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Eclipses
Wonderful eclipses
The size, shape and positions of the Earth, Moon and Sun bring us wonderful eclipses.
Guillermo Gonzalez considers how this happy state of affairs arose.
he circumstances of total
eclipses of the Sun by the Moon
are discussed. It is shown that total
eclipses of the Sun from the Earth
are much closer to perfect than
eclipses produced by other moons
in the solar system. We can expect
to enjoy total eclipses of the Sun for
about another 250 million years.
T
T
otal eclipses of the Sun have both
inspired and frightened people since
ancient times. Even today, although no
mystery remains about them, total solar
eclipses still draw thousands along a long narrow strip of land to witness a mere few minutes
of darkness. Have eclipses always appeared as
they do today? Will they be any different in the
distant future? What are eclipses like on other
planets? Are they any more spectacular? In the
following discussion I hope to be able to
answer these questions.
1a (right): A computer combination of seven
of the author’s colour images of the
24 October 1995 eclipse in Nim Ka Thana,
India. The image processing procedure
employed is the same as that described
by Pellett (1998). It results in an
image with a very large dynamic
range in the radial direction.
In order to try to understand why total solar
eclipses on the Earth inspire such awe, we will
consider a few “what if?” questions. They are
motivated by the basic requirements for total
eclipses: an alignment of three bodies in a
straight line such that the middle body completely obscures the luminous body as seen by
an observer on the surface of the third body.
Super eclipses and perfect eclipses
First, what if the Moon were significantly closer to the Earth? About 2.5 Gyrs ago the
Moon’s mean distance from the Earth was
about 87% its present value (Walker and
Zahnle 1986). At that epoch, total eclipses of
the Sun would have been more common and
visible over a wider region of the Earth’s surface (we will call these “super-eclipses”). During a super-eclipse, the pink chromosphere and
parts of the inner corona will be visible only
near the start and end, unlike the present situation, where we can observe the entire corona
throughout the eclipse. With more frequent
eclipses and greater visibility from the Earth,
super-eclipses would inspire no more awe than
sunrises and sunsets (which are, after all, just
total eclipses of the Sun by the Earth).
For eclipses like the one that occurred on 24
October 1995, during which the Moon’s
apparent size was only about 45 arc seconds
greater than the Sun’s, the full extent of the
Sun’s extended atmosphere was visible for just
under one minute. I will refer to an eclipse of
this type as a “perfect eclipse”, because it is of
sufficient duration for an observer to take in
the full event, and the Moon is just large
enough to fully block the bright photosphere,
but it is not so large as to block the chromosphere. A total eclipse of shorter duration
would result in a brighter sky, and there would
not be sufficient time for significant dark adaptation of the eye. In such a case, the faint outer
corona would be more difficult to see.
Angular coincidences
1b: Colorized image of the 24 October 1995 total solar eclipse obtained through a small telescope. The
original was a high-resolution black and white photo. Also shown as a yellow disk is the properly scaled
solar disk (32′ 09″). The maximum (35′ 11″) and minimum (28′ 47″) sizes reached by the Moon in the
present epoch are indicated by the red markers. The angular diameter of the Moon during the eclipse was
32′ 54″. Original photo courtesy of Dr Jagdev Singh of the Indian Institute of Astrophysics, Bangalore, India.
3.18
At the present epoch (today plus or minus a
few thousand years) the maximum difference
between the apparent sizes of the Moon and
the Sun (when the Moon is at perigee and the
Earth is at aphelion) is about 3.7 arc minutes.
According to the lunar orbital elements given
by Simon et al. (1994), the full range in the
Moon’s apparent angular size is 28′ 47″ to
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Eclipses
35′ 11″; this calculation includes both the mean
and the leading periodic terms of the lunar
osculating a and e elements. The smaller sizes
result in annular eclipses, and the larger ones
obscure the chromosphere during mid-totality.
Shown in figure 1b is a short exposure image
of the 24 October 1995 solar eclipse with the
properly scaled disk of the Sun superimposed.
2 Range of angular
size ratio of a
satellite (the
minimum
dimension) to that
of the Sun for all
the known natural
satellites in the
solar system. Most
of the data are from
the 1999
Astronomical
Almanac; the
satellites are
arranged from top
to bottom in the
same order as in
the almanac, except
for two new
additions to Uranus.
