Explaining familiar phenomena

Even though the Sun and Moon are such familiar objects in the night sky, many children and adults alike struggle to explain cyclical events such as night and day, the seasons and the changing appearance of the Moon.

In this episode we address these familiar phenomena, not only providing explanations but also offering some ideas about the origins of those explanations.

Day and night

The cycle of day and night is caused by the rotation of the Earth as it spins on its axis once every 24 hours. Because of this spinning motion, the Sun appears to move through the sky but in reality it is the Earth that does the moving.

This effect is like being on a train when the train next to you starts moving. Often you think you are moving only to realise, when you look out of the other window, that it is the other train that is pulling away.

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The Earth spins

Although the Earth spinning explanation is relatively straightforward, justifying it is not so simple. The common-sense notion is that it is the Sun that moves. After all, we do not appear to be moving and if we jump up we land on the same spot on the Earth's surface.

A crucial piece of evidence that led people to believe in the idea that the Earth spins was provided by a long and heavy pendulum called Foucault's pendulum. This was first hung in the Pantheon in Paris in 1855. The length and mass of the pendulum means that it will keep swinging for over a day. During that time, the plane in which it swings appears to turn. As it is suspended by a friction free pivot, the only simple explanation for this effect is that the ground underneath the pendulum is turning. When it was first shown people were invited, in Foucault's own words, to come and watch the world turn.

The night sky

The other piece of significant evidence comes from long exposure photographs of the night sky. To create these photographs, the camera is pointed at the northern pole star. All the stars come out as long circular trails as if they are all turning around the North Star.

The same effect is observed with the camera pointing at the Southern Celestial Pole, as shown.

There are two possible explanations for this effect. Either all the stars are turning around a single point or the Earth on which the camera is fixed is turning.

The second explanation is correct. The axis on which the Earth spins is currently pointing at the North Star and so as the Earth rotates all of the stars appear to move on circular paths around that star. This apparent circular motion of the stars can easily be seen on a clear night if you pick out the North Star and then follow the progress of the other stars around it as the night progresses.

Occam's razor: simplicity is a guiding principle when constructing theories

The important point about the photographic evidence provided by a camera pointed at the Pole star is that we cannot decide between the two possible explanations. Both fit with the evidence.

We choose to believe the explanation that the Earth on which the camera is fixed is turning. Why? Because one of the values that scientists work with is parsimony, to put it in simple language, the KISS (keep it simple stupid) principle.

If you were to take the first explanation you'd have to explain why all the stars are turning around one point. That would require another theory.

William of Occam, a medieval philosopher, summarised the principle in what is commonly known as Occam's razor: That you should never multiply the entities beyond those required for the explanation.

This value lies at the heart of science which (nearly!) always looks for the simplest explanation possible.

A European view of the temperatures over the year

The monthly average temperatures (both the monthly low and the monthly high) vary over the year. At the beginning and the end of the year, the temperatures are low. In the middle of the year, the temperatures are high.

An antipodean view of the temperatures over the year

In the southern hemisphere this pattern is reversed: at the beginning and the end of the year the temperatures are high, and in the middle of the year the temperatures are low.

This is what we know.

Now why is there this annual variation in the average temperatures?

A better explanation

There must be another explanation for the seasonal changes. Here is a loop showing the variation of the solar radiation arriving over a year (repeated a few times, so you can see the pattern).

The explanation depends on the amount each square metre of Earth is warmed by the Sun; most in the summer, least in the winter.

The annual variation in warming

This annual variation in warming is the result of a combination of two factors:

• The annual movement of the Earth around the Sun.
• The tilt of the Earth.

These factors combine so that in the winter:

• The days are shorter, so that the Sun warms the ground for less time each day.
• The Sun is lower in the sky in the winter, so the warming effect of it is spread over more ground.

The angle of incidence of the Sun's rays

Even without movement and tilt, the fact that the Earth is a sphere means that the angle of incidence of the Sun's beams on the Earth's surface will not be the same everywhere, although the length of day would be. The tilted axis of rotation affects both the angles and the lengths of the days. Both of these affect the warming effect of the Sun.

It is the annual movement of the Earth around the Sun, together with the tilt of the axis of rotation, that changes the angle at which the light from the Sun hits the ground. As the Earth moves around the Sun, the axis of rotation maintains its tilt such that the Northern Hemisphere leans away from the Sun in the winter, and towards the Sun in summer.

The axis of rotation of Earth is tilted by 23.5 degrees with respect to its plane of orbit. Over a year this tilt affects the angles at which the Sun's beams strike the ground, so how large an area they warm.

Bringing it home to Birmingham

Birmingham, in England, is 52.5 degrees north. So at noon in the middle of winter, the Sun's rays strike Birmingham at 29 degrees (52.5°-23.5°) to the horizontal. At noon in the summer they strike Birmingham at 77 degrees (52.5°+23.5°) to the horizontal.

Maximum warming would happen if the beam hit at 90 degrees to the horizontal. At the autumn and the spring equinoxes, when the axis of rotation is not tilted towards or away from the Sun, the beams just hit the ground in Birmingham at 52.5 degrees from the horizontal, again measured at noon.

The effect of this reduction in the angle during winter is that the Sun's rays are now spread out over an area that is 2.7 times larger than the point where the Sun is directly overhead. The consequence is that the ground and the air will be a lot cooler so it will feel like winter.

In summary, the seasonal changes are due to the movement of the Earth around the Sun over a year and the tilt of the Earth's axis. These in turn affect the angle at which the Sun's rays strike the surface of the Earth and the length of each day.

• It is hotter in the summer because our part of the Earth is tilted towards the Sun, so the Sun's beams are spread out over a smaller area and strike the ground for more time each day.
• It is colder in the winter because our part of the Earth is tilted away from the Sun, so the Sun's rays are spread out over a bigger area and strike the ground for less time each day.

