Reference Document

EDUCATIONAL ACTIVITY - Reference Document.
Measuring local atmospheric changes during the
solar eclipse (2012 Total Solar Eclipse).
Authors:
○ Mr. Miguel Ángel Pío Jiménez. Astronomer of the Institute of Astrophysics of
Canary Islands.
○ Dr. Miquel Serra-Ricart. Astronomer of the Institute of Astrophysics of Canary
Islands.
○ Sr. Juan Carlos Casado. Astrophotographer of tierrayestrellas.com, Barcelona.
○ Dr. Lorraine Hanlon. Astronomer University College Dublin, Irland.
○ Dr. Luciano Nicastro. Astronomer Istituto Nazionale di Astrofisica, IASF Bologna.
○ Dr. Davide Ricci. Astronomer Istituto Nazionale di Astrofisica, IASF Bologna.
Collaborators:
○ Dr. Eliana Palazzi. Astronomer Istituto Nazionale di Astrofisica, IASF Bologna.
○ Ms. Emer O Boyle. University College Dublin, Ireland.
1. Activity goals
In this activity we will observe atmospheric changes, specifically changes in temperature
due to the decrease in solar radiation caused by the blocking of the Solar disk by the Moon during a
total solar eclipse. For this, a weather station located in Australia will be used.
The objectives are:
○
○
To understand the basic phenomenology of eclipses
To apply mathematics (algebra) and basic physics (thermodynamics) to calculate
temperature and radiation measurements from a weather station.
○ To develop an understanding and to apply basic statistical analysis techniques
(error calculation).
○ To work cooperatively, as part of a team, valuing individual contributions.
2. Instrumentation
A weather station that has sensors for measuring temperature and solar radiation intensity
will be used for this activity. The students will have access to live data or a database of archived
data at a later time. A web-tool will be available to allow students to do the activity.
1
3. Phenomenon
3.1 What is an Eclipse?
An eclipse is the temporarily obscuration of a celestial body caused by the interposition of
another body between this body and the source of illumination. In the following we will consider
eclipses occurring in the Sun-Earth-Moon system where the term eclipse applies to two very
different phenomena:
1. A solar eclipse occurs when the Moon passes between the Sun and Earth, and the
Moon fully or partially blocks the Sun. This can happen only at New Moon (Moon between the Sun
and Earth) and if the Sun and the Moon are perfectly aligned as seen from Earth. In a total eclipse,
the disk of the Sun is fully obscured by the Moon. In partial and annular eclipses only part of the
Sun is obscured.
2. A lunar eclipse occurs when the Moon passes directly into the Earth’s shadow. This can
occur only when the Sun, Earth, and Moon are aligned exactly, or very closely, with the Earth in the
middle. Hence, a lunar eclipse can only occur the night of a Full Moon.
3.2 Historical significance of eclipses
There are numerous historical references to this phenomenon in different times and
cultures; there are documented eclipses in 709 B.C. in China or in 332 B.C. in Babylon. The oldest
solar eclipse recorded happened in China on 22 October 2137 B.C., and apparently it costed the
lives of the real astronomers Hsi and Ho, which failed to predict it well.
The modern era of observing eclipses can be said to have begun in 1715, with the first
prediction method as a map, made by Edmond Halley, of the land where they drew a path where
the total eclipse would happen. The observing path just covered a few dozen kilometers from the
predictions, and in the review was drawn the real path with the predictions for the eclipse in Europe
in 1724.
It was very important to predict the occurrences of solar eclipses because they
represented the best conditions to study the higher layers of the solar atmosphere, especially that
called “chromosphere” which was clearly visible only during eclipses.
But it was mainly from the mid-nineteenth century, with the development of spectrographs,
when observing the Sun and of course, phenomena like eclipses, went on to have considerable
relevance. Although there was also another invention, nowadays very common and recognizable,
which saw its first light in the early nineteenth century and whose improvement conducted primarily
in the middle of that century, that was the photography. Thus, the possibility of taking photographs
and spectra in expeditions, led to the realization of these for observation of solar eclipses mainly
because, in those days there was still no theory about the sun and its composition or physical
description, and Astrophysics of the time was focused primarily on astrometry. Still, during the
total eclipse that occurred in 1868 and was observable from India, P. J. C. Janssen observed the
spectrum of the solar chromosphere, and noticed a very bright emission line very close to the
known wavelength of the sodium D doublet. As the line was very bright, he prophesied that this line
should be even visible though it was not an eclipse, and was N. Lockyer (founder of the renowned
2
journal Nature) in England, who measured in detail the position of the line and found that it had
nothing to do with the sodium D lines and was only observable in the spectrum of the Sun, so he
said that this line was coming from the "helium" (name of the King Sun in greek, Helios). It was not
until 1895 that the helium could be isolated on Earth.
After the helium, there were also other discoveries, for example, very bright lines that
initially called "coronium" because they was coming from the corona, but did not have, as helium
at the time, no explanation and only could be could deciphered much later, in 1939 and thereafter,
indicating that lines were due to energy transitions between different levels of iron or nickel,
transitions that needed a lot of energy to be able to carry out, what we came to say one of the
greatest enigmas of the Sun which is still unresolved, and was that the upper layers of the Sun are
at much higher temperatures (of the order of millions of degrees) than the temperature of the layer
visible with naked eye, called the photosphere which is about 5800 degrees kelvin.
3.3 Conditions for Eclipses occurring
We know that the orbits of the Earth and the Moon are not coplanar, so most of the time the
Moon is above or below the plane of the ecliptic (the plane defined by the Earth's orbit around the
Sun). For an eclipse to occur, the Moon has to be in, or very close to, the plane of the ecliptic and in
New Moon phase (solar eclipse) or Full Moon (lunar eclipse).
