The Celestial Clockwork

Ask most people what they associate with astronomy and they will mention planets, stars, galaxies, etc. Ask them what they associate with astronomers, however, and the answer will probably be telescopes – but it is less than four hundred years since the invention of the telescope. By contrast, human awareness of the heavens goes back millennia; almost certainly deep into prehistoric times. Until comparatively recently, astronomers have studied the heavens with nothing more sophisticated than the naked eye. From earliest times, they would have tried to make sense of the great complexity of what can be seen in the skies.

Even the most casual observer will be aware the skies present a differing appearance from hour to hour, as the Sun, Moon and stars march steadily across the heavens. They will realise, however, that the stars are fixed in relation to one another, often making distinctive patterns in the sky. They will also realise that the Moon changes its appearance from night to night, sometimes waxing sometimes waning. But why does the Sun rise and set in different places at different times of the year? Why is the Moon sometimes visible in broad daylight? Why do some stars remain close to the same point in the sky and never set? And what is to be made of the bright star-like objects that do not remain in a fixed position in relation to their neighbours, but move at differing speeds across the starry background, always keeping to the roughly same plane as the Moon in its wanderings.

Today, we know that the Moon goes round the Earth and the Earth and other planets go round the Sun. However, this does not even begin to tell the full picture and the achievements of people such as the Maya and the ancient Babylonians – who were not even armed with these basic facts – cannot be overstated. The workings of the celestial clockwork make the achievements of the finest Swiss watchmaker pale into insignificance, yet from a modern perspective they are not difficult to understand; the object of this short (9,000 word) work is to give the reader just such an understanding.

The Celestial Sphere
Astronomers often use a model known as a celestial sphere to illustrate the movements of the Sun, Moon, planets and stars as seen from Earth. This can be thought of as being similar to a geographer’s globe, except it surrounds the Earth and we look at it from the inside. Another way of thinking of it is as a grid system projected onto the heavens to help us find our way around. To demonstrate such a grid would at one time have required the facilities of a planetarium, but there are now many ‘augmented reality’ smartphone apps available that can achieve almost the same effect.

Let’s first consider the finer points of the celestial sphere itself. Like the geographer’s globe, it will have two poles, an equator and lines of latitude and longitude. The celestial North and South Poles and the celestial equator (usually referred to simply as the “equator”) are projections of their terrestrial counterparts onto the grid system. The coordinate system used to define a point on the grid system differs slightly to that used by geographers. The position of an object to the north or south of the equator is given by declination (Dec.). Like latitude, it is measured in degrees, but instead of suffixing the declination with an N or an S, northern declinations are given positive values and southern declinations negative values. The equivalent of longitude is right ascension (R.A.), which has a zero line similar to the Greenwich meridian that passes through a point known as the vernal point (to be discussed shortly) or first point of Ares. Right ascension is measured eastwards from the first point of Ares. It can be measured in degrees but is usually measured in hours, minutes and seconds. An hour corresponds to 15 degrees, so 24 hours is equivalent to 360 degrees.

From anywhere in the world, our field of view will be bounded by the horizon, which divides the celestial sphere exactly into two. The point directly above us is known as the zenith. Running through both poles and the zenith is a great circle known as the meridian. The angle of elevation of any object above the horizon is known as the altitude; the angular distance around the horizon, measured clockwise from due North is known as the azimuth.

Let us take an imaginary or smartphone augmented reality trip to the (geographical) North Pole. The celestial North Pole is directly overhead, at the zenith, and the equator lies exactly on the horizon. Between the equator and the Pole are a series of concentric circles, growing ever smaller the nearer they are to the Pole. These represent differing declinations. A series of lines extend upwards from the equator, converging at the Pole. These are the lines of right ascension. Note that because the declination circles are parallel to the horizon, we can see them in their entirety. However, we cannot see anything south of the equator at all.

If we observe the sky for a few hours, the grid and stars will appears to revolve in a clockwise around the celestial North Pole. This is happening because the Earth is rotating on its axis, in a west to east direction, or anticlockwise as viewed from “above” the North Pole. This motion is known as diurnal motion. During the course of its diurnal motion, a star will reach its highest point in the sky when it is on the meridian. When a star reaches the meridian, it is said to culminate.

If we look close to the Pole, we will see a bright star. This is Polaris, the Pole Star. It appears to be almost fixed while everything else wheels around it. The further a star is from the Pole, the larger the circle in which it moves, with those near the equator moving in the largest circle of all. Note that no star ever rises or sets; we can see half of the stars the whole of the time.

Before we move on, how long do you think it takes the stars to make a complete circuit of the skies? The answer is of course the same length of time it takes the Earth to make a complete turn on its axis – but this is not 24 hours. The Earth makes a complete turn on its axis once every 23 hours 56 minutes and four seconds. This period of time is known as the sidereal day. However, we reckon time by the Sun rather than the stars, and as we shall see, the solar day is slightly longer.

Now we will travel to London, which is at latitude 51.5 degrees N. The first thing we notice is that the grid now appears tipped over towards one side. The celestial North Pole is no longer at the zenith; in fact its altitude will be equal to the geographical latitude. The declination circles are now no longer parallel to the horizon, so only those close to the Pole will be visible in their entirety and the others will be visible only as ever-decreasing arcs. However, we can now partially at least see declination circles that are south of the equator. Exactly half of the equator is visible, and it cuts the horizon at points due east and due west. The celestial North Pole lies due north.

There is a declination circle whose southernmost point just touches the northern horizon, and only the stars within this circle now remain permanently above the horizon or, as Homer put it in The Odyssey, “never bathe in Ocean’s stream”. Such stars are said to be circumpolar from that latitude (at either Pole, as we have seen, all the stars are circumpolar). Stars further south do spend increasing amounts of time below the horizon, though those North of the equator are still up for more than half of a sidereal day. Stars lying directly on the equator are visible for exactly half of a sidereal day. Note that these stars rise due east and set due west. Stars located still further south are visible for less than half of a sidereal day. Finally, on the southern horizon, is the northernmost point of a declination circle that lies entirely below the horizon. Stars lying within this circle are permanently out of view and include those making up the Southern Cross and our nearest stellar neighbour, Alpha Centauri.

Next let us go down to the equator. The grid will now appear to be completely tipped onto its side, and the declination circles will now lie at right-angles to the horizon. Exactly half of each circle will be visible, but our observer can now see all of them. The celestial North Pole lies exactly on the northern horizon and, 180 degrees away, the celestial South Pole has come into view. Every single star will be above the horizon for half of the sidereal day.

It will now be clear that were we to continue south, the celestial North Pole would dip below the horizon and the process we have just witnessed would occur in reverse until upon reaching the geographical South Pole, we would see the celestial South Pole at the zenith.

The Sun and Seasons
Now let us observe the Sun and stars as a sidereal day passes. At the end of one sidereal day, all the stars will be back where they started – but the Sun will be lagging behind. In fact, it will take approximately four minutes for the Sun to catch up. This is because while the Earth has been spinning on its axis, it has also been moving in its orbit around the Sun, completing a 1/365.24th of a circuit. Like the axial rotation, the orbital motion is west to east, or anticlockwise. (Astronomers refer to such motion as direct; clockwise motion (which is rare in the Solar System) is said to be retrograde.) The Sun, as viewed from Earth, appears to have changed its position slightly with respect to the stars. A solar day is defined as the time between successive crossings of the meridian by the Sun, but because the Earth’s orbital speed varies slightly over the course of a year, the solar day is not constant in length. It is only over the course of a year that it averages out to the familiar 24 hours.

The result of the solar day being about four minutes longer than the sidereal day is that any given star will rise four minutes earlier each (solar) day. This is why the constellations visible at a given time vary over the course of the year. After a year has passed, the solar and sidereal days come back into step. Our star will rise at the same time that it did on the corresponding day a year ago.

If we follow the Sun’s apparent movement over the course of a year, we will see that it will make a complete circuit of the celestial sphere. The path it traces out is known as the ecliptic. The ecliptic represents the plane of the Earth’s orbit around the Sun and it is inclined to the equator at an angle of 23.5 degrees. The reason for this is that the Earth’s axis of rotation is not perpendicular to the plane of its orbit, but inclined at an angle of 23.5 degrees. This inclination is known as the obliquity of the ecliptic.