Describing the phases of the Moon

The Moon's appearance changes in a regular way, moving through a sequence of phases in one lunar month.

The Moon orbits the Earth once every 27.3 days. This means that its position relative to someone standing on the Earth at midnight will change over the course of a month. The phases of the Moon are caused by the changing position of the Moon relative to the Sun and to an observer on the Earth.

Explaining the phases of the Moon

The term New Moon is slightly confusing because what it actually means is that the Moon is not visible at all as it is on the other side of the Earth from an observer at midnight.

Why, you might ask, is it not visible during the day?

For two reasons:

• The unlit face is facing towards us.
• The brightness of sunlight is so high that it makes it very difficult to see other objects unless they are very bright.

Imagine somebody standing on the Earth at midnight. If the Moon is in the position shown in screen 1 of the interactive, the whole of the illuminated half of the Moon will be visible to the observer: a full Moon. Harder to explain though, is why the Moon appears to wax and wane. This requires the ability to imagine what an observer on the Earth would see if the Moon was, for example, in either of the following positions:

With the Moon as it is on step 3 of pane 1 of the interactive, the observer on the Earth at midnight sees the illuminated face sideways on and observes a half Moon (although, if you think about it, just one quarter of the Moon's surface is visible to the observer). This is the First Quarter.

As the Moon moves between this position and the full Moon position (imagine the Moon orbiting the Earth in an anti-clockwise direction as seen from above), more of the illuminated half will be seen and it is said to wax (waxing gibbous).

As the Moon moves between the full Moon position and where it is on step 7 of pane 1 of the interactive, less of the illuminated half will be seen and it is said to wane (waning gibbous) until in this position a half Moon is seen (last quarter).

The lunar month, an issue with the diagrams and the far side

As the Moon moves on from this position towards the New Moon position, even less of the illuminated hemisphere will be visible from the Earth and it is said to wane (waning crescent).

The part of the Moon that we can see is the fraction of the side that is lit up, which is visible from Earth. Half of the Moon is always lit up, but how much of this we see depends on where the Moon is in its orbit. As the Moon travels around the Earth, the fraction first grows larger, until the Moon is full (directly opposite the Sun). The fraction then grows smaller again, until the Moon is on the same side of the Earth as the Sun.

In the course of one night, the 24 hour spinning motion of the Earth takes us past one of these distinctive phases of the Moon, and as the month progresses (and the Moon moves farther around its orbit of the Earth) the observed phase gradually changes.

These simple diagrams raise a question. Why is the full Moon not in the shadow of the Earth? In other words, when the Moon travels around to the opposite side of the Earth to the Sun, why does the Earth not block the light from the Sun?

The answer to this is that the Moon does not orbit the Earth in the same plane as the Earth orbits the Sun (the plane of the ecliptic). The consequence is that the Earth rarely stops light from reaching the Moon. When it does a lunar eclipse results.

The slightly odd thing about the Moon is that it rotates once on its axis in exactly the same time (27.3 days) that it takes to orbit the Earth. The result is that it always keeps the same face towards us so that we never see the other side of the Moon. The effect is not so strange as it may seem. It is caused by the interaction between the Earth, the Moon and the tides. The Moon did not always spin at this rate.

The dark side of the Moon is not totally dark as it is illuminated by reflected light. It has been observed by satellites and space probes and by astronauts who have orbited the Moon.

The Moon blocking the Sun

A total eclipse of the Sun, a solar eclipse, is caused by the Moon passing between the Sun and the Earth.

It is important to recognise that this diagram is not drawn to scale. While the proportions of the Earth and Moon are correct, the distance between the Earth and the Moon is far too small, as is the size of the Sun. If it was drawn fully to scale, the Sun would be nearly 4 metre to the left and 70 times as big.

As depicted, the Moon is in the New Moon position, but solar eclipses do not occur every month. This is because the orbit of the Moon (around the Earth) is tilted by about five degrees with respect to the Earth's orbit (around the Sun), so that the Moon usually passes slightly above or below the line between the Sun and the Earth.

The path of the umbra part of the shadow, cast by the Moon across the Earth, is known as the path of totality. It is only about 50–200 kilometre wide.

It is quite remarkable that total solar eclipses even occur at all.

The Sun and the Moon appear the same size, allowing you to see an eclipse

Solar eclipses do occur because the Sun and the Moon appear from Earth to be about the same size in the sky. The Sun, whose diameter is 400 times that of the Moon, happens to be about 400 times as far away from the Earth. This condition permits the Moon to just cover up the Sun.

In fact, if the Moon's diameter (3480 km) were just 230 km smaller, it would not be large enough to completely cover the Sun. In this case, a total solar eclipse would never happen anywhere on Earth!

In addition to the total eclipse, there are partial or annular eclipses in which the Moon does not quite cover the Sun.

This video clip shows a total eclipse. These are remarkable events lasting anywhere between 30 and 120 second. When totality is reached it is possible to see the Solar Corona – the outer part of the Sun's atmosphere.

The outer parts of the corona break away and move outwards from the Sun, forming a high-speed flow of particles known as the solar wind.

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The Earth blocking the Sun

Lunar eclipses occur when the Earth comes between the Sun and the Moon so that the Earth casts its shadow on the Moon. As the Earth is much larger than the Moon, lunar eclipses occur more frequently than solar eclipses.

The photograph shows one that occurred in 2007.

Such eclipses are normally total.

Illumination and three-dimensional geometry predict the

The reasons for the seasons, for phases, and for day and night all depend on models that are three-dimensional. To account for the phenomena requires that you are able to predict the (relative) illumination in the different arrangements.