Figure 1: The ecliptic plane and the Moon's orbit. The "critical zone" indicates a strip in which an eclipse
may occur. (Diagram starryearth.com). The ‘Moon node line’ refers to the line joining the centre of the Earth
to the point where the Moon’s orbit intersects the ecliptic plane.
In solar eclipses at least the penumbra mole should reach Earth, producing a partial solar
eclipse visible somewhere on our planet. For this, the moon must be at a point that is at most to 18°
31' from the node measured along the ecliptic or length. For the lunar umbra can be projected in the
Earth the length should be a maximum of 11° 50'.
3
Figure 2: Diagram of umbra and penumbra zones in an eclipse.
Also needed latitude conditions or perpendicular distance to the ecliptic. For partial solar
eclipses should be a maximum of 1° 35’ and that the Moon's shadow reaches Earth the maximum
value is 1° 03’.
The extent of these limits vary with the distance from the Earth to the Moon, and to the Sun.
To the Moon can be reached by the Earth’s shadow, is necessary that the length for the
node does not exceed 12º 15’. If less than 9º 30’, there will be a total lunar eclipse. In latitude,
maximum is 1° 25’ and total penumbral eclipses 24’.
Therefore, in these circumstances proximity to node, a "window" opens for 37 ½ days that
will eclipse conditions. These configurations occur two or three times a year -every 173.31 daysin the calls eclipses stations. The eclipse year is the time between two alignments of Sun, Moon
and Earth and it is 346.62 days. During this time two eclipse seasons happen.
The Moon’s orbital node lines don’t have a fixed orientation, but rotate by about 20° per
year, going through one full turn in 18.6 years. This means that the dates on which the eclipses
happen change each year. For example the eclipses of 2001 were in the months of JanuaryFebruary, June-July and December, the eclipses of 2003 were in May and November and those of
2006 in March and September. The movement of the orbital nodes means that the eclipses occur
throughout the ecliptic.
The movement of nodes causes that the eclipses occur throughout the ecliptic, serving all
the zodiac constellations as stage.
3.4 Total eclipses per year
The minimum is four (including lunar eclipses by the penumbra), two solar eclipses and two
lunar eclipses. For example in 1999, 2003, 2005, etc. (Figure 3).
4
Figure 3: Solar and Moon eclipses between 1990 and 2012 (Diagram from I.M.C.C.E).
This amount can be lowered to two on usual calendars, which often not indicate penumbral
lunar eclipses. In this case, the two important eclipses solar eclipses would be total or annular, one
at each eclipse station.
5
It often happens that, when in the same station of eclipses, it begins with a major solar
eclipse, is followed by a weak lunar eclipse.
The maximum number of eclipses in a calendar year may reach seven. It may be that
both eclipse stations can each contain three eclipses. But also, as the eclipses year is shorter than
the calendar year, may take place a third season of eclipses, as occurred in 2000 and 2001, and
happen also in 2009, 2010 and 2011, although the stations were not complete and the maximum
number of eclipses that we found in these cases were six eclipses.
The maximum possible number of eclipses per year, seven, is a circumstance that happens
very rarely. This can only occur in these combinations:
●
●
●
●
5 solar eclipses and 2 lunar eclipses
5 lunar eclipses and 2 solar eclipses
4 solar eclipses and 3 lunar eclipses
4 lunar eclipses and 3 solar eclipses
In any case will be partial solar eclipses, unimportant. The next year with 7 eclipses was
1982 even more remarkable by the fact that the three lunar eclipses were total eclipses. This
situation will not be repeated until 2485.
3.5 Cycles of eclipses
Stations eclipses are repeated year after year, but the time of each eclipse in successive
seasons do not follow a regular pattern. The lunar month, from New Moon to New Moon (29.53
days) is called synodic. A year of eclipses (346.62 days) does not contain an integral number
of synodic months (between eleven and twelve). If you are looking for a longer period, which
is approximately exact multiple of both cycles, ie what is known in mathematics least common
multiple, we will have a new cycle that can provide predictions of eclipses.
This is called the Saros cycle, apparently known to astronomers in ancient Chaldeans. The
Saros comprises exactly 223 synodic months. This period is 18 years and 11 days (18 years and 10
days if it includes February 29). The Saros practically coincides with 19 years of eclipses. Ie:
223 synodic months (29,5306 days each/one) = 6.585,32 days
19 years of eclipses (346,6200 days each/one) = 6.585,78 days
This resonance occurs between this two cycles produce a repeat of eclipses in short times,
astronomical speaking.
The Saros has a fraction of a day included in the period (6585.32 days). When the cycle is
repeated, the Earth has rotated to a position corresponding to this portion of the day. The eclipse
will be seen in an area of ​the land west of the preceding, distant third the perimeter of the globe.
After three Saros cycles, a solar eclipse occurs in an area close in longitude to where it was 54
years earlier. However, the eclipse will have experienced a slight drift in latitude toward one pole.
Each eclipse of the same "family" or Saros series follows the same direction of drift toward
the pole involved (north or south). To illustrate, we can see in Figure 9, which shows the total solar
6
eclipses of 1925, 1943, 1961.1997, 2015 and 2033, all members of the same series of Saros 120.