The data for the
Galilean satellites
are from Davies et
al. (1998), and the
data for Metis,
Adrastea, Amalthea,
and Thebe (all
belonging to
Jupiter) are from
Thomas et al.
(1998).
Earth
Mars
Jupiter
Moon shape
Secondly, what if the Moon were “less round”?
Clearly, this would result in fewer eclipses with
the present configuration of the Earth–Moon–
Sun system. Eclipses would still occur if the
apparent size of the minor axis of a squashed
Moon were larger than the Sun’s apparent size.
But such eclipses would be “less perfect”; the
chromosphere would be obscured along the
major axis during mid-totality.
The Moon and the Sun, as it happens, are
two of the roundest measured bodies in the
solar system. The oblateness of the lunar profile on the sky is about 0.06% (Runcorn and
Hofmann 1972). However, the lunar axis
pointing towards the Earth is larger than the
other two axes by about 5 km; had the Moon
not yet achieved a tidally locked orbit, the
longer axis would lead to a less round lunar
profile. For a rocky body, it is generally the
case that the smaller its size, the more irregular
its shape. This is true for the small satellites
and for the few asteroids that have been directly imaged. Even among the four Galilean
moons, the degree of roundness varies. It
increases with increasing distance from Jupiter;
Io is the most irregular, with its major axis
greater by 14 km than its minor axis, and Callisto is the roundest, with no measurable deviation from a perfect sphere (Davies et al.
1998). This trend probably results from the
increasing fraction of water with increasing
distance from Jupiter, since ice is more easily
deformed than rock. Some of the water may
even be in a liquid state for a couple of the
Galilean moons.
The oblateness of the Sun is 0.0009% (Lydon
and Sofia 1996). Rotation is the primary cause
of flattening in a star (Paternò et al. 1996).
However, the Sun’s oblateness was significant
probably only for the first few million years of
its life.
Eclipses on other planets
Thirdly, what if we were living on another
planet in the solar system? Shown in figure 2 is
the range in the ratio of apparent sizes of a
satellite to that of the Sun for each of the
known natural satellites in the solar system. If
a satellite is non-spherical, then its minimum
dimension is used for calculating its apparent
size. The apparent size of a satellite corresponds to what an observer at the equator of
the parent planet would observe; for the gas
June 1999 Vol 40
Saturn
Uranus
Neptune
Pluto
0.01
0.1
1
angular size ratio (satellite/Sun)
giants, we might imagine an observer floating
in a large research balloon!
The calculations include the eccentricities of
the orbits of the satellites and their parent
planets (the periodic terms of the lunar osculating elements a and e were not included for
consistency). The Galilean moons produce
large shadows on the cloud tops of Jupiter,
which are familiar to amateurs who have spent
any time observing it. Had the Galilean moons
come closer to matching the apparent disk of
the Sun, their shadows would probably not be
visible in amateur telescopes.
Evident in figure 2 is a trend of increasing
size ratio with increasing distance from the
Sun, as expected. Of the 63 satellites plotted,
only two span a ratio of unity: the Moon and
Prometheus. The latter is an irregular satellite
of Saturn. From Saturn the eclipsed Sun would
appear much smaller than it does from the
Earth, and the duration of eclipses produced
by Prometheus would be very brief, given its
short orbital period (0.61 days). Therefore,
compared with the other satellites in the solar
system, total eclipses produced by the Moon
are atypical.
What does the future hold?
Lunar laser ranging is arguably the most
important enduring legacy of NASA’s Apollo
programme. The positioning of several retro-
10
reflectors on the lunar surface by the astronauts has made it possible to measure the distance of the Moon to within a few centimetres.
Twenty-five years of laser ranging have yielded
a lunar recession rate of 3.82 ± 0.07 cm/year
(Dickey et al. 1994), which is due to the Mooninduced tides on the Earth.
Employing sedimentary rock records, specifically “tidalites”, going back 900 Myrs, Sonett
and Chan (1998 and references therein) find
that the lunar recession rate has been approximately constant during that time interval.
Assuming that this rate remains constant, it
will result in a significant decrease in the
apparent size of the Moon on a timescale of
107 to 108 years.
But the Moon’s distance from the Earth is not
the only changing parameter relevant to our
present discussion. Also important is the gradual expansion of the Sun due to ordinary stellar evolution. According to the calculations of
Sackmann et al. (1993), the Sun’s diameter is
increasing by 6 cm/year. Add to this the slow
decrease in the mean e of the lunar orbit at a
rate of 1.6 ×10–8 per century (Simon et al.).