Constellations straddling the ecliptic are said to be zodiacal. These include the familiar twelve signs of the Zodiac, but to make matters confusing there is actually a thirteenth zodiacal constellation, Ophiuchus the Serpent Bearer, that has been ignored by astrologers and is not considered to be part of the Zodiac. The two points at which the ecliptic and the equator intersect are known as the vernal point (which we have already encountered) and the autumnal point.

What effect will the Sun’s movement along the ecliptic have over the course of a year? The ecliptic is inclined to the equator, so the Sun will spend half of the year north of the equator and the other half of the year south of it. Recall that for the Northern Hemisphere, if a star is north of the equator it will be up for more than half of the sidereal day, but if it is south of the equator it will be up for less than half of the sidereal day. The same applies to anything on the celestial sphere, and this includes the Sun.
Thus for half of the year, day will be longer than night and for the other half it will be shorter. On the two days of the year known as equinoxes, day and night will be of equal length; this will occur when the Sun is at the vernal or autumnal point. The vernal point is known as the Sun’s ascending node because this is where it crosses into the northern hemisphere from the south. Similarly, the autumnal point is known as the descending node. Mid-way between the equinox points, the Sun will reach its most northerly and most southerly positions; these points are known as the solstices. In the northern hemisphere, the summer solstice occurs when the Sun is at the most northerly point on the celestial sphere and the winter solstice when it is at the most southerly point. This is the explanation for the seasons.

In lower latitudes, the Sun attains greater elevations above the horizon. When it is at either equinox, the Sun will be directly overhead at midday along the equator. At the summer solstice, it will be directly overhead at midday in the latitude defined by the Tropic of Cancer and at the winter solstice it will be directly overhead at midday in the latitude defined by Tropic of Capricorn. This is why it gets rather hot in these parts of the world. Conversely, the Sun is circumpolar during the summer months within the Arctic Circle, but never rises at all during the winter months. This is the explanation for the famous ‘Midnight Sun’. The situation is reversed for the Antarctic Circle.

Most people think of the Sun rising in the East and setting in the West. But the rising point of the Sun is actually only due East on two days of the year, those when it is at one or other of the equinox points. In the summer months, the azimuth of rising point moves north, reaching its maximum extent at the summer solstice, before returning south. In the winter months, the azimuth of the rising point moves south reaching its maximum extent at the winter solstice, before returning north. Around the solstices, the rising appears to stand still for a few days; the word ‘solstice’ is derived from this phenomenon. The setting points move in the same manner, with the winter sunset limit lying opposite the summer sunrise limit, and the summer sunset limit lying opposite the winter sunrise limit. These seasonal variations in the rising and setting points vary with latitude, being more pronounced in higher latitudes.

The Earth’s Orbit 
Let us now consider the Earth’s orbit around the Sun in a little more detail. The orbit is not circular but elliptical, meaning that distance between the Earth and the Sun isn’t constant but varies over the course of the year, ranging from 147 million km (when Earth is said to be at perihelion) to 152 million km (aphelion). The Earth’s orbital speed is at its greatest at perihelion and at its least at aphelion. This is because its movements are governed by Kepler’s Laws of Planetary Motion, which we will examine in more detail presently. The mean distance is 149.6 million km (93 million miles) and this distance is referred to as the astronomical unit (AU). The departure of the orbit from a perfect circle is known as the orbital eccentricity. Perihelion does not occur in the same place each year, but advances by 11.64 seconds of an arc on each orbit. This is due to gravitational effects of other planets in the Solar System.

Precession, Nutation and other cycles
There are in addition a number of more gradual motions which are only significant over a long term. The most important of these is precession. In addition to rotating on its axis, the Earth also oscillates like a spinning top, each oscillation taking about 25,800 years and causing the Earth’s spatial orientation to gradually change. This motion is due chiefly to the pull of the Sun and the Moon, though the planets make a small contribution.

The observable effect is to make the nodes of the ecliptic gradually move westwards at about 50 seconds of an arc per year. The stars will remain fixed in relation to the ecliptic, but as our celestial sphere grid system uses the Earth as its frame of reference, they will appear to move very slightly against it. This means that star maps have to be calibrated for a particular epoch which since 1984 has been Epoch 2000.0, the start of the year 2000.

The effect, though small, is cumulative and just about visible to the naked eye over a lifetime (a good amateur telescope on a suitable mount could show it in a matter of weeks if not days). More significant effects are experienced over longer periods – in antiquity, for example, the Southern Cross could be seen from Greece and the ancient Greeks included it in their star charts. 14,000 years from now it will be visible all over Britain. The precessional motion is not smooth but slightly wavy. This irregularity is known as nutation and it is the result of a slight nodding of the Earth due to variations in the distances and positions of the Sun and the Moon.

In addition to these effects, the obliquity of the ecliptic varies with time, chiefly due to nutation, though the gravitational effects of other planets also play a part. Finally the eccentricity also varies, albeit very gradually. Again, this is due to the gravitational effects of other planets. The precessional cycle and the cyclical changes in the obliquity and orbital eccentricity are now known as the Milanković cycles. They are named for the Serbian mathematician Milutin Milanković, who proposed a link between them and cyclical changes in Earth’s climate while interned in Budapest during World War I. Climatologists now accept that Milanković was right, but his views attracted little interest in his lifetime.

Four types of year
Up until now, we have used the term ‘year’ rather loosely. Most people think of a ‘year’ as being the time it takes the Earth to go once round the Sun. That is certainly a type of year, but not the only type. The Earth in fact has four different types of year. The first is the sidereal year (365.256 days), and this is indeed the time it takes the Earth to go once round the Sun – but this is not the ‘year’ we base our calendar on.

The Gregorian calendar, which is now used throughout the Christian world, is actually based on the tropical year (365.243 days), which is defined as the time between the Sun making two passages through the vernal point. The vernal point is moving slowly in the opposite direction to the Sun along the ecliptic as a result of precession, so the Sun ‘arrives’ there about twenty minutes before it completes its circuit of the celestial sphere. Hence the tropical year is slightly shorter than the sidereal year. However, the progression of seasons is dictated by the former, so the calendar is based upon it.

The third type of year is the anomalistic year (365.260 days), which is defined as the time between the Earth making two returns to perihelion. As we have seen, the perihelion advances with each circuit, the Earth requires a bit longer to ‘catch up’; hence the anomalistic year is fractionally longer than the sidereal year.

Finally there is the eclipse year (346.620 days), which we shall encounter presently.

The Moon and its Orbit
Most people will think nothing if they happen to see the Moon in the night sky, but are often surprised to see it in broad daylight. In fact, the Moon spends on average as much of its time above the horizon in day time as it does in night time. The most singular feature of the Moon is, in fact, something which most of us take completely for granted. This is that it appears almost exactly the same size as the Sun. The explanation is simple – the Sun is about four hundred times larger in diameter than the Moon, but it is also about four hundred times further away. The odds against this happening – if not quite astronomical – are pretty low.

The Moon’s orbit around the Earth is inclined at an angle of 5 degrees to the ecliptic. The Moon’s apparent path around the celestial sphere intersects the ecliptic at two points again known as nodes; as with the intersections between the ecliptic and equator there is an ascending node and a descending node. These nodes do not remain fixed, but move westwards on the celestial sphere at 19 degrees per year due to perturbation by the Sun, taking 18.61 years to complete a nodal cycle. This phenomenon is known as the regression of nodes.

The orbit itself is rather more elliptical than that of the Earth around the Sun. Distance from Earth (centre to centre) varies from between 356,410 kilometres (minimum distance, or perigee) to 406,697 kilometres (maximum distance, or apogee). The Moon’s orbital speed increases at perigee, and it decreases at apogee. Like the Earth, this is due to Kepler’s Laws of Planetary Motion, which apply to all orbiting bodies. The eccentricity of the orbit is quite pronounced, so the effect is quite noticeable in terms of nightly movement on the celestial sphere, and this has been known since ancient times. In a manner similar to the Earth’s perihelion, the Moon’s perigee advances with each orbit, taking 8.85 years to complete a cycle.