The series began with a partial eclipse in the South Pole in the year 915 of our era, to go in each
event moving gradually towards the north, as seen in the same figure, where the oldest occupied
lower latitudes. This shift in latitude occurs because the New Moon moves slightly its position from
the node in each successive Saros. The half-day difference between 19-year of eclipses and the
Saros (6585.78 to 6585.32 = 0.46 days) causes this change. In the example in Figure 4, the Saros
series end with a partial eclipse in the north pole in the year 2195.
Figure 4: Bands of all solar eclipses in the same Saros series 120. (F. Espenak,
NASA RP 1178, adapted by J.C. Casado)
The Saros cycle operates similarly for the lunar eclipses. In each lunar eclipse the moon
position moves from the previous one to the north or south respect to the center of Earth's shadow.
A Saros series is developed for over 1200 years, producing about 80 solar eclipses and the
same of Moon eclipses for all types.
Inside one Saros we can observe short series of eclipses of the Sun and Moon. Comprise
eight or nine consecutive eclipses, divided into eight eclipses stations. The type of these eclipses
increases in relevance until the fourth or fifth in the series, and then decreased.
7
Also it can be seen long series of eclipses studying not the evolution of eclipses in
one Saros, but the evolution of homologous eclipses to one to another Saros, ie those that
take place in the same lunation (numbered from 1 to n in successive Saros). It is observed that
in a period of 72 Saros (about 1300 years), a solar eclipse evolves as follows: a dozen partial
eclipses increasingly important, after 48 total or annular eclipses, followed by 12 partial eclipses of
decreasing importance.
The numbering of the long or Saros series was established by the Dutch astronomer G.
Van den Bergh in 1955 from 8,000 eclipses Oppolzer's canon.
In the Figure 3, as mentioned above, represents eclipses for 23 years, from 1990 to 2012.
It can be seen, for example, a Saros running from June 1993 to June 2011. This Saros contains 81
eclipses, 40 of Sun and 41 of Moon. From the 40 solar eclipses, 15 are partial and 25 centrals (12
rings, 12 total and one mixed).
This figure shows several properties watched on the eclipses:
●
●
●
●
●
●
Eclipses stations (correlation between eclipses and steps by nodes)
The fact that there is at least a lunar eclipse and a solar eclipse in each eclipses station.
The short series of eclipses of Moon and Sun (red to the Moon, and blue to the Sun).
The minimum number of eclipse year.
When there are three eclipses, the central eclipse is maximum (very important) and the
others, at the ends, are weak.
The four eclipse of 2011 are homologs of the eclipses of 1993 and the four eclipses of 2012
are counterparts of 1994.
3.6 Canon of Eclipses
Lists of lunar and Sun eclipses are published on works called canon of eclipses.
The most famous is from Theodor Ritter von Oppolzer. Its first edition, the "Canon der
Finsternisse" ("Canon of eclipses" in German) was published in 1887 in Volume 52 of the Memoirs
of Mathematics and Natural Sciences of the Imperial Academy of Vienna. This monumental work,
corrected, was reissued by Dover American publisher, but is currently flat. In the canon are 8000
solar eclipses between -1207 and 2161, and 5200 lunar eclipses between -1206 and 2132. The
canon contains geometric and trigonometric quantities needed, called elements of the eclipse, to
calculate all the circumstances of each eclipse at every place on Earth. Also include maps of solar
eclipses (Figure 5). This canon, however, does not cover penumbral eclipses of moon -unimportantand suffers from certain errors in eclipses of antiquity, because at the time it was drafted was not
well known dynamics of the Earth-Moon system.
8
Figure 5: A map of the Canon of Oppolzer, showing the center line of solar eclipses
from May 19, 1985 and February 7, 2008. Total eclipses appear as solid lines and
the ring, as dashed lines. Note that some lines may show discrepancies centrality
to modern maps. This is because the path of these lines is performed by calculating
three points that are joined by a circular arc. For an exact calculation Oppolzer
himself recommended using the Canon numerical tables.
More recently Jean Meeus and Hermann Mucke (1979 and 1983, Astronomisches Büro,
Vienna), have posted a canon of solar eclipses using computers, containing all eclipses between 2003 and +2526 and another canon of lunar eclipses between -2002 and +2526.
The latest canons appeared to be at NASA astrophysicist Fred Espenak, and covers all
solar and lunar eclipses from 1901 to 2100, with special relevance, with maps and detailed data
to eclipses between 1986 and 2035. These canons are available on its website (see bibliography
and information), and several catalogs of eclipses, solar eclipses highlighting of -1999 to +4000 and
lunar eclipses from -1999 to +3000.
9
3.7 Types of Eclipse
1) Partial: Only the Moon’s penumbral shadow reaches the Earth's surface (see Figure 10,
position C). These eclipses always occur at high latitudes (north or south) and correspond to the
first and last events of a Saros cycle (Figure 6).
Figure 6: Schema of a partial solar eclipse.
2) No central: The umbra reaches the Earth, resulting in a solar eclipse that can be as we shall see - annular, total or mixed, but the threshold cone axis does not touch the earth,
disappearing in space. Such eclipses always affects polar regions. Obviously a partial eclipse is
also not central, but the expression is reserved for total and annular eclipses.
3) Central: The umbra cone axis from the Moon intersects the Earth. In rare cases it may
happen that the eclipse is central, but has no limit north or south, because the umbra projected on
polar areas, near the Earth's limb.
The conditions of central eclipses are complicated by the fact that the ecliptic, as we have
seen, is an ellipse. As a result, the sun's apparent diameter varies from 31’ 28” at aphelion at 32’
32” at perihelion. This variation of 3% is unobservable to the naked eye, but has implications for
eclipses. More influential still is the fact that the moon's orbit around Earth is also elliptical. The
variation from the apogee to the perigee reaches 12%, causing an oscillation in the apparent lunar
diameter from 29’ 24” to 33’ 32”. As follows from these considerations, changes in the apparent
diameters of the Sun and Moon are the cause of the type of central eclipses: total, annular, or
mixed.
