of between zero and ninety degrees to the Earth’s surface.
How tidal forces make water move – Something which many websites get wrong.
The magnitude of the tidal field is strongest at locations A and B. However at these locations, because the direction of the tidal force is upwards, it is dwarfed by the strength of of the Earth’s gravity acting downwards, which is roughly 10 million times at stronger.
The force which causes ocean water to move is the horizontal component of the tidal force, known as the “tractive force”. The tractive force is zero where:
- the tidal field direction is upwards (points A and B) and
- downwards (locations C).
At all other locations the tractive force is non zero.
The tractive force causes the movement in water seen in tides because, although weak, it acts constantly over a large volume of water and it is unopposed by any other horizontal force apart from friction at the sea bed (which is negligible). The diagram below shows how the tractive force varies across the surface of the Earth.
VARIATION OF THE TRACTIVE FORCE ACROSS THE EARTH
The tractive force is zero at the locations A (closest to the Moon), B (furthest from the Moon). At these two locations the tidal field is directed upwards and there is no horizontal component. It is also zero where the tidal field is directed downwards (the ring marked C)
The net effect of the tractive force over the entire Earth causes the tidal bulges along the line of the Earth-Moon axis. This gives the widely-held impression that the Moon’s gravity has “lifted the oceans up”. Instead the ocean water is pushed up around the sides of points A and B by the tractive force.
Unfortunately there are a lot of videos and “science websites” out there which promote the very popular (but incorrect!!!) impression that the Moon’s gravity lifts up the water on the side of the Earth facing the Moon.
I’ve included a link below to a typical “bad video”. It was published by an organisation called the Associated Free Press (AFP). Like many such videos it has good graphics but poor contents! AFP have blocked display of the video thumbnail image. So to view it you will have to click “Watch on YouTube”.
The tidal lunar day
Taken together these two tidal bulges mean that at a given location there should be two high tides every 24 hours 50 minutes. This period of time, which is sometimes called a ‘tidal lunar day’ is the interval of time between successive occasions when the Moon is at its highest in the sky. However, in reality, tides are more complicated than this simple model suggests
Spring and Neap Tides
The Sun also contributes to tides but, because the Sun is 400 times further away than the Moon, the difference between the pull of the Sun’s gravity at the location on Earth closest to the Sun and the location furthest away is smaller than compared to the Moon.
The average strength of the Sun’s gravitational field at the area of the Earth closest to the Sun is 0.000 604 3g. The average strength of the Sun’s gravitational field at the area of the Earth furthest away from the Sun is slightly weaker at 0.000 604 2g. Because the difference between the two values is smaller, the tidal force due to the Sun is only 46% of the tidal force due to the Moon.
When the Earth, Sun and Moon are in a line, which happens at full moon and new moon the tidal force of the Sun adds to the tidal force of the Moon and the total tidal force is larger than average. On these occasions, which are called spring tides, high tides will be higher than average and low tides will be lower. The word spring in this case has nothing to do with the season, instead it comes from the verb to move or jump suddenly or rapidly upwards or forwards.
Conversely, when the Earth, Sun and Moon are at ninety degrees to each other, which happens at first and last quarter, the tidal force of the Sun subtracts from the tidal force of the Moon and the total tidal forces are lower than average. On these occasions, which are called neap tides, the tidal range is smaller. High tides are less high than average and low tides are not so low. The word neap is derived from the Middle English word neep which means scant or lacking.
Additional factors affecting tides
Most locations on the Earth have two high tides every 25 hours. However, the water levels at the two high tides are not always the same and for many areas the time when high water occurs is out of step with what would be expected in the simple model discussed earlier. There are other factors which come in to play as well and here are a few of them
Flow of water, shape of coastline, large landmasses
The Earth is not entirely covered by deep ocean and when water flows from an area of low tide to an area of high tide there may be large landmasses in the way preventing or delaying this flow. If we consider the UK as an example, the shape of the coastline and the water depth results in different tide times around its coast. When the mass movement of water caused by tidal forces crosses into shallow seas, its speed decreases. Also, the outline of the coast prevents the tidal wave from moving in a uniform direction. For example, St Mary’s in the Isles of Scilly (A) experiences high tide whilst at the other end of the south coast, Dover (B) is experiencing low tide.
The tidal range, which is the difference in water level between high tide and low tide, varies widely around the UK coast. In general, the tidal range is larger when water is forced through a narrow channel and smaller in flat open coastline. The Bristol Channel(C), a narrow strip of sea 120 km long which separates South West England from South Wales, experiences the third highest range of anywhere in the world, with a mean spring tidal range of 12.3 m. On the east coast Lowestoft (D) experiences a mean spring tidal range of only 1.9 m. As a general rule, the shapes of the shoreline and ocean floor affect the way that tides propagate to such a degree that there is no simple formula to predict the time of high water from the Moon’s position in the sky.
Inclination of the Moon’s orbit
Another factor is the inclination of the Moon’s orbit to the Earth’s equator. This means, for many locations, one of the daily high tides is significantly higher than the other.
For example, if we take a location in the Southern Hemisphere, marked as A in the diagram, when the Moon is directly overhead A lies near the centre of the tidal bulge. However, twelve and a half hours later, after the Earth has rotated, location A is no longer centred in the tidal bulge (its new location is shown as A’) and the tidal force is significantly weaker. The tidal bulge is now centred at location B, in the Northern Hemisphere.
To complicate matters further the inclination of the Moon’s orbit, to the Earth’s equator varies over a period of 18.6 years between a maximum of 28 degrees and minimum of 18 degrees.
Shape of the Moon’s orbit around the Earth
Another factor to consider is that because the Moon moves in an elliptical obit and its distance from the Earth constantly changes during its orbit , the tidal force due to the Moon will vary as well. It is at its greatest when the Moon is at perigee (when it is on average 363 300 km from Earth) and at its weakest when the Moon is at apogee (on 405 500 km from Earth. when there is a a supermoon – i.e. a full moon at perigee the tidal range will be be particular.
The Earth’s orbit around the Sun is also elliptical which affects the strength of tides, but to a lesser degree.
The Earth rotates on its axis in just under 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.
The tidal bulge is always ahead of the Moon’s orbital position. This ‘pulls the Moon along’ in its orbit.
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.
These effects are discussed in a previous post The Days are getting Longer.
Could the Moon be responsible for the Origins of Life on Earth?
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 up 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.
Tides are actually very complex and in my post overview I can only summarises some of the factors at work.
Unfortunately there are a lot of videos out there which promote the very popular (but totally incorrect!!!) impression that the Moon’s gravity lifts up the water on the side of the Earth facing the Moon.
I’ve included a link below to a typical “bad video” made by an organisation called the Associaites Free Press (AFP). This has good graphics but poor contents.
I hope you have enjoyed this post and are staying safe in these difficult times. For any readers wanting further mathematical detail on tidal forces, please click on the link below