Phases of the Moon
The most noticeable feature of the Moon is that its appearance changes from night to night. These phases are due to differing portions of its day-lit side being presented to us as it moves around the Earth. At the start of the cycle it cannot be seen because it lies in the same direction as the Sun and its illuminated side faces away from us. A few days later it will have moved eastwards away from the Sun and will be seen as a slim crescent in the evening sky. As the days pass, the Moon is seen ever higher in the evening sky as it continues to grow or wax. After seven to eight days the Moon will be 90 degrees east of the Sun in the sky; this point is known as the first quarter and the right half of the Earth-facing side is illuminated. At around fifteen days, the Moon’s distance from the Sun reaches 180 degrees. At this point the Moon rises at sunset. The entire Earth-facing side is now illuminated and we see a full Moon. Thereafter, the Moon begins to wane, going through its phases in reverse as its angular distance from the Sun begins to decrease once more. After about 22 days the Moon is 90 degrees west of the Sun; this point is known as the third quarter and the left half of the Earth-facing side is illuminated. Subsequently the Moon becomes an increasingly slim crescent, moving ever closer to the Sun and appearing only just before sunrise. Finally, after 29.531 days on average, it disappears from view and the cycle begins again.

Five types of month
Most people think of this cycle of 29.531 days as being a month, but they also think of the Moon going round the Earth once a month. In fact, the Moon takes only 27.321 days to go round the Earth. So which ‘month’ is right? Well actually both are. It all depends on what is meant by a month. As we have seen, the Earth has four types of year; the Moon, not to be outdone, has five types of month.

The most obvious, perhaps, is the time the moon takes to go once round the Earth. This is known as the sidereal month and as we have seen, it is 27.321 days. But because the Earth is moving round the Sun at the same time the Moon is moving round the Earth, it takes the Moon a bit longer than a sidereal month to return to the same position with respect to the Sun and the Earth. As it is this which governs the phases, it takes more than a sidereal month to go through a complete cycle or lunation. The time for a lunation is known as the synodic month. The Earth’s orbital speed varies slightly over the course of a year, so the synodic month is not fixed. 29.531 days is only the average figure.

The tropical month is slightly shorter than the sidereal month. It is defined as the time from one lunar equinox to another. The lunar equinox occurs when the Moon crosses the equator; this takes slightly less than a sidereal month due to the effects of precession (c.f. tropical year).

Next is the anomalistic month, the time taken for the Moon to go from perigee to perigee. The perigee advances, so this is longer than the sidereal month and is 27.554 days.

Finally we have the draconic month of 27.212 days. This is the time between successive passages by the Moon through the same node. The nodes are moving westwards and the Moon is moving eastwards along the celestial sphere, so it takes less than a complete orbit for the Moon to return to the node, and thus the draconic month is shorter than the sidereal month. The word ‘draconic’ refers to a mythical dragon thought to devour the Sun and the Moon during solar and lunar eclipses; the eclipse year is also sometimes referred to as the draconic year for this reason.

The interrelationship of various types of month and year are of great importance when it comes to predicting eclipses, and these cycles may have been understood as far back as prehistoric times.

Lunar and Solar Calendars
In the Western world, we have long been accustomed to a year of 365 days, with a leap day inserted into February every fourth year. The Gregorian calendar, now the most widely used civil calendar in the world, does have exceptions to this leap year every fourth year rule, but the last such ‘non-leap year’ was in 1900 and the next will not occur until 2100. Most of us will live our lives without ever having been troubled by such details, but they are important.

The Gregorian calendar is an example of a solar calendar, or one based on the tropical year. Since this is not an exact number of days, a leap day must be intercalated (inserted) at intervals, and the Gregorian calendar provides for an extra day in February if the year is divisible by four. An exception to the rule is made if the year is divisible by 100 but not by 400, as is the case for 1900 and 2100, but not 2000. The Gregorian calendar was introduced in 1582 in the time of Pope Gregory XIII. It was a refinement to the earlier Julian calendar, which inserted the leap day every fourth year without exception. This gave a year of 365.25 days, which is slightly longer than the tropical year of 365.243 days. The Julian calendar was introduced by Julius Caesar in 46 BC and the error, though small, had amounted to several days by the sixteenth century. The Gregorian was not immediately adopted everywhere, due to resistance in Protestant countries to a Catholic innovation. In Britain, the changeover did not occur until 1752, by which time the correction amounted to eleven days and so Wednesday, 2 September was followed by Thursday, 14 September. The story that this led to riots by people demanding the return of their eleven days is probably apocryphal. In Russia the new system was not adopted until early in the communist era, by which time thirteen days had to be dropped from the calendar. An ironic consequence was that the date of the Great October Socialist Revolution was shifted into November.

Solar calendars follow the seasons, but the months do not follow the phases of the Moon because there are not an exact number of synodic months in a tropical year. A lunar calendar is one based on the phases of the Moon and examples include the Islamic calendar, which comprises twelve synodic months and therefore lags the solar calendar by 11 to 12 days each (tropical) year. The Islamic calendar is the official calendar of Saudi Arabia, but elsewhere in the Islamic world it is used mainly for religious purposes.

To get round the problem of a lunar calendar fairly rapidly drifting out of synch with the tropical year, some calendrical systems insert an intercalary month every so often, though various calendars use different systems for determining how and when these occur. Such systems are known as lunisolar; examples include the Hebrew and Chinese calendars.

Lunar and solar calendars generally come into line every 19 years. This is because 19 tropical years are almost exactly 235 synodic months; thus every 19 years the Moon will have the same phase on the same day of the year. This 19-year cycle is known as the Metonic cycle after the Greek philosopher Meton of Athens (ca 440 BC) who noticed it, though it was undoubtedly known earlier. The Metonic cycle formed the basis of the Greek calendar until 46 BC, when the Julian calendar was adopted.

Moonrise, Moonset and lunar movements
Like the Sun, the Moon does not rise and set in exactly the same place every day. The azimuth of the rising and setting points varies cyclically over the course of a sidereal month between northern and southern limits and, as with the Sun, these variations are more pronounced in higher latitudes. Note that the ‘month’ in question here is the sidereal rather than synodic month hence the Moon will not be at the same phase at two successive risings or settings at a particular point. Another way of looking at this is to consider only the azimuth of rising and setting of the full Moon, which will vary between the same limits over the course of a year.

However, these limits themselves open out and close up over the course of the 18.61 year nodal cycle. In the Northern hemisphere, the variation reaches a maximum when the ascending node is co-incident with the summer solstice; these are the major standstill points. When the descending node reaches this point, the variation is at a minimum; these are the minor standstill points. Between these limits, the standstill points gradually close up and then re-open. The situation is reversed in the Southern Hemisphere.

In simpler terms, at the major standstill the Moon’s 5 degree orbital inclination is added to the effect of the Earth’s axial tilt; at the minor standstill it is subtracted. Thus the variation exceeds that of the Sun at major standstill, but is less than it at the minor standstill.

As we have seen, the cycle is driven by the sidereal and not the synodic month, so different phases of the Moon will be best observed at different times of the year. The full Moon, for example, rides majestically high in the winter skies, but in summer its performance is decidedly lacklustre. It struggles into the sky, staggers wearily along the southern horizon for a few hours before giving up and disappearing again. The explanation is straightforward enough: when full the Moon is in the opposite part of the sky to the Sun, so in winter it behaves as the Sun in summer, and vice-versa. In spring, the waxing first quarter Moon is most favourably presented for observation, and in autumn it is the turn of the waning last quarter Moon. The waxing crescent is best seen in mid-spring; the waning crescent in mid-summer. These rules hold in both hemispheres, because the seasons are reversed in the Southern Hemisphere. As with the standstill points, these effects are accentuated and diminished over the course of the 18.61 year nodal cycle.

The Dark side of the Moon
When people refer to ‘the dark side of the Moon’ they really mean the side that cannot be seen from here on Earth. As is correctly pointed out in the eponymous Pink Floyd album, there is no dark side of the Moon and both sides experience equal portions of day and night. It is, however, true that the Moon’s sidereal day is exactly one sidereal month, so in the main one side permanently faces the Earth. However, it is not strictly speaking true to say that we can only see one side from Earth.

