We view a universe continually in motion. The most obvious movements, apparent to even the casual observer, are the paths of the Sun across the sky on a daily basis and the rising and setting of the Moon on an apparently slightly less reliable basis.
The equivalent nocturnal rhythm of the rising and setting of the constellations also is easily discernible, though much less familiar to increasingly urban populations.
Those who are more careful watchers of the sky will notice two longer rhythms, the march of a changing Moon progres- sively through the day and night skies on a 28- to 29-day basis, and the annual ritual of the slow climb of the Sun toward a more northerly path in the sky during summer and toward a more southerly path during winter (readers in the southern hemisphere should reverse north and south in the description). At any given location the Moon occasionally wanders into a region of dark- ness, and reddens in what is called a lunar eclipse. The Sun’s light is partially blocked once every few years from a given loca- tion, and totally blocked much more rarely at any given place, in a solar eclipse.
9
1023 Size
(km) Significant distances
Alpha Centauri Sun
Sun Pluto
Sun Earth
magnitude larger than
Earth
19 Diameter of universe
Distance to nearest galaxy like ours
Distance to nearest star
Diameter of solar system
Astronomical unit
Diameter of sun Diameter of jupiter Diameter of earth
Child
Cell
Atom
Nucleus
Electron Diameter of our galaxy 18
17 16 15 14 13 12 11 10 9 8 7 6 5 4
2 1 0
7
12
17
20
24 3 1022
1021 1020 1019 1018 1017 1016 1015 1014 1013 1012 1011 1010 109 108 107 106 105 104
10–3
10–8
10–13
10–16
10–20
Figure 2.1Sizes of various objects over the enormous range that the natural world encompasses. From Robbins and Jeffreys (1988) by permission of John Wiley and Sons.
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Even more subtle motions are available in the skies for those with the patience to watch. Five “stars” in the sky can be seen, without a telescope, to move against the background of the fixed stars on paths that execute peculiar back-and-forth dances; the speed with which these planets (from the Greekplanetes, mean- ing wandering) move varies greatly, corresponding to timescales of months to centuries to orbit the Sun.
All of these motions are fully understandable on the basis of the Copernican model of a spinning Earth, tipped modestly on its axis, orbiting about the Sun once each year, with other planets orbiting at greater or lesser distances from the Sun, and the Moon orbiting about the Earth. We take this picture, quite appropriately, as fact, but few of us have paused to ponder the subtleties associated with working out such motions. Further- more, slight changes in the shape of Earth’s orbit have affected climate on cycles of tens of thousands of years, and the pres- ence of the Moon in orbit about Earth apparently has prevented rather extreme swings in Earth’s axial tilt, which could have led to very large climate instabilities in the past. Far from being a quaint part of the traditional curriculum of science in schools, the arrangement of the Sun, Earth, Moon, and other planets is in fact critical to understanding the stability of, and variations in, our climate on a range of timescales.
We discuss such climatic issues in Part III, but now we return to the basics of Earth’s motions through the cosmos. The percep- tion of movement of the Sun and constellations through the sky is akin to our experiences as children (or adults) on a carousel, watching people, trees, structures, and so on swing past us in regular, repetitive cycles. Because there is little sense of accel- eration on the larger, slower (and hence grander) carousels, very quickly one can experience the illusion of being on a fixed world around which the external “universe” is moving.
The Moon’s motion is somewhat more complicated; because it is orbiting Earth once every 28 to 29 days, it rises and sets at significantly different times from one night to another. The anal- ogy on our carousel is to watch a person who is walking briskly in the direction of the carousel’s motion. Relative to fixed objects (standing adults, trees), our moving person will reappear later during each rotation of the carousel. Because our Moon is almost entirely illuminated by the distant Sun (some contribution from Earthlight is detectable on the otherwise unilluminated portion), different portions of the Moon are illuminated at different times of the month, creatingphases(Figure 2.2).