When the moon is at apogee and the Earth is at perihelion, the umbra falls to 39,400 km
from the center of the Earth. In this case, the apparent diameter moon is 10% or 3’ lower than solar.
Conversely, if the Moon is at perigee and the Earth at aphelion, the umbra extends 23,500 km
10
beyond the geocenter, exceeding the lunar apparent diameter 7% or 2’ to the Sun. These distances
represent the extreme limits of both situations (Figure 7).
Figure 7: Extreme positions of the lunar umbra relative to the Earth.
In the first case we just saw above, the extension of the umbra generates a negative
umbra or anti-umbra (Figure 8). From there, the image of the moon appears smaller than the Sun,
showing silhouetted on the bright solar photosphere. This type of eclipse -annular- takes the name
of ring of sunlight that surrounds the Moon in the middle phase of the phenomenon.
Figure 8: Schema of an annular central eclipse.
When the situation is inverse to that described above, ie, the Moon is at perigee and the
Earth at aphelion, the umbra intersects with Earth, causing a total solar eclipse. The shadow’s
cones projected by the moon (umbra and penumbra) produce, due to translational movement
11
of the Moon and rotation movement of our planet, a sweep over the surface of the Earth, which
determines the regions where the phenomenon was seen (Figure 9). If we stick to the umbra,
will be a long and narrow corridor called full band, from which the phenomenon shall be seen as
complete. The typical length of this path of darkness is about 14,000 km, with a maximum width of
273 km, which represents less than 0.5% of the Earth's surface. As in the annular eclipses, on both
sides of the path of totality, is a wide expanse penumbral, thousands of kilometers wide, from which
the event is perceived as partial, lighter is the farther the observer is from the path.
Figure 9: Schema of a total solar eclipse center.
A third type of central eclipse can produce when, at the same phenomenon, a transition
between annular and total. This eclipse is called mixed, hybrid, or annular-total. It occurs when
the tip of the umbra matches to any place on Earth. In this case, due to the curvature of the globe,
the umbra reaches a part of the surface of our planet, and in another interval of its trajectory,
the umbra "falls short", resulting in an anti-umbra and the resulting annular eclipse. The band of
annularity-totality usually (but not always) begin and end as annular eclipse, changing to total during
the central travel. These eclipses are only 4% of the total.
12
Figure 10: Diagram showing eclipse types depending on the relative position of the Moon with respect to
Earth. When Earth is in region (A), a total solar eclipse is seen; in (B) an annular eclipse is seen, while in
(c) a partial eclipse is observed.
To produce a solar eclipse the moon has to be in, or close to one of its nodes, and be the
same size as the Sun.
Every year without fail two solar eclipses happen near the nodes of the lunar orbit, but can
happen four or even five eclipses. Five solar eclipses happen in a year when the first of which takes
place shortly after the first of January. Then the second will take place at the next new moon, the
third and the fourth will happen before the expiry of six months, and the fifth will take place after 345
days after the first, since that is the number of days that contain 12 synodic months.
On average happens a total solar eclipse on the same ground point every 200-300 years.
For that to happen a solar eclipse, the moon must be in inferior conjunction (New Moon) and also
that the Sun must be between 18° 31’ and 15º 21' of one of the nodes of the lunar orbit.
It is worth pointing out that solar eclipses are seen on Earth only because of the happy
coincidence that, at some times during the year, the angular sizes of the Moon and Sun are
identical. Hundreds of millions of years in the past, the Moon was too close to the Earth to precisely
cover the Sun as we can now observe. Tidal forces cause the orbit of the Moon around Earth to
increase by about 3.8 cm each year and in just under 1.4 billion years, the distance from Earth to
the Moon will have increased by 23,500 km. After that, the Moon will no longer completely cover the
Sun's disk as seen from Earth. Therefore, the last total solar eclipse on Earth will occur in about 1.4
billion years from now!
13
3.8 How are they seen.
Partial eclipse: During a partial eclipse there are two points of contact. The first point is
the moment of contact between the discs of the Sun and the Moon, which marks the beginning of
the phenomenon. As the Moon continues along its orbit, an increasing fraction of the solar disk is
covered, until the maximum, after which the shadow departs from Earth’s surface and the full disk is
visible again. The ‘magnitude’ of an eclipse is the fraction of solar diameter obscured by the Moon
(Figure 12). The magnitude can be expressed both in percentage and decimal fraction (60% or
0.60). The term ‘dimming’ refers to the fraction of the solar surface covered by the Moon (Figure 4).
Figure 11: Phases of a partial eclipse of the sun (or a total or annular eclipse seen as partial).
VERY IMPORTANT EYE SAFETY: In a partial eclipse, the Sun is still very bright, so
normal precautions apply to observing the Sun in that case.
14
Figure 12: Magnitude and dimming of a solar eclipse. The magnitude expresses the fraction of the Sun’s
diameter hidden while the dimming is the fraction of the Sun’s surface that is overshadowed.
Annular eclipse: Although the magnitude of the eclipse is high and perfectly perceptible a
decrease in ambient lighting, the residual lumen of the solar disk is sufficient to continue to impede
the vision of the solar corona, and necessitate ALL THE SAFE MEDIUM OF OBSERVATION AS IF
IT TRIED A PARTIAL ECLIPSE
15
Figure 13: Sequence of the total solar eclipse of August 1, 2008 on the sea Ob in
Novosibirsk, Russia. (Photo J.C. Casado / starryearth.com).