The orbital speed is not constant, so the orbit and rotation get slightly out of step at times, which causes a slightly different face to be presented. This effect is known as libration in longitude. In addition, because the Moon’s axis is inclined by 6.5 degrees to its orbit, it appears to ‘nod’ back and forth over the course of a month – this is libration in latitude. Finally, parallax effects result in slightly different faces being presented to the observer at different times of the day; in total 59 percent of the Moon’s surface may be seen from Earth (though of course no more than 50 percent at any one time).

The Wanderers
The word ‘planet’ comes from the Greek word planetes, meaning ‘wanderer’. Long before the time of the Classical Greek civilisation, man would have been aware of bright star-like objects that did not did not remain fixed in relation to the stars but moved in roughly the same narrow band to which the Sun and Moon are constrained. Five planets (excluding the Earth) have been known since prehistoric times – Mercury, Venus, Mars, Jupiter and Saturn. They fall into two groups, the inferior planets, whose orbits lie close to the sun that of the Earth (Mercury and Venus) and the superior planets whose orbits whose orbits lie further away from the Sun (all the other planets, excluding Earth). The distance of each planet from the Sun is often given in astronomical units. Incidentally, the terms ‘superior’ and ‘inferior’ do not mean that the superior planets are ‘better’ planets.

The motion of each planet around the Sun is governed by Kepler’s Laws of Planetary Motion, which were formulated by the German mathematician Johannes Kepler between 1609 and 1618 and they apply not just to planets but all orbiting bodies, such as the Moon, satellites of other planets and even artificial Earth satellites.

The First Law states that the orbit of any planet around the Sun will be an ellipse, with the Sun at one focus. (If you add the distances of any point on an ellipse from each of the two foci you will always get the same result. By comparison, if you measure the distance of any point on a circle from the centre of that circle, you will always get the same result. In fact these properties define circles and ellipses, which are both examples of what are termed conic sections by mathematicians.

The Second Law states that the movement of any planet in its orbit is such that its radius vector (an imaginary line joining the planet to the Sun) sweeps out equal areas in equal times. This explains why the Earth and other planets move faster when they are close to perihelion and why the Moon moves faster when it is close to perigee. The sector swept out in, say, 24 hours, is shorter at these times, but because the Earth (or Moon) is moving faster, it is also ‘fatter’ and these two effects exactly cancel out.

The Third Law states that the square of a planet’s orbital period in years is equal to the cube of its mean distance from the Sun in astronomical units. More generally, the square of the orbital period of any orbiting body is proportional to its mean distance from the body it orbits.

These laws arise naturally from Newton’s Law of Universal Gravitation, which states that between any two objects, there exists an attractive force that is proportional to their masses multiplied together and divided by the square of their distance apart. Objects under consideration can be stars, planets, satellites or even the apocryphal apple that is said to have given Newton the idea in the first place.

Aspects of the planets
As seen from the Earth, certain positions of the planets relative to the Sun are known as aspects. For superior planets the two principal aspects are opposition and conjunction.

At opposition, a planet is opposite to the Sun in the sky, i.e. they are 180 degrees apart. It will be visible throughout the night and will reach the meridian it midnight. Opposition is the best time to observe a superior planet, because it is at its closest to the Earth. At conjunction, a superior planet is on the opposite side of the Sun to the Earth. It will not be visible from earth at this time, being lost in the Sun’s glare.

When a planet is at either opposition or conjunction (i.e. it, the Earth and the Sun are in a straight line) it is said to be at syzgy. The Moon is at syzgy when it is both new and full. When a planet is at an angle of 90 degrees from the Sun as seen from Earth, it is said to be at quadrature. We see a half-Moon when it is at quadrature.

Inferior planets cannot reach opposition or quadrature, but have two types of conjunction, inferior conjunction, when they lie between the Earth and the Sun and superior conjunction, when they are on the far side of the Sun. When an inferior planet is at its greatest angular separation from the Sun it is at greatest elongation. At its greatest elongation west it will appear in the morning sky; at greatest elongation east it will appear in the evening sky. An inferior planet can never be seen throughout the night.

The inferior planets display phases like the Moon but when best seen (i.e. at elongation) they are crescent. They will be at full phase at superior conjunction and “new” at inferior conjunction, but cannot be seen at these times. The superior planets show very little phase effect; only Mars shows a pronounced gibbous phase when it is at quadrature.

Movements of the planets
As seen from the Earth, the planets normally appear to move from west to east. However, around opposition a superior planet can appear to halt and then move briefly in an east to west direction before resuming its normal progress. This retrograde motion, so beloved of astrologers, occurs because the Earth, which is moving more rapidly, catches up and overtakes the planet in question. The points where the planet halts before changing direction are known as stationary points.

The planets all keep fairly close to the ecliptic, but all have orbits that are slightly inclined to it. Orbits are defined in terms of six elements or quantities. These are the semi-major axis (a) or mean distance from the Sun; the eccentricity (e); the inclination to the ecliptic (i); the longitude of the ascending node (Ω); the argument of perihelion (ω) which is angular displacement from Ω; and the time of perihelion passage (T).

A planet’s ‘year’ is known as its sidereal period, corresponding to the Earth’s sidereal year. The time taken for a planet to return to a particular aspect (such as opposition) as seen from Earth is known as the synodic period (c.f. the Moon’s synodic month).

Eclipses
There is little doubt that a total eclipse of the Sun is one of the most awesome spectacles of Nature available anywhere in the Solar System. On no other planet is there such an exact match between the apparent size of the Sun and the apparent size of a satellite – despite some planets having upwards on fifty of the latter to choose from, while we on Earth have to make do with just the one. Not quite as spectacular, perhaps, but still noteworthy is the sight of the Moon turning a deep blood-red as it enters the Earth’s shadow during a lunar eclipse.

The phenomena are related, but strictly speaking a solar eclipse is an occultation or hiding of a self-luminous body (in this case the Sun) by the Moon. In principle there is no difference between this and the occultation of stars that occur throughout the month as the Moon pursues its course around the Earth. By contrast, a lunar eclipse entails the Moon being cut off from the source of its illumination as it enters the Earth’s shadow.

Unlike point sources (such as a distant searchlight), extended luminous objects such as the Sun do not cast sharp shadows. A shadow will of course be cast when an object is interposed between the observer and the light source, but it will have two regions: the umbra in which the light source is wholly obscured and the penumbra in which it is only partially obscured.

For a disc such as the Moon, the Earth as seen from the Moon’s surface or a hot-air balloon drifting in front of the Sun as seen by an observer on the ground, the umbra will be cone-shaped, converging to a point; the umbra will be fan-shaped and diverging.

Types of Solar eclipse
The Moon’s umbra under favourable conditions will just reach the Earth. It does not remain stationary but races across the Earth’s surface as the Moon moves in its orbit. The path it follows is known as the track. Observers inside the umbra will see a total solar eclipse; those outside it but still within the penumbra will see a partial solar eclipse; those completely outside the Moon’s shadow will see nothing.

The degree of obscuration of the Sun by the Moon or magnitude will increase the closer an observer is to the zone of totality. Magnitude ranges for 0 (no obscuration) to 1 (totality) and it refers to the solar diameter covered, not area. A 0.5 magnitude eclipse is one in which half the Sun’s diameter is covered, but a little geometry will show that only 40 percent of the Sun’s area will actually be hidden by such an eclipse.

The actual duration of totality for any eclipse varies and is dictated by three factors: the distance of the Earth from the Sun when the eclipse occurs; the distance of Moon from the Earth when the eclipse occurs; and the latitude at which the eclipse occurs.

If the Earth is at its maximum distance from the Sun its apparent diameter will be diminished and if the Moon is at its minimum distance from Earth its apparent diameter will be increased; these factors favour long eclipses.

The Earth is rotating in the same direction as the Moon’s shadow is moving, and this has the effect of prolonging the time the latter will linger over a particular region. The speed the Earth’s surface is moving depends on latitude – at 40 degrees north or south of the equator, the west to east motion is 1,270 kilometres per hour but at the equator it is 1,670 kilometres per hour. The relative speed of the Moon’s shadow is thus lower at lower latitudes and thus eclipses that take place in tropical latitudes tend to be of greater duration than those occurring in temperate latitudes.