The orbit of the Moon is not aligned with the apparent path that the Sun takes around our sky (called the ecliptic plane) but rather is inclined from it by about 5 degrees. Because of this, during the time of the month when Earth, the Sun, and the Moon are all aligned in a given direction (the times of full and new Moon), the Moon generally appears on the sky significantly above or below the path of the Sun. Only when the time of full Moon coincides with the Moon crossing the plane defined by Earth’s orbit around the Sun – the ecliptic– do we have true alignment. At this time, the full Moon gives way to a lunar eclipse, in which Earth’s shadow obscures the Moon, or the new Moon is replaced by the dramatic solar eclipse, in which the disk of the Moon blocks out the light of the Sun (Figure 2.2).
Eclipse prediction is not easy, because three motions are involved: the revolution of the Moon around Earth, the motion of Earth around the Sun, and the so-calledregression of nodes,
wherein the points at which the Moon crosses the plane of the Earth’s orbit around the Sun rotate slowly in an 18.6-year cycle.
This last motion can be visualized by imagining the orbit of the Moon as a circular glass sheet that cuts through Earth at a slight angle relative to the ecliptic. This sheet slowly revolves relative to Earth, completing one spin in 18.6 years. (The physical cause of the regression lies in the gravitational pull of the Sun, which exerts a torque because the lunar orbit is tilted orinclinedrel- ative to the plane of the Earth’s orbit around the Sun, which is the ecliptic plane.)
These three motions are such that any particular sequence of eclipses recurs at an interval just over 18 years. The frequency of lunar eclipses is greater than the frequency of solar eclipses.
Because Earth’s shadow is much larger than the Moon when projected at the distance of the Moon from Earth, slight misses in crossing the node still produce a lunar eclipse. The lunar shadow is smaller and, coincidentally, the size of the Moon in the sky is just roughly that of the Sun. Thus the solar eclipse must occur very close to a node crossing for it to be total. Further, the orbit of the Moon around Earth is not a circle but an ellipse (see below); if the eclipse occurs when the Moon is farthest from Earth, the apparent size of the Moon is smaller than the Sun’s disk, and a much less spectacular,annular, eclipse transpires.
Two remarkable cultures demonstrate both the subtlety and universality of tracking the rhythms of solar system objects.
Stonehenge is a series of large rock monuments and circles laid out on the Salisbury Plain of England. The earliest such construction, most significant astronomically though least spec- tacular to the eye, is a large circle of 56Aubreyholes, spanning roughly 50 meters across, with a so-called heelstone off to the northeast. This was set up by a Stone Age people about 4,800 years ago, perhaps a millennium before the large stone struc- tures more familiar to tourists. Spurred by an initial suggestion by astronomer Gerald Hawkins, British astrophysicist Sir Fred Hoyle (1972) demonstrated that the 56 Aubrey holes could be used as an eclipse counter.
By moving stones representing the Sun and the Moon coun- terclockwise at certain prescribed rates (two holes every 13 days for the Sun and two holes each day for the Moon), one predicts the positions of the Sun and the Moon relative to the observer, on Earth, in the center of the ring. By moving two other stones, each 180 degrees apart, clockwise three holes each year to represent the precession of the lunar nodes, eclipses could be predicted reliably. When the Moon and the Sun are on opposite sides of the circle, and less than one or two Aubrey holes away from the node stones, a lunar eclipse would occur; when the Moon and Sun stones cross each other and are less than one or two Aubrey holes away from a node stone, a solar eclipse is predicted to occur (Figure 2.3). The counter scheme was not perfect, because about half of the predicted eclipses would not be visible in the skies above Stonehenge (the Aubrey circle representing the full 360 degrees of the sky including that beneath the horizon at Stonehenge); nonetheless, if correctly interpreted, it is a clever astronomical calculator.
Because none of the solar, lunar, or nodal cycles are exact multiples of the 56 holes, the counting rules are not exact.
The marker positions would need resetting regularly by sight- ing the Sun and the Moon in the sky at key times of the year.