An observer of an annular eclipse will see four moments of contact between the solar and
lunar discs. The first contact is the moment when both disks appear to touch. Slowly, in a process
that takes about an hour and 30 minutes, the lunar disk appears to fully cover the solar surface; this
is the second contact. Then the central or annularity phase, culminating in third contact of the
event begins. This phase, can reach about 12 minutes and 30 seconds. The fourth contact refers
to the end of the eclipse (Figure 14). Outside the area annularity the observer on the penumbra, see
the phenomenon as partial.
16
Figure 14: Phases of an annular eclipse.
Total Eclipse: A total eclipse also has four contacts. The first contact and the preceding
stage are similar to those in an annular eclipse. But now, before second contact, the observer will
see a dramatic change in light. Atmospheric parameters such as temperature and relative humidity
are also changed (such as notes, for example, in studies conducted by Marcos Penaloza, Essex
University and Dr Edward Hanna, Institute of Marine Studies Plymouth).
Figure 15: Diamond ring in the total solar eclipse of March 29, 2006,
photographed near Al Jaghbub in the Libyan desert. (Photo J.C.
Casado / starryearth.com)
If the observer is located in a high place with a good view of the distant landscape, the
moon’s shadow can be seen approaching the western horizon at high speed. At the instant of
the second contact it produces a diamond ring (Figure 15), a brightness which happens at the
17
point when the sun is almost completely hidden. But before the last portion of the sun disappears,
because of the rugged terrain of the edge of the lunar disk, luminous fragments of light, called
Baily's beads (Figure 16) can be seen. Then suddenly the outer atmosphere of the sun (the solar
corona) appears (Figure 17). In the first few seconds some of the sun’s chromosphere (gases)
can be seen as a thin arc of intense red color with bright bumps. These quickly disappear after the
advance of the lunar disk (Figure 18).
Figure 16: Composition of images showing the second and third contacts,
Baily’s beads, bumps and inner corona in the solar eclipse of July 22, 2009,
near the city of Chongqing, China. (Photo J.C. Casado / starryearth.com).
The solar corona (Sun’s outer atmosphere), an intense pearly white colour, shows
structures that follow the arrangement of the magnetic field of the Sun. It is not normally visible
because it is about 100,000 times less intense than sunlight. In the centre is the lunar disk, like
a black hole in the sky. The shape and brightness of the corona depend on where the Sun is in
its 11 year cycle. At solar maximum the corona has radial symmetry (Figure 17 right), while at its
minimum the coronal feathers are asymmetrical (Figure 17 left).
18
Figure 17: Left. Picture of the total solar eclipse of August 1, 2008 from Novosibirsk, Russia. Combination
of 67 digital images showing long stretches of the corona, bumps, Earthshine and stars. Right. Picture of
the total solar eclipse of November 23, 2003 taken on board an aircraft flying over Antarctica. Photos and
processing: JC Casado / starryearth.com.
The planets are visible with naked-eye and the brightest stars appear in the sky, creating
an artificial "night", although the lighting is rather like a twilight advanced (Figure 19). About the full
circle of the horizon is similar to the colors of a sunset, while there in the distance, the eclipse is not
total.
Figure 18: Chromosphere and prominences visible in the total solar
eclipse of March 29, 2006, photographed near Al Jaghbub in the Libyan
desert. Combination of photographs taken at the beginning and end of
totality. Picture: J.C. Casado/ starryearth.com.
The totality ends soon, such is the psychological effect it produces, surely to be between
two long partial phases. In the best case, i.e. at the equator, duration reaches a maximum of 7 ½
minutes. For all latitudes can last six minutes in the best and only 3 minutes in the polar regions.
Statistically it is found that the average length of the whole is about 3 minutes. With the third contact
(second diamond ring), events happen similarly, but in reverse order of the previous phase.
19
Figure 19: Panoramic that get the approximation of the lunar umbra over 4500
km/h just before the second contact in the eclipse of November 23, 2003 flying
over Antarctica. (Photo J.C. Casado / starryearth.com).
Total eclipses (and almost the same could be said of the annular) are not uncommon
phenomena as it might seem, since, on average, occur once every 18 months. However, to a point
on the earth's surface, such as a city, the phenomenon occurs on average once every 375 years. It
is therefore necessary to make long journeys to be in the band of totality.
3.9 Maps eclipses
To represent and visualize areas of the Earth through which a solar eclipse will be visible,
terrestrial maps are used with curves superimposed by demarcating the areas from which the
phenomenon will be visible.
The interpretation of such maps is easier than it seems, also providing a fairly
comprehensive information on general and local circumstances of the event.
The main problem is the inability of intuitively represent a spherical surface (the Earth) on
a map, because it's a plane. Depending on the application that is intended to be used, a certain
type of projection map is used. Most maps of solar eclipses, as those in the Ephemeris published
annually by the National Astronomical Observatory or the Royal Institute and Observatory of the
Navy in San Fernando, uses stereographic projection, which allows a good representation of the
areas overshadowed, albeit marginal deformations to areas of the map.
As an example we chose the map (Figure 20) of the total solar eclipse of November 13,
2012.
20
Figure 20: Global map of the total solar eclipse of November 13, 2012.
The areas in which the eclipse will be visible - to a greater or lesser extent - are those that
remain within the central area colored. From the outside, even if you see the sun, the eclipse will
21
not take place, for being outside the lunar shadow zone. The long narrow central band is the band
of totality. From inside the eclipse will be total. The red colored asterisk, located approximately in
the center of totality band represents the point of maximum duration of the eclipse.