If the Moon is at or close to its maximum distance from Earth, even if it passes directly in front of the Sun the umbra will not quite reach Earth and a ring of sunlight is left showing. Such eclipses are said to be annular. Total and annular eclipses are referred to as central eclipses, and annular eclipses are the slightly more frequent of the two types.

Occasionally, an eclipse is just total at mid-track, but due to the curvature of the Earth the umbra doesn’t touch the end-points. The result is a hybrid total/annular eclipse with observers at mid-track experiencing a total eclipse but those at either end-point viewing only an annular eclipse.

Finally in about one third of all solar eclipses only the penumbra reaches the Earth with the umbra missing it altogether. Such eclipses are partial only; nowhere on Earth is a total eclipse seen.

Stages of a Solar eclipse
The key events in a solar eclipse as viewed from a particular site are known as contacts. First Contact occurs when the Moon’s western edge begins to slide across the Sun and is the point at which the penumbra first begins to move across the site. It is abbreviated to P1, for first penumbral contact. Second Contact occurs when the Moon’s eastern edge touches the Sun’s eastern edge. The marks the onset of totality or annularity, and for a total eclipse is the point at which the umbra begins to move across the site. It is abbreviated to U1 for first umbral contact (though strictly speaking this term is only appropriate for a total eclipse). Third Contact occurs when the Moon’s western edge leaves the Sun’s western edge. This marks the end of totality or annularity and is the point at which the umbra leaves the site. It is abbreviated to U1. Finally Fourth Contact, abbreviated to P2, marks the departure of the penumbra from the site and the end of the eclipse. In a partial eclipse, only P1 and P2 occur.

Types of Lunar eclipse
Whereas the Moon’s umbra will affect only a small portion of the Earth, the Earth’s umbra is large enough to fully immerse the Moon. During a lunar eclipse, the Moon never entirely disappears from view but appears reddish. This is due to refraction or bending of sunlight by the Earth atmosphere into the umbra; red light is more easily refracted. There are three types of lunar eclipse; total, when the whole of the Moon enters the umbra; partial when only a portion does; and penumbral when the Moon just grazes the penumbra. The latter type generally results in only a slight dimming of a portion of the Moon and is often undetectable to the naked eye. Unlike a solar eclipse, a lunar eclipse may be viewed anywhere on Earth where the Moon is above the horizon.

Stages of a Lunar eclipse
As with solar eclipses, the key stages of a lunar eclipse are referred to as contacts though unlike a solar eclipse these are the same from any point on Earth. P1 occurs when the Moon begins to enter the Earth’s penumbra. U1 is the point at which the Moon begins to enter the umbra; U2 is the point at which it is fully inside the umbra, marking the onset of totality. U3 is the point at which the Moon begins to leave the umbra, marking the end of totality; U4 is the point at which the Moon leaves the umbra altogether. P2 is the point at which the Moon leaves the penumbra and the eclipse ends. U2 and U3 do not occur in a partial eclipse. In a penumbral eclipse, U1 and U4 do not occur either.

When do solar eclipses occur?
As you might have inferred, a solar eclipse can only occur at new Moon – but why don’t they occur at every new Moon, i.e. once every lunation? Recall that the Moon’s orbit is inclined at about 5 degrees to the ecliptic. So the Moon usually ‘misses’ the Sun. Recall that there are two nodes where the Moon’s path crosses the ecliptic. Only when the Sun is close to a node at new Moon can an eclipse occur, although it does not have to be exactly at a node for an eclipse to occur; for the two discs to touch in a ‘grazing’ encounter will at minimum produce a partial eclipse.

The region the Sun has to occupy at new Moon to produce an eclipse is known as the eclipse limit. This varies, depending on the distance of the Moon from Earth at the time the new Moon occurs, and that of the Earth from the Sun. It ranges from between 30.70 degrees to 37.02 degrees in total, or from 15.35 to 18.51 degrees each side of the node. For a central eclipse to occur, the limit is less, ranging from 9.92 to 11.83 degrees each side of the node.

With the Sun moving along the celestial sphere at just under one degree per day, it will be apparent that it will take it more than a synodic month of 29.53 days to traverse even the minimum distance. In other words, the Sun will never be able to get through one of these ‘danger zones’ without the Moon catching up with it at some stage and causing an eclipse. Furthermore, if the Sun has only just entered the eclipse limit when the Moon comes around, the latter will have time to cause a second eclipse before the Sun can get out of the way.

The time period during which the Sun is within the eclipse limit is known as an eclipse season. Eclipses can only occur during an eclipse season and as we have just seen, at least one must occur. How many eclipses will occur in a calendar year, given at least one must occur whenever the Sun approaches a node?

Recall the nodes are moving along the celestial sphere in the opposite direction to the Sun, completing a complete cycle every 18.61 years. It will therefore take the Sun slightly less than a year to make successive passages through the same node. This is the ‘fourth kind of year’, the eclipse year mentioned earlier, of 346.62 days. There will be two eclipse seasons in each eclipse year and a minimum of two solar eclipses and a maximum of four.

The calendar year is longer than an eclipse year and so the eclipse year will end at different times of the calendar year. Normally there will only be two eclipse seasons (and hence a minimum of two eclipses) in a calendar year, but if an eclipse year ends in December, a portion of a third eclipse season can be squeezed into that calendar year, meaning that a maximum of five solar eclipses could occur. Unfortunately, you will have to wait until 2206 before this next happens.

When do lunar eclipses occur?
Just as solar eclipse can only occur at new Moon, so a lunar eclipse can only occur when the Moon is full. The condition for a lunar eclipse is for the Moon to pass through the opposite node to the one through which the Sun is passing during an eclipse season. As with a solar eclipse, this must happen at least once during an eclipse season, and can happen twice.

The maximum number of both types combined in an eclipse season is only three, because it would take 1 ½ lunations to produce two solar and two lunar eclipses, which is longer than the maximum length of an eclipse season. However, there will always be at least one of each. This rule does include penumbral lunar eclipses, which many authorities omit from eclipse statistics.

The Saros
The word ‘saros’ is taken from an ancient Babylonian word meaning ‘repetitive’ and was adopted by Sir Edmund Halley to describe an 18-year cycle of eclipses first recorded by the Babylonians in 400 BC, though it may well have been known much earlier.

The saros results from a series of coincidences of nature: 223 synodic months (6585.32 days) is almost exactly the same length of time as 19 eclipse years (6585.78 days) and also coincides with 239 anomalistic months (6585.54). The net effect is that at the conclusion of 223 synodic months from the time of an eclipse, not only are the Sun and Moon in the same places in the sky (thus giving rise to another eclipse) but the Moon will be at the same distance from the Earth as for the previous eclipse and the eclipse limit will thus be the same. This latter factor is equally important because were the Moon to be at a greater distance from Earth than previously, the eclipse limit would be smaller and an eclipse might not occur at all.

However, there is one important difference. 223 synodic months does not contain a whole number of days. The odd 0.32 of a day means the second eclipse will occur at a longitude of 0.32 times 360 degrees, i.e. approximately 115 degrees west of the first eclipse due to the Earth’s additional rotation.

Eclipses occur more frequently than every 18 years, so there are a number of saros cycles in operation at any one time, and each one is given a number. Saros cycles involving the Moon’s descending node receive even numbers and those involving the ascending node receive odd numbers. Each saros cycle evolves and has a finite life. For a saros cycle involving the Moon’s descending node, the series begins with an eclipse at the South Pole. Each successive eclipse then has a track more northerly than the last, until a final eclipse at the North Pole concludes the cycle. For a saros cycle involving the Moon’s ascending node, the reverse happens, with the series beginning at the North Pole and concluding at the South Pole.

At any one time there will be 43 saros cycles in operation and as soon as one concludes at one Pole another one will begin at the other Pole. The length of a cycle ranges from between 1,206 to 1,442 years. This all happens because 19 eclipse years are actually 0.46 days longer than 223 synodic months, and the Sun will not be in exactly the same place for successive eclipses. Given the Sun moves approximately one degree per day along the celestial sphere, each eclipse will occur about 0.46 degrees west of its predecessor. The Moon of course will also be 0.46 degrees further west than before. For the descending node, this will additionally put the Moon slightly further north than before; for the ascending node, the Moon is slightly further south than before.