Superimposed on these slow secular changes
are the short-term variations in the lunar
orbital elements noted above, plus the intermediate timescale variations in the mean e of the
Earth’s orbit (figure 3); the mean a of the
Earth’s orbit changes very little.
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Eclipses
35
60
angular size (arc minutes)
34
e × 1000
40
20
33
32
31
30
0
0
200
400
600
time (kiloyears)
800
1000
3 Evolution of the eccentricity of the Earth’s orbit for the next million
years. The data were provided by Thomas Quinn and are based on Laskar
et al. (1992).
The combined effect of these long-term
trends is shown in figure 4. The mean apparent
sizes of the Sun and Moon will be equivalent in
about 150 Myrs. However, we cannot say precisely when total eclipses will cease, because of
the short-term variations. If in the future shortterm variations of the lunar orbit are as today,
then total eclipses will remain visible up to
300 Myrs in the future. Beyond that, total
eclipses will be visible intermittently, when the
eccentricity of the Earth’s orbit is large. However, as we noted above, the Moon’s apparent
size should be at least 30 arc seconds larger
than that of the Sun to produce a “perfect
eclipse.” This criterion reduces the visibility
time by about 50 Myrs.
Eclipses and life on Earth
Is there any connection between life on Earth
and the occurrence of nearly perfect total solar
eclipses? Recent work on habitability leads us
to answer this question in the affirmative. This
topic is usually discussed with the framework
of the anthropic principle in one of its several
forms (see Gonzalez 1999 for application of
the weak anthropic principle to the Sun’s characteristics). However, here we reverse the usual
association – it is not that nearly perfect
eclipses are a requirement for habitability but,
rather, that they are an indication of the likelihood of habitability.
There are many characteristics of the Earth’s
environment that, were they slightly different
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0
100
200
300
time (Myrs)
400
500
4 Evolution of the angular sizes of the Sun and Moon for the next several
hundred million years. The solid curves show the evolution of the
apparent sizes of: 1) the Sun neglecting the eccentricity of the Earth’s
orbit, and 2) the Moon neglecting short-term variations in the eccentricity
and semi-major axis of its orbit. The dashed curve indicates the evolution
of the maximum apparent size of the Moon taking into account the shortterm variations. The short-dashed curve just below the solid solar curve
shows the evolution of the minimum apparent size of the Sun for a
minimum orbital eccentricity value; the lower one shows the minimum
apparent size for the maximum orbital eccentricity.
from their present state, might not permit the
existence of complex life. We narrow our consideration only to those three bodies involved
in producing total solar eclipses on the Earth.
First, strong arguments can be given for the
necessity of a star similar to the Sun (see Gonzalez 1999). This establishes the physical size
of the eclipsed body, and, with the addition of
the concept of the circumstellar habitable zone,
the distance between the eclipsed body and the
other two is also set.
Secondly, Laskar et al. (1993) have shown
that the Moon keeps the Earth’s obliquity from
varying over a large range, which would cause
large climate fluctuations. For this mechanism
to be effective, the Moon’s mass must be a significant fraction of the Earth’s mass.
A glancing blow to the early Earth is the preferred mechanism to form such a large Moon
(Lissauer 1997 and references therein). Following the impact, the ejecta coalesce near the terrestrial planet, so a large amount of orbital
expansion over several Gyrs is necessary before
perfect eclipses are visible from its surface.
This timescale is similar to that for the appearance of advanced life capable of understanding
eclipses.
Thirdly, a terrestrial planet will need to be
similar in size to the Earth in order to maintain
plate tectonics, and to retain an atmosphere.
Therefore, while they do not offer a guarantee,
the requirements for habitability (of advanced
life) on a terrestrial planet strongly constrain
the configuration of the three bodies involved
in producing total solar eclipses. In other
words, it seems that nearly perfect solar
eclipses are thrown in as a free prize for intelligent beings on a habitable world!
Concluding remarks
We are indeed living in a special time and place
as far as the observability of nearly perfect
total solar eclipses is concerned. We will continue to experience such eclipses without interruption for roughly another 250 Myrs. ●
Guillermo Gonzalez is a postdoctoral research
astronomer at the University of Washington. He
studies the chemical abundance patterns of stars.
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