Outside the totality band, the partial eclipse will be seen, with decreasing magnitude as the
observer's position is furthest removed perpendicularly to this band.
The times of the beginning and end of the eclipse are indicated by dotted lines at intervals
of one hour, with the time in Universal Time. Also shown in red, the first contact and last contact,
which mark the places on Earth where, respectively, are held the first and last contact with the lunar
shadow.
3.10 What to study
Solar eclipses, particularly total, offer a unique opportunity to perform a variety of
observations and experiments, despite the brevity of the middle phase. Some of these are focused
on the study of the Sun itself and the surrounding space and others, in its broadest sense, have to
do with the relationship with our planet.
Furthermore, satellites as the SOHO, that monitor the sun in different wavelengths, offer a
reference for comparison between observations of ground stations and space.
These are, by and large, the studies can be conducted on solar eclipses:
The Sun as astronomical body:
Studies in the solar corona (the most abundant), which as we have seen in the introduction,
has an average temperature of 1 million °C, while still not well known mechanism of
heating. These investigations may include: density and structures of the corona, shock
waves, interrelationship coronary-protrusions, "cold" coronal matter (800,000 °C!), Magnetic
fields, neutral matter in the inner corona, polarization.
● High-precision measurements of the solar diameter. The start and end contacts of the total
phase offer some references to make this measurement. These studies may answer the
question whether the size of the sun varies.
● Study of space and matter around the Sun (possible dust ring).
● Checks of the theory of general relativity.
●
Interaction with the Earth:
● Gravitational perturbations in the Earth-Moon system, their study allows improving the
accuracy of astronomical events.
● Weather alterations: pressure, temperature, relative humidity, air conductivity. This is an
area where the amateur can work with the scientist.
● Environmental alterations: optical effects (changes in color and brightness of the sky),
appearance of shadow bands, studies of solar radiation and its relation to atmospheric
layers. Chemical effects in Earth's atmosphere as part of the solar radiation is absorbed by
particles (atoms and molecules), which changes its characteristics as day or night.
● Reactions and changes in the behavior of wild fauna and flora.
● Historical aspects: eclipses have been used as elements of dating historical events.
● Ethnographic aspects: legends, myths and beliefs in popular and local culture.
22
3.11 Influence on the local climate
Solar eclipses have always been, a very attractive phenomena to meteorologists, because
is the best time to study the response of the atmosphere together to a sudden and abrupt of the
incident solar radiation. So, there are a number of studies that have attempted to investigate the
effects in weather of these phenomena, taking measurements of air or the ground temperature
during the course of the eclipse, and measures the change in humidity, speed and direction wind,
and other important parameters for the study of the atmosphere.
For example, temperature changes during a solar eclipse are of great interest because it is
a variable that observers are very sensitive. In general, the fall in temperature, for example, began
to be noticeable when the Sun is partially covered, although some observers are able to identify an
immediate response of the temperature, and others indicate a response after the fourth contact (the
end of eclipse). Furthermore, the pattern and extent of the temperature drop is different for each
location and can vary from less than one to several degrees, depending on many factors such as
the percentage of sun covered, the latitude, the season in which we are and the time of day, the
synoptic conditions, the level where we are and take the values​​, climate, and other local factors
such as topography, vegetation present, etc ... Thus, the time that elapses between when the
temperature reaches the minimum and the maximum of the solar eclipse occurs is a direct result
of the thermal inertia of the atmosphere, and its interaction with the soil, in a manner similar to that
which occurs when the maximum temperatures during a clear day standard, because the maximum
temperature always occurs a few hours after the sun has passed its Zenith (or higher position on
the sky).
Many authors also speak of changes in atmospheric pressure during the course of the
eclipse (in the literature, the article by Jay Andersen, for example). So some describe creating a
pressure disturbance in waves, moving out of the path followed by the shadow of the Moon on the
Earth's surface (refer to the different positions of the Earth's surface where it can eclipse be visible
in full, see figure 21). Thus, these waves would move out of the way as a boat create waves on the
bow when it is sailing. However, although most likely be an effect produced by the cooling of the
atmosphere that we discussed earlier, is a very difficult to watch, but we will try to see it so we will
take pressure measures.
3.12 The Total Solar Eclipse of 2012
After more than a year without total solar eclipses (the last took place on July 11, 2010)
the Moon's shadow will revisit the Earth's surface on 13 November 2012. The tour of the shadow
begins in Australia and will then move to the Pacific Ocean. The maximum of the eclipse occurs
in the middle of the Pacific Ocean with a duration of 4 minutes and 2 seconds with the Sun at 68
degrees above the horizon at 22:11 UT.
23
Figure 21: Full band (blue lines) of the eclipse of November 13, 2012 as reported by NASA. The green
dot indicates where the maximum duration of the eclipse can be seen. The observation point of the
expedition will be around the city of Cairns (Queensland state) northeast of Australia.
GLORIA will broadcast the event from three observation points in northwestern Australia
(State of Queensland), around the city of Cairns, where the eclipse will have an average duration of
about 2 minutes (see Figure 22):
○
○
○
G3. In the Coast, in the surroundings of Oak Beach.
G2. Inside. Highway Rt-81.
G1. Inside. Town of Mareeba, the coordination and drafting group.
24
Figure 22: Observation points of the expedition. The red line indicates the centre of the whole
band. The observation points are located on the coast and inland (red dots G1, G2 and G3).