Everything you wanted to know about the Moon

Most people will think nothing of the Moon should they happen to see it in the sky. This is hardly surprising, the Moon is after all one of only two distinct, instantly recognisable objects (the other being the Sun) that we are guaranteed to see (even here in Britain!) during our lifetime; there can be nobody alive who has not known of it from their earliest childhood. The Moon is a ubiquitous part of our culture and almost certainly has been since earliest times. Its beauty in the night skies has inspired writers, poets and artists for centuries. Reaching for the Moon was once synonymous with desiring the impossible – until man reached it. Even now, almost four decades on from Armstrong’s momentous giant leap for mankind, the Moon remains the only astronomical body other than Earth to be visited by humans.

What’s in a name?

Many people think the “official” name of the moon is the Latin form Luna, but in common with Terra (Earth) and Sol (the Sun) the term Luna has no official standing and is rarely encountered outside of science-fiction novels, though the adjectival forms “lunar”, “terrestrial” and “solar” are in common usage. The “official” name for the Moon is – the Moon (capitalised)! The uncapitalised form – “moon” – is a generic term for any natural satellite of any planet, including our own. Some prefer this term over “satellite” thinking the latter implies something manmade. Strictly speaking a manmade satellite should be referred to as an “artificial satellite” but this usage is now very rare.

The phases of the Moon

The most obvious thing about the Moon is that its appearance changes from night to night. The Moon is not the only body visible from Earth to exhibit phases – Venus and Mercury do also – but without a telescope those of Venus are very difficult to see and those of Mercury are way beyond human perception. The explanation for the phase is straightforward; only one hemisphere of the Moon is illuminated by the Sun at any one time (in common with all other non-luminous solar system objects) and the portion of the illuminated hemisphere visible from Earth changes as the Moon travels round the Earth on its orbit. When the Moon and Sun are on opposite sides of the Earth a full moon is seen; when they are on the same side the Moon disappears altogether. When they are 90 degrees apart a half moon is seen.

The time taken for the Moon to cycle through its phases (the synodic month, defined as the time taken for the Moon to return to the same position relative to both Earth and Sun) is actually longer than the time taken for it to complete a single orbit (the sidereal month) – 29.53 days on average, as opposed to 27.32 days. The reason for this is while the Moon is completing an orbit of the Earth, the latter is moving on its own orbit around the Sun, and the Moon has to move slightly further before it can return to the same position relative to both Earth and Sun.

The wrong time of the month

In 1972 the American researcher Alexander Marshack claimed that people were making records of the phases of the Moon 30,000 years ago. After extensive research that entailed examining just about every prehistoric artefact he could lay his hands on for calendrical notches, he published his findings in a book entitled The Roots of Civilization. Marshack claimed that the tallies corresponded to lunar months. On the face of it, this seems highly plausible. It is now generally accepted that the people of that era were every bit as mentally capable as we are today, and there is little doubt that they would have been aware that the phase of the Moon changes from night to night in a predictable manner. But there are two problems – firstly, it seems unnecessary to record, say, the days since the last full moon when one can simply look at the Moon, note the current phase, and work forward to when the next full moon will occur. The second problem is the tallies vary in numbers of days by more than can be explained by the small seasonal variations in the length of the lunar cycle, or by observational error. However there is another cycle with an average length almost identical to the lunar cycle that does show a certain amount of variation – the human menstrual cycle. It is my guess that this is what was being recorded, since the advantages of knowing when that time of the month is approaching are fairly obvious, and this was probably also the case 30,000 years ago!

That the menstrual cycle is almost exactly one lunar month in duration is now thought to be pure co-incidence, but it is one that was noticed many thousand years ago. The words “moon”, “month”, “menstruate” and “measure” (time) all have the same Proto-Indo-European root. The proto-Indo-European language is the hypothetical common ancestor of the Indo-European languages, which include Latin, Greek, Sanskrit and the modern languages derived from them. According to one popular theory, the Proto-Indo-Europeans were warlike nomads who originally expanded from the Eurasian steppes at around 4000 BC, taking their language with them. A rival theory, proposed in the mid-1980s, claims that Proto-Indo-European origins go even further back, and that they were originally farmers living in Asia Minor, shortly after the end of the last Ice Age. Regardless of which theory is correct (I personally favour the farming theory), the origin of the word “moon” is very ancient indeed.

The Moon from an astronomical viewpoint

The Moon is ranked as a satellite of the Earth. Most of us will be aware that the Earth is in astronomical terms quite undistinguished, and that the same goes for the Sun. Even though the Milky Way, of which the Sun is a part, is classed as a large galaxy one doesn’t have to look far (in fact a mere two million light years) to find a larger galaxy (the Andromeda Galaxy). In a way this is exactly what we should expect from the Copernican Principle or Principle of Mediocrity, an important principle in the philosophy of science which states that Earth holds no special place in the universe and that humans are not privileged observers. Right, so this presumably means that the Moon is equally average? Well, actually, no.

The Moon is a remarkable object and as far as the Solar System is concerned, it is unique. The Moon is a fully paid-up member of the Solar System’s “Big Seven” group of satellites, all of which are larger than Pluto and Eris (the two smallest planets(or largest “dwarf planets” if you insist)). The Moon is by no means the largest member of this group, but all the other six are satellites of giant planets: the Earth is at best only medium-sized. Indeed many astronomers take the view that the Moon is too large in relation to the Earth to be considered a mere satellite and elevate it to the rank of a sister world, classifying the Earth-Moon system as a binary planet. However this view is not really valid. Large though the Moon is, it is still only 1/81 the mass of the Earth; the centre of mass for the Earth/Moon system lies below the surface of the Earth and the Moon cannot be classed as anything other than a satellite of Earth.

Lunar geography – or Selenography

Though most will know what it means, terms like “lunar geography” , “lunar geology”, etc, are oxymorons as the prefix “geo-“ means pertaining to the Earth. The correct terms are “selenography”, “selenology”, etc; the prefix “seleno-“comes from Selene, the Greek goddess of the Moon.

It is not true, as is often believed, that Galileo was the first to map the Moon using a telescope. That distinction must go to Thomas Harriot in 1609, a year before Galileo. However, both men clearly observed mountains, valleys, craters and comparatively smooth areas known as maria or seas. It was at one time believed that these latter features actually were seas, or at least dried-up sea beds, but we now know from samples brought back from the Moon that they have never contained any water.

However, in 1998, it was widely reported that NASA’s Lunar Prospector probe had found water on the Moon, allegedly from comets that had landed in polar regions permanently hidden from the Sun and thus remained frozen. In fact, the probe had only detected evidence of hydrogen on the Moon’s surface. While this could be due to water, I have to say I am highly dubious. Any comet impacting the Moon would almost certainly do so at a relative velocity high enough to vaporise it instantly as its kinetic energy is transformed into heat.

Another theory, popular before the Space Age, was that the maria were great dust-bowls, and any spacecraft landing there would be swallowed up. The idea was featured in two vintage novels by Sir Arthur C. Clarke, Earthlight and A Fall of Moondust, the latter telling the story of a “dust cruiser” designed to “sail” the lunar “seas”.

Today we know that the maria are large dark plains of basalt, formed by volcanic activity billions of years ago.

The origin of the lunar craters has been the subject of considerable controversy over the years. It was once believed that they were volcanic in origin, similar to calderas, but it is now generally accepted that they are the result of meteoric impacts. It was however quite a long time before the volcanic theory was abandoned and a number of astronomers, including Sir Patrick Moore, continued to argue for it until as late as the 1990s.

A Canterbury Tale

Assuming that the impact theory is correct could any new craters have appeared in historic times? In theory, there is no reason why not, though in practice it seems unlikely with impacts forming craters visible from Earth being fairly rare events. However in the 1970s an American astronomer named Jack Hartung claimed that a report made on 18 June 1178 by a Canterbury monk named Gervase could be interpreted as an eye-witness account of the formation of the crater Giordano Bruno.