The heelstone and nearby additional holes were used, according
first quarter
waxing gibbous waxing crescent
full Moon Earth
quadrature
waning crescent new Moon
Solar rays
Lunar phases
third quarter
(a)
quadrature
opposition
waning gibbous
conjunction
Earth orbit
lunar orbit descending
node
Moon
ascending node Sun
(b)
Earth
Figure 2.2(a) Geometry of Earth, the Moon, and the Sun leading to the monthly cycle of phases; an Earth-bound observer’s view is shown next to each corresponding lunar position (adapted from Snow [1991, p. 31]); (b) alignments of Earth, the Moon, and the Sun during total solar and lunar eclipses (after Hartmann [1983]).
to Hoyle’s model, for sighting and hence correcting the board positions.
Intriguing as the eclipse counter itself is, Hoyle brought up the significant issue of what the node stones would have meant to the people of early Stonehenge. The need for node stones to determine when full or new Moon points would have eclipses must have been derived empirically, because as invisible math- ematical constructs one cannot see nodes in the sky. Given that the Sun and the Moon are common objects of worship in many cultures – even our own, as technologically advanced as it is – it is interesting to ask what the Stonehenge people might have thought their node stones represented. It is tempting, as Hoyle wrote, to think that the node stones suggested to the Stone- henge culture the existence of a powerful yet unseen deity that controlled the motions of the Sun and the Moon. But this is piling speculation on top of an already interesting but specu- lative interpretation of an artifact, namely the eclipse counter itself!
The Mayan people live in the Yucatan peninsula region of Mexico and Central America. From roughly 100 B.C. to A.D.
900, they produced large numbers of stone sculptures, or stelae, on which a complex system of calendar dates was engraved. The classical culture of organized city-states had several calendars, including one of 365 days and a 260-day religious calendar.
This latter is close to, but not quite, the orbit period of Venus.
Astronomer–archeologist Edward Krupp (1983) also has sug- gested that it might refer to the interval between passages of the Sun across the high point (zenith) of the sky at the latitude of important Mayan cities, occurring in May and August. There are other astronomical and biological cycles of significance close to 260, including the human gestation interval.
Most striking about the classical Maya was their sophisticated numbering system for precisely recording dates of major events in their history. The system allowed for extension of dates back in time, and some Mayan sculptures do so – back to arbitrar- ily large values. The longest date recorded on a Mayan stela
Stonehenge ii Stonehenge III
N
0 20 scale (feet)
40 60 80
Stonehenge I
ascending lunar node
post holes post holes
heel stone
descending lunar node Sun stone
Moon stone
Aubrey holes Stonehenge II
Figure 2.3Map of the three stages of Stonehenge construction. The Aubrey holes and other sight points of Stonehenge I are identified. Adapted from Hoyle (1972 p. 22, Fig. 2.4) by permission of W. H. Freeman and Company.
corresponds to 1.4×1036 years, or 1026 times the age of the universe as determined by modern cosmology!
The classical Mayans regarded human history as one cycle embedded in nested sets of larger cycles. The Mayans estab- lished a “zero” date, prior to which events were played out by deities, which human events then mirrored. Hence history was already determined, in a sense, because it had been played out before on a larger scale. The progression of time was thus cycli- cal, but it was linear as well, in that the classical Mayan culture had a detailed chronological history of human events – battles, conquests, accessions – for which definite dates were assigned.
Both significant human events and their mirrored supernatural events before the zero date often were pinned to particular points in the cycles of bodies in the sky, and the Mayans spent much time tracking and recording celestial movements so as to predict when significant events in human history might occur.
One might wonder whether this dual cyclical–linear concept of history arose out of the preoccupation of the classical Maya with calendar keeping, sky watching, and recording of dates, or vice versa. As with our own decimal system, where each digit placed to the left of preexisting digits represents a new power of 10 (and hence a larger supercycle of years, decades, centuries, millennia, etc.), the Mayan system of counting in
twenties allowed cycles nested within cycles to be similarly expressed. In a different sense, our own Western concept of time also embodies both linear and cyclical elements; we will see this in our study of the history of Earth and its sister planets that forms the major part of the book.