The expedition and retransmission will be coordinated and directed by Dr. Miquel SerraRicart (Astronomer, Institute of Astrophysics of the Canary Islands and Manager of the Teide
Observatory).
4. Performing the activity
4.1 Calculation of the thermal response of the atmosphere from atmospheric
measurements in a total solar eclipse
An interesting effect that occurs during the course of an eclipse, more remarkable in a total
eclipse, is the decrease of the environmental temperature due to the decrease of the solar radiation
or ambient brightness (see Ref. 8 in the reference document). The interesting thing is that the
phenomenon does not occur instantaneously when the sun is completely covered (maximum eclipse
or second contact), but is an effect that occurs after a time ranging from 2 to 20 minutes.
This time delay depends on many factors, such as the time of day when the eclipse occurs,
the presence of nearby bodies of water such as a lake or ocean, proximity to wooded areas, but it
is easily measurable. The time at which the minimum intensity of light occurs, coincident with the
maximum Eclipse (second contact) must be noted. Then, the time at which the temperature is a
minimum is also recorded. The thermal response of the atmosphere or the atmospheric thermal
inertia is the time interval between these two minima.
25
The following exercises (Method 1 and Method 2) can be used to estimate the thermal response of
the atmosphere.
4.2 Brief introduction to the theory of errors and sampling
To Measure is compared to a standard. For example, if we measure the width of the lab
putting one foot in front of another, we can say that the width of the lab is 18 feet, one foot being our
patron. However, a measure can never be exact, ie, we always make a mistake, so our measure
is not complete without the error estimation. Sometimes this error is because the measuring
instruments, others to our own perception, etc.. Every measure has an inherent error.
●
●
Depending on the nature of the error we can define two types of error:
Systematic errors: Are due to problems in the operation of the measuring apparatus or the
fact that when we entering the measuring device in the system, it is altered and modified,
therefore, the magnitude that we wish to measure changes its value. Usually act in the
same direction.
Random errors: They are due to causes uncontrollable that randomly alter the measures.
Upon the measures are distributed randomly around the true value, so a statistical
treatment let us to estimate its value.
Due to the existence of errors is impossible to know the real value of the measurand. If we
are careful we can control the systematic errors, and in terms of random errors it can be reduced
using statistical techniques. We will take as the estimated value of the measure, the average value
of the different measurements.
Suppose that we want to measure the length L of a bar and you get two sets of measures:
Group a : 146 cm, 146 cm, 146 cm
Group b : 140 cm, 152 cm, 146 cm
In both cases the estimated value is the same (146 cm). However, the measurement
accuracy is not the same. How can we distinguish the accuracy of two measures? Using the
concept of error or uncertainty.
When expressing a measure, must always indicate the observed value with its error and the
units too. We can say that the true value of the measure is a high probability in an interval whose
boundaries are the estimate value of the measure plus / minus the estimated error.
Measure = Observed value ± Error (Unit)
In the last example, once estimated the error, it might be written as: L = 146 ± 4 cm.
4.2.1. Random errors
As mentioned, these errors are due to causes that can not be controlled and randomly
altering the measures, either upward or downward. They are difficult to evaluate, this is achieved
from the characteristics of the measurement system and making repetitive measurements with
subsequent statistical treatment. Thus, from repetitive measurements can calculate the standard
26
deviation
.
4.2.1.1 Standard deviation
To get good results from any action, minimizing the effect of accidental errors, you should
repeat the measurement several times. The average is that we will take as a result of the measure,
as it probably is closer to the real value. The same applies if you have a set of data taken with an
interval of measurement or sampling determined, and we want to change that interval, so we group
the data into equal groups and we take as the measurement value, the mean value of each group.
The mean value in each group must be calculated using the expression:
where Xi is each of the points belonging to the study group and N is the number of total
data. For example, assuming a set of values ​representing the temperature, the average value would
be given by the expression:
being X0 , X1 , X2 , X3 , and X4 , the values of temperature for a group of 5 data.
And the standard deviation is defined according to the following expression:
The standard deviation is an estimate of the random errors of measurement and therefore
we can express:
X=Xm ± ? (Unit)
as we saw in the previous section.
4.2.2 Graphing and sampling
Finally, to represent the values ​of a variable in a graph, these values ​are plotted as points
on the graph in terms of its value according to the axes of the graph, and the value of its error is
represented as a vertical or horizontal line, depending on whether the error is represented in the xaxis or y-axis, respectively, where the length of the line is proportional to the error value, also in the
scale of the axes. Thus the larger the error the greater the size of the line that each dot have.
In the figure below are shown the data of solar radiation and temperature taken during the
annular eclipse of 2005 from the village of Los Pedrones in Valencia
27
Figure 23: Representation of the drop in solar radiation or luminosity (blue) and temperature (yellow) as a
function of time produced during the annular eclipse that occurred in October 2005.
Another very important factor to take into account when representing a data sampling is
to decide to be held. In the case of Figure 23, data collection, and ultimately the sampling was
a "dynamic sampling" so that was changing as advancing the phenomenon (baseline data every 5
minutes, every minute later, and the critical zone every 20 seconds, after following in reverse). This
type of sampling allows us to make a much finer adjustment of the most interesting of our measure,
without losing the overall trend of the variable when we are out of the critical zone of measurement.
For this reason, in Figure 23 we see that the central zone is much stronger (more dot density) than
the rest of the representation.
28
Figure 24: Representation of the drop in solar radiation (or luminosity) during the
annular eclipse occurred on October 3, 2005. Blue dots indicate the original points of the
measure of luminosity in the critical zone of the eclipse (second contact). The orange
dots are generated after an adjustment averaging every 5 minutes, with its error bars.