… after sunset when the moon had first become visible a marvellous phenomenon was witnessed by some five or more men who were sitting there facing the moon. Now there was a bright new moon, and as usual in that phase its horns were tilted toward the east; and suddenly the upper horn split in two. From the midpoint of this division a flaming torch sprang up, spewing out, over a considerable distance, fire, hot coals, and sparks. Meanwhile the body of the moon which was below writhed, as it were, in anxiety, and, to put it in the words of those who reported it to me and saw it with their own eyes, the moon throbbed like a wounded snake. Afterwards, it returned to its proper state. This phenomenon was repeated a dozen times or more, the flame assuming various twisting shapes at random and then returning to normal. Then after these transformations the moon from horn to horn, that is along its whole length, took on a blackish appearance.

It has been suggested that Gervaise saw a meteorite impact, and that the crater Giordano Bruno (named for the Italian philosopher who was burned at the stake for heresy in 1600) was formed as a result. Proponents of this idea point out that the time of the year is consistent with an impact from the so-called Taurid Complex, associated with Enke’s Comet, but the whole thing really has to be taken with a king-sized pinch of salt. Surely a small group of men in Canterbury would not have been the only people in the whole world to see and note such a major disturbance in the natural order of things? A more recent mathematical treatment of the theory showed that Earth would have been bombarded with ejecta from the impact. This would have resulted in spectacular meteor showers of roughly 50,000 meteors an hour being visible all over the world for a week – yet there is absolutely no record of anything of the sort being seen.

Crucially, the Moon was close to the horizon at the time and what Gervaise reported was almost certainly an unusual cloud phenomenon or atmospheric disturbance.

The Moon in fiction

What is arguably the world’s first ever work of science-fiction, entitled A True Story, was written by the Greek satirist Lucian of Samosata in the 2nd Century A.D. and dealt with imaginary voyages to the Moon, but the topic did not become popular until the invention of the telescope in the 17th Century. Authors who wrote about journeys to the Moon included Johannes Kepler, Francis Godwin and Cyrano de Bergerac though the heroes tended to travel by unlikely means such as harnessing a flock of geese.

About a hundred years before Project Apollo, Jules Verne described an American moon program in which a projectile is launched from a space gun in Florida and splashes down in the Pacific, just as Apollo would later do. Some 35 years later, H.G. Wells sent his characters to the Moon in a vehicle utilising anti-gravity – much to the disgust of the by then elderly Verne. This criticism evidently affected Wells, who much later used a space gun himself in the moon shot sequence at the end of the movie Things to Come.

The Moon featured in innumerable works by the 20th Century’s “Holy Trinity” of Sir Arthur C. Clarke, Isaac Asimov and Robert Heinlein.

Inevitably the Moon has featured in many science fiction movies and television series, with manned moonbases being a popular theme for the latter. Gerry Anderson, best known for his classic puppet shows such as Thunderbirds, made two live-action series featuring moonbases. In the first, UFO, interceptors were launched from a moonbase to destroy hostile alien spacecraft. The second, Space 1999, was an altogether more ambitious affair. It was billed as a British answer to Star Trek but despite a huge budget, excellent special effects and a star cast that included Martin Landau, Barbara Baines, Barry Morse, Catherine Schell, Joan Collins, Brian Blessed and Judy Geeson, the series was not a success and was cancelled mid-way through its second run. The main problem was an utterly implausible plot device in which a nuclear explosion sent the Moon careering off into outer space at what one must presume was many times the speed of light (a physical impossibility in itself), given that most weeks would find it hurtling towards a new planetary system. Hopes would rise among those marooned on Moonbase Alpha that the new system would contain an inhabitable world on which they could settle, but on the occasions that it did something would always prevent colonisation, be it paranoid aliens fearing cultural contamination by “primitive” humans (this one cropped up on several occasions); an interplanetary battle of the sexes (a group of rather butch-looking women hijacked Alpha and used it as a platform to lob nuclear missiles at the men, who had already been banished to another planet for being “unreasonable”); a time-warp that reverted the crew to cavemen (this provided an excuse to put the lovely Zienia Merton in a leopard-skin), or the putative new home turning out to be rather inconveniently composed of antimatter. Even when the Moon was in interstellar space things were rarely quiet: black holes and time warps were as frequent as tailbacks on the M25; other menaces included a space brain, a monster dwelling in a Sargasso Sea of abandoned spaceships and miscellaneous aliens in suspended animation, who invariably turned out to be bad guys sent into exile by their peace-loving compatriots.

Is the Moon Earth’s only natural satellite?

Could the Earth have a second, undetected satellite? On the face of it, there is absolutely no reason why not. Jupiter is now known to have at least 63 satellites; Saturn has about the same number; and even Pluto has three. However if a second Earth satellite were to exist, it would have to be very small indeed to avoid detection. It is not often appreciated that were the Moon only two miles in diameter, it would still be visible to the naked eye.

Nevertheless, the idea that the Moon might not be our planet’s sole attendant has intrigued astronomers for the better part of two hundred years. In 1846 Frederic Petit, Director of the Toulouse Observatory, claimed that a second Earth satellite had indeed been discovered. Petit’s claim was soon refuted, but he became obsessed with the idea of a second satellite. Fifteen years later, he published an abstract in which he proposed the existence of a second satellite to account for then-unexplained anomalies in the Moon’s orbit. The theory attracted little interest among astronomers, and doubtless would have been entirely forgotten by now had a young French writer by the name of Jules Verne not read the abstract and immortalised Petit and his satellite in the novel From the Earth to the Moon, in which the Petit object passes close to the space travellers projectile, pulling it off course and swinging it into an orbit around the Moon.

The idea of a second moon was revived several times during the last century, and shortly after the end of the Second World War, Clyde Tombaugh, discoverer of Pluto, carried out a most comprehensive search. He used equipment so sensitive that it would have shown a lump of coal the size of a football a thousand miles away. He failed to find anything.

It is now believed that the combined gravitational effects of the Earth, Moon and Sun would rapidly eject any small satellite from Earth’s orbit, ruling out the existence of a second moon. Nevertheless in 2002 an object known as J002E3 was discovered in Earth orbit – but it was soon discovered to be almost certainly the discarded third-stage booster from the Apollo XII mission in November 1969. It is believed that the object left orbit in June 2003 and may return around 2032.

It is sometimes claimed that the asteroid 3753 Cruithne ranks as a second Earth satellite. Discovered in 1986, Cruithne has an unusual orbit, known as a “horse-shoe” orbit, due to the influence of Earth. However it is in orbit around the Sun, not the Earth and therefore it is not an Earth satellite.

A Cosmic Coincidence

One of the most singular features of the Moon is the fact that it appears almost exactly the same size as the Sun in the sky. The reason for this is that while the Sun is 400 times the diameter of the moon, it is also 400 times further away, so both objects appear the same size when viewed from Earth. This is a pure co-incidence, but it is responsible for what is surely one of the most spectacular phenomena to be seen anywhere in the Solar System – a total eclipse of the Sun. A solar eclipse is, of course, due to the Moon passing directly between the Sun and the Earth, casting its shadow upon the latter (strictly speaking, the phenomenon is an occultation, not an eclipse). Because the Moon’s disc is just sufficient to hide that of the Sun, the latter’s atmosphere, the so-called corona can be seen in all its splendour. In fact it is a close call and for a total eclipse to occur, the Moon must be close to perigee (i.e. its minimum distance from Earth). Otherwise, a thin ring of the Sun’s disc is left showing, quite enough to drown out the glorious corona, and the eclipse is said to be annular. Because the Moon’s orbit is inclined at five degrees, an eclipse does not occur every month, though at least two must occur in a given year. However this figure includes partial eclipses, when the Moon does not pass directly in front of the Sun. Even when a total eclipse does occur, the area experiencing totality is only a small corridor, though it may extend for thousands of miles as the Moon’s shadow races across the Earth’s surface.

I have only witnessed one total eclipse of the Sun, that being the one in Cornwall in August 1999. Although cloudy skies prevented me from seeing totality, it was still an awesome experience as day became night in a matter of seconds. Sea birds, believing night really had fallen, hooted in great excitement. On the horizon was seen a band of orange light, marking the limits of totality. The scene was one of great beauty and although it was disappointing to have missed something I had been waiting to see since my childhood, it was still a worthwhile experience.

