BackI freely concede that the producers of 'Do We Really Need The Moon?' (and their researchers) were faced with a considerable dilemma when compiling the programme: how could they accurately but succinctly explain the complex topics they wanted to cover to a viewer with a possible interest in science but no background in physics or mathematics? Simplification was clearly required but, unfortunately, this process often went off-track and the final result ended up by being just plain wrong. Is it, therefore, even possible to explain these concepts briefly but fundamentally correctly or are they so difficult that an imprecise analogy is the best one can do? I believe it is possible, and these paragraphs are my attempt to show how I would have done it.
This section of the programme was actually more interested in the [possible] connection between the tides and the conditions for the emergence of life, and what would happen to the tides if the Moon was much closer to the Earth (cue scenes of mass destruction!), than it was about how the tides are created. I would therefore suggest that the following is all that needed to be said.
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The gravitational attraction of the Moon causes the water in the oceans to be drawn slightly towards it, creating a region of deeper water referred to as a "tidal bulge" [animation of Earth and Moon showing tidal bulge, exaggerated for clarity]. The regions from where the water has been drawn to create this bulge will therefore be slightly shallower than average. The tidal bulge is held in place by the Moon's attraction and so, as the Earth rotates, its landmasses must pass through the bulge: the higher water-level experienced at this time produces high tides. Passage through the corresponding regions of shallower water gives us low tides [further animation, in close up to show the land passing through the bulge].
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One could quite easily extend the above to include the influence of the Sun, thus explaining spring and neap tides, but the producers of the programme and I agreed that any attempt to give a simple explanation of why there are two bulges not one would quickly get complicated if accuracy of description was not to be compromised and so was best avoided in a popular science programme.
If I were to attempt such a description in a slightly higher-level programme I would base my explanation on this sequence of statements: 1) for an object to be in a stable orbit around another it needs to be experiencing an amount of inwards force exactly correct for its orbital distance and to be moving at the correct speed for that distance; 2) gravity provides the inwards force in the case of Solar System bodies; 3) the strength of the gravitational force reduces with increasing distance; 4) an orbiting body of appreciable size, whose parts are therefore at slightly different distances from the parent but are constrained to have the same orbit speed, will thus experience the correct amount of force for a stable orbit only at its centre; 5) the part of the body nearer to the parent will tend to be pulled inwards, as the speed at which it is moving is insufficient to balance the slightly increased force on it, and the part away from the parent will tend to move outwards, as the slightly reduced force on it is too little to keep it in orbit at its current speed; 6) ipso facto, two bulges are formed - one towards the parent and one away from it. In each case, the size of the bulges is determined by the strength of the material the object is made of. Once the excess force inwards or outwards is balanced by the tensile force exerted by the material, the bulges stop growing.
One would then simply extend this principle to the case of the Earth by pointing out that for bodies of somewhat comparable size (such as the Earth and Moon), the idea of one orbiting the other must be replaced by the concept that both of them orbit their common centre-of-gravity. The Earth really is in orbit, therefore, and so the earlier analysis applies to it just as well as to the Moon. QED. Not entirely simple, admittedly, but accurate and (importantly) avoiding any mention of centrifugal force!
A simplified explanation of lunar recession must avoid two key issues: Conservation of Angular Momentum, which the lay public are unlikely to understand, and that dreadful phrase "to every action there is an equal and opposite reaction", which does not relate to this situation. I would suggest the following.
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The tidal bulge is held in place by the Moon's attraction and therefore the Earth's landmasses must be pushed through it [or them!] as the Earth rotates. As in the case of moving your hand through bathwater, energy is needed to achieve this, which is taken from the only source available - the rotational energy of the Earth. The energy is dissipated as heat, and thus lost, and so the Earth's spin speed gradually slows as the rotational energy decreases. However, the frictional resistance of the tidal bulge to the passage of the land through it also has another consequence - the bulge is carried slightly forward. This places it a little ahead of the Moon rather than directly below it [diagram]. The bulge thus exerts a very small forwards gravitational attraction on the Moon, which causes it to speed up slightly [diagram]. This increase in orbital speed leads to a corresponding increase in orbit size, resulting in the Moon slowly spiralling away from the Earth [animation]. Over time, therefore, the spin rate of the Earth slows down and the orbital period of the Moon increases (as larger orbits take longer to traverse). Or, to put it another way, as the Moon recedes the length of the day and the length of the lunar month both increase.
The problem we face here is that the description is not just flawed, it is based on an entirely false premise: the Moon does not, in fact, act as Guardian Angel. However, since the idea is quite prevalent this would be a good opportunity to dispel it by the same sequence of arguments as I use in my article: basically that the imbalance of crater numbers between near and far sides is not due to an excess on the far side (hypothetically caused by those impacts which the Moon is supposed to have saved the Earth from) but rather a reduced number on the near side, due to craters having been obliterated by lava flows during the periods when the lunar mare were formed. This is, in any case, a more interesting story as it shows how the development of the Moon has been influenced by the Earth rather than the other way round: the mare are thought to be present on just the near side because it is only there that the crust is thin enough (because of differentiation of the Moon's sub-surface structure through Earth-induced tidal effects) for lava to have been able to break through.
The programme's explanation of this effect was so entirely wrong that almost any other description would have been nearer to the mark! However, it is a complex subject, touching on many topics the interested but non-scientific viewer would not know much about, and so a brief but correct explanation will need to rely on analogies. The programme tried to take this approach, but the one it used (the spinning basketball) was ill-chosen, as it hardly related to the actual problem. In addition, the programme managed to completely omit any discussion of the role played by the Moon and so failed to even address its own question! Here's how I would have gone about it.
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The Earth is somewhat similar to a gyroscope in that they are both, because of their spin, able to remain stable in situations which would not be possible were they not spinning. A gyroscope can thus balance on a string [demonstration of gyroscope doing so], while the Earth can resist the disturbing gravitational influence of the Sun and Moon, both of which exert a force tending to make it topple over. However, because of the spin, any perturbing force produces an unexpected result: rather than the spinning body falling over, its axis of rotation starts to move round in a circle [demonstration of gyroscope precessing when leant over]. The greater the disturbance, the faster it circles round [demonstration of gyroscope precessing faster when weight is added to top of axis]. Not only does the axis circle round, it also "nods up and down" [demonstration of precession and nutation].
These effects can also work the other way round - if the axis of rotation is forced to move in a circle, the axis itself will swing up and down [demonstration] - and of course both these things can happen at the same time: if a body whose axis is already circling is momentarily caused to circle faster by an external force, its axis will "nod" [demonstration].
Importantly, the Sun and Moon are not the only disturbing influences on the Earth - the other planets also have their effect. However, as they are a lot further away the force they can exert is much smaller. Nevertheless, the inherently very minor disturbance they can produce to the circling motion of the Earth's axis, and thus to any nodding movement, can become significant when amplified through the phenomenon of resonance. This is when a small force applied at exactly the right time perfectly reinforces something which is already happening. An excellent example is pushing a swing: if the pusher times their push correctly, the swing will rise higher and higher with relatively little effort [demonstration of swing being pushed correctly]. On the other hand, if the push is at the wrong time the swing might hardly move [demonstration of swing being pushed incorrectly]. The key thing is that the timing has to be right - in step with the natural motion.
Although it takes a very long time for the Earth's axis to complete one circle under the attraction of the Sun and Moon - about 26,000 years in fact - the influences of the other planets due to the slight variations in their orbits have similar timescales, typically ranging from about 72,000 to 260,000 years, and so a planetary resonance might indeed be possible. It is known that the planet Mars (whose natural rate is one circle in 170,000 years) is definitely subject to a resonance, which greatly magnifies the nodding motion resulting in the tilt of its axis being quite unpredictable over timescales of hundreds of thousands of years [animation of Mars with chaotically varying obliquity. It is important that the magnitude of the instability is not over-played though, in accord with the simulation results which show that it would not be as severe as earlier analyses had suggested].
In the case of the Earth, 26,000 years is reasonably well outside the resonance range and so the planetary effect is in fact quite small - the tilt varies by just +/- 1.2 degrees [animation of Earth with slightly varying obliquity]. However, if the Moon were not present the Earth's axis would take longer to circle round, as the force causing it to do so would be much less. In fact it would take about 81,000 years, which would make it very susceptible to a resonance effect leading to larger changes in its axial tilt. This would clearly have serious consequences for the development of life on the planet, as it would dramatically affect the seasons.
We can see, therefore, that the presence of the Moon modifies the natural motions of the Earth's axis, preventing it being greatly affected by planetary influences and thus ensuring that the tilt of the axis has remained within narrow limits for hundreds of millions of years. This has enabled life to emerge and develop in an environment whose seasons are constant and predictable.
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As with the explanation of why there are two tidal bulges not just one, not trivially simple perhaps but at least quite straightforward (particularly when aided by the demonstrations) and basically correct. There are many examples of precession and nutation on YouTube that can be used as a basis for the demonstrations: I have even checked that they will work by building my own 3-axis gyroscope! To further emphasise the point about the different resonance conditions with and without the Moon one could add in another analogy/demonstration, showing that a canoe with an outrigger [=Sun+Moon] is relatively stable against waves approaching from the side but one without an outrigger [=Sun only] rocks around alarmingly.
While it may be considered outside the scope of the programme, it might also be worth adding a corollary to the conclusion to say that although the Moon is a stabilising influence in the situation which currently exists, it is rather hard to determine what the state of the Earth would now be if it never had a Moon right from day zero. We thus cannot state for certain whether the Moon is, on balance, a stabilising influence or not: an originally fast-spinning moonless Earth would have been stable anyway. This statement would be a counter to the oft-quoted view that the presence of a Moon is necessary in all cases to stabilise an Earth-like planet, which current work shows to be probably untrue. Though interesting, a full discussion of the effects of the Moon's recession on the current situation (and thus on the overall conclusion as to whether the presence of the Moon is a good thing or not), would probably be a step too far, however.