We will not always be able to enjoy the spectacle of a solar eclipse, because tidal effects are causing the Moon to recede from the Earth by 3.8 centimetres per year. That might not seem like a lot, but it adds up. When the first maps of the Moon were being drawn up, three centuries ago, the Moon was 11.4 metres (just under 40 feet) closer to the Earth. When modern humans first reached Australia, 50,000 years ago, the Moon was 1900 metres (rather more than a mile) closer; when the dinosaurs became extinct 65 million years ago, it was 2470 kilometres closer.

Eventually it will be too far away for its disc to fully block out the Sun, even at perigee. These effects are also causing the Earth’s spin to slow and the day is gradually lengthening. Again, these effects are small but they add up over time and account for discrepancies amounting to several hours in the timing of eclipses observed in antiquity.

The Dark Side of the Moon

As is correctly pointed out in the eponymous Pink Floyd album, there is no “dark” side of the Moon: each part of the Moon experiences as much daylight as it does night time. So where does the idea that the Moon has a “dark” side come from? In common with almost all bodies circling a larger primary, the Moon exhibits so-called “captured rotation”, meaning that it turns on its axis exactly once in each circuit of its primary. In other words, a lunar day is exactly a month long. It is often said that this results in half the Moon’s surface being permanently hidden from view on Earth, leading to the misconception that the hidden side is in permanent darkness. If this were true, we’d see a full moon all the month round! The phase is of course due the part of the Earth-facing side being in darkness. In fact it is not strictly true that only half of the Moon’s surface can be seen from Earth. Because the Moon (in common with all other objects in the Solar System) does not move in a perfectly circular orbit, its orbital velocity varies slightly during the course of a month in accordance with Kepler’s Laws of Planetary Motion. This means that the orbital motion and axial spin are at times slightly out of step, and in consequence we can see portions of the “hidden” side. Because the Moon’s orbit is inclined at five degrees to that of Earth, we can also see alternately beyond the north and south lunar poles. Finally, parallax effects result in observers being presented with slightly different portions of the Moon’s surface at different times of the day and in total, about 59 percent of the Moon’s surface may be observed from Earth at various times.

Origin of the Moon

As one might expect, the origin of the Moon has been the subject of many theories over the years. The first theory to gain widespread acceptance was put forward by Sir George Darwin (son of Charles). Darwin suggested that the Earth and Moon had originally formed a single rapidly rotating, molten mass. The tidal forces raised by the Sun and the centripetal forces of its own motion caused it to become pear-shaped and eventually split into two objects of unequal size. A strong supporter of the fission theory was the American astronomer W.H. Pickering, who suggested that the scar left by the Moon’s breakaway was now the basin of the Pacific Ocean.
Unfortunately the theory was pear-shaped in more ways than one. A mathematical treatment of the dynamics involved showed that it was unsound and it had to be abandoned. This did not prevent it from being used as the basis of an ingenious science fiction movie, Crack in the World, in which an attempt to tap energy from the Earth’s molten core goes disastrously awry and triggers a series of earthquakes. A growing rupture in the Earth’s crust threatens to tear the planet apart and rival scientists Stephen Sorenson (Dana Andrews) and Ted Rampion (Kieron Moore) are forced to put aside their differences and try to come up with a solution. An attempt to avert disaster by exploding a hydrogen bomb in the shaft of an active volcano is only partially successful, and a whole portion of the Earth is blasted away into space, where it forms a new satellite. The movie’s closing reel shows the Moon and its new sibling in the sky together, the whole process having been observed from no more than a few hundred yards by Rampion – accompanied, of course, by the movie’s love-interest (Janette Scott).

The next theory to be put forward suggested that the Moon was originally an independent body, but it wandered too close to the Earth and was captured. There is little doubt that this has happened elsewhere in the Solar System, Mars’s dwarf attendants and several satellites of the giant outer worlds, including Neptune’s major satellite Triton – only slightly smaller than the Moon – were almost certainly captured from independent orbits. The theory was popular for a time and in the middle part of the last century an Austrian researcher named H.S. Bellamy even suggested that it might have happened fairly recently (needless to say, this accounts for the destruction of Atlantis). But captures that are believed to have occurred all involve objects that are very small in relation to their captors, and as we have observed, the Moon is fairly large in relation to the Earth.

Another theory states that the Moon simply formed in Earth’s orbit from the same primordial material, but this model fails to explain why the Moon is less dense and deficient in iron in comparison to Earth.

The currently popular theory, put forward by American scientists W.K. Hartmann and D.R. Davis in 1974, proposes that an object about the size of Mars collided with Earth, and while the bulk of its mass including its iron core merged with the Earth, enough debris was ejected into space from Earth’s mantle to form the Moon. The theory explains why the Moon is rather less dense than the Earth, as denser materials were not blasted into space by the impact. The theory is not without its problems, but seems to be the most plausible explanation put forward to date.

From the Earth to the Moon

As we have seen, some 59 percent of the Moon’s surface can be seen under various conditions from Earth. Not until the dawn of the space age was anything definite learned about the remaining 41 percent. In October 1959, the Soviet probe Lunik III made a fly-by of the far side of the Moon. Because the probe was out of radio contact with Earth as it passed behind the Moon’s far side, the pictures it took could not be simply beamed back to Earth. Accordingly, film was automatically exposed and developed. As the probe emerged from behind the Moon, the developed film was imaged by a TV camera and the first blurry images of the Moon’s hidden side were transmitted back to Earth. It sounds crude, and by today’s standards it was, but it was a tremendous technical feat for the time.

As the Cold War ratcheted up tensions between East and West, so the Soviets continued to score an impressive succession of “firsts” in space, but the US was galvanised into a response and on 25 May 1961 President John F. Kennedy threw down his historic challenge:

I believe that this nation should commit itself to achieving the goal, before this decade is out, of landing a man on the Moon and returning him safely to Earth. No single space project in this period will be more impressive to mankind, or more important for the long-range exploration of space; and none will be so difficult or expensive to accomplish.

In May 1961, Alan Shepard had only just become the first American to fly in space, yet little over nine years later after the flight of Lunik III, men saw the Moon’s hidden side with their own eyes as Apollo VIII made its historic circumnavigation of the Moon at Christmas 1968. Seven months later Armstrong and Aldrin became the first men to actually land there, realising Kennedy’s goal with less than six months to spare. The technological leap that made this possible might sound incredible, but it must be remembered that even the technology of Project Apollo was quite primitive by today’s standards. It is a fact that the Eagle’s on-board computer was actually far less powerful than that of a modern-day mobile phone! (I refuse to comment on conspiracy theories that the Moon landings were faked because it is patently obvious that the idea is absurd.)

At all events, the US won the race to the Moon. Not until much later did it emerge that early Soviet successes owed more to the genius of Chief Designer Sergei Korolev than to any superiority of communism over capitalism. But Korolev’s health had been ruined by a spell in the gulag during Stalin’s reign of terror and he died in 1966 during a botched operation to remove a tumour. With his death ended any hopes of perfecting the N1 booster with which he had hoped to put a man on the Moon. The race to the Moon lost, the Soviets turned their attention to establishing a near-permanent human presence in Earth orbit – which in the long run was of far more benefit than simply duplicating the efforts of the US.

When will people go back to the Moon? In 1972, when Cernan and Schmitt blasted off from the Moon’s surface, it was said that nobody would be going back in the 20th Century. I did not believe this (I assumed that men would be on Mars before the century was out), but the public’s attention-span is short and after the Moon landing had been made, only the astonishing drama of Apollo XIII made the headlines (and, a quarter of a century later, an excellent if not entirely accurate Hollywood movie). NASA turned its attention to the Space Shuttle, setting back the manned exploration of space by decades. As an experimental proof-of-concept spaceship, there is no doubt that the Shuttle was a technological triumph. As a practical manned reusable heavy-lift system however it has been an unmitigated disaster that cost the lives of the crews of Challenger and Columbia. It was the latter tragedy that prompted President George W. Bush, in one of the very few highlights of his presidency, to announce what has since become known as Project Constellation, which will return humans to the Moon, and on to Mars – using designs that draw heavily from Project Apollo, albeit using hardware developed originally for the Shuttle.

A permanently inhabited base on the Moon should be established no later than the middle part of this century. When it is, one of science fiction’s oldest and most central themes will be a reality at last.

© Christopher Seddon 2007