Now, based on the same data set, we will make a change in the sampling of the same
area equating to sampling the start of the shot, then considering that the value to be given to each
interval is the mean value of all the points and the error the standard deviation (see figure 24). In
it we see that the tendency of these points is the same as with the blue dots but, however, in this
orange curve called "Luminosity (mean)", we see error bars appears both in the x-axis as in the yaxis and which are due to the uncertainty that exists for that value, as obtained by performing a
subsequent statistical points.
In sum, we need to always indicate during a series of measures, not only the values ​
reached by the variable in question but also, the error.
4.3. Method 1: Direct shot. Pressure values​​, radiation intensity and
temperature
The live broadcast of the solar eclipse on November 13, 2012 as seen from Australia can
be followed on the GLORIA project website (www.gloria-project.eu). Simultaneously in a parallel
web channel, the data measured by a weather station located at point G1 (Mareeba, Australia) of
the expedition, can be seen. Students can then record temperature values​​, solar radiation intensity
and air pressure, as if they were in front of the weather station taking the values themselves.
The measurement interval should be periodic and can be established by the student or
the teacher. It is recommended that the interval between two measurements does not exceed 2
29
minutes and that it reaches 5 seconds when approaching the maximum point of the eclipse (second
contact).
Figure 23 shows an example of solar radiation and temperature data taken during the
annular eclipse of 2005, where the measurement interval was variable, with data being taken every
5 minutes initially, then every minute and finally, around the maximum point of the eclipse, every
20 seconds. This measurement sequence was repeated in reverse during the second half of the
eclipse. This type of measurement is called "dynamic sampling".
After taking measurements, there will be a graphical representation of recorded values for
each of the variables over time, using any software that allows representation of numeric data (e.g.
Excel, OpenOffice, LibreOffice, Origin ...) so that the trend in each of the observables can be seen.
Use these graphs to determine the exact time when the minimum occurs for both temperature and
solar radiation intensity. By determining the time difference between these values, the value of
the "atmospheric thermal inertia" can be obtained.
For an exact calculation of the minimum, curve fitting to the data can be performed. The
teacher will decide whether to instruct students in the curve fitting because it is a topic not included
in this unit.
Following the eclipse, a video of the complete recording of data from the weather station will be
available.
4.4 Method 2: Database
During the broadcast of the event, the weather station will periodically save (about every
5 seconds) the values ​for each of the variables discussed earlier, so that they can be accessed at
any time from the GLORIA website (www.gloria-project.eu). Web tools will be provided to enable
detailed examination of the data in any time interval requested. For example, time intervals can
be selected from different moments during the eclipse. Values of temperature and solar radiation
intensity will be plotted on a graph, along with the errors on these values. The interval can be
changed (‘zoomed in’), so that more detailed data can be plotted in a particular time interval, to get
more accurate determinations of the minimum values for the radiation intensity and temperature.
After selecting the data and making the graphical representation, the "atmospheric thermal
inertia" can be calculated as in the previous method.
30
REFERENCES
1. SERRA-RICART, M. et al. Eclipses. Tras la sombra de la Luna. Shelios, 2000. Ameno and
colorful book without losing rigor, especially dedicated expeditions to observe total solar
eclipses.
2. GIL CHICA, F.J. Teoría de eclipses, ocultaciones y tránsitos. Alicante University, Murcia,
1996. Treatise on the theory of eclipses and blockout bodies in general. This is a book that
develops in detail the mathematical aspect of these phenomena, which requires advanced
knowledge of mathematics.
The wider literature on the subject is in English :
3. ESPENAK, F. Fifty Year Canon of Solar Eclipses : 1986-2035. NASA Reference
Publication 1178. Sky Publishing Corporation, Cambridge (USA), 1987. Canon or catalog
reference made by one of the best specialists, Fred Espenak. Contains data and maps
for all solar eclipses from 1986 to 2035 with details and general information for the period
1901-2100.
4. ESPENAK, F. Fifty Year Canon of Lunar Eclipses : 1986-2035. NASA Reference
Publication 1216. Sky Publishing Corporation, Cambridge (USA), 1987. Canon containing
all data and maps of lunar eclipses between 1986-2035 in detail and general information for
the period 1901-2100.
5. MEEUS, J. Elements of solar eclipses 1951-2200. Willmann-Bell, Inc, Richmond (USA).
It contains elements of the 570 besselianos eclipses between 1951 and 2200, that let
estimate the general and local circumstances thereof. The formulas, with high precision,
have been developed by the Bureau des Longitudes in Paris. There is also a version on
data with recorded items, but not with a routine use, so it must be programmed.
6. GUILLERMIER, P. y KOUTCHMY, S. Total Eclipses. Springer, 1999. Science,
observations, myths and legends about eclipses, especially total solar A great book for
anyone who wants to learn more about eclipses and observation.
7. REYNOLDS, M.D. y SWEETSIR, R.A. Observe eclipses. Observe Astronomical League
Publications, Washington (USA), 1995. Excellent work of outreach and manual observation,
covering all aspects that can span the amateur. It can be purchased through the publisher
of U.S. magazine Sky and Telescope, Sky Publishing Corporation
8. JAY ANDERSON. Environment Canada. Weather, Volume 54, Issue 7, pages 207–215,
July 1999. Magazine specializing in the publication of scientific papers focused on the study
of the atmosphere and climate.
Finally note the NASA Technical Publication, published some eighteen months before each annular
or total eclipse. Collect maps, charts, forecasts and information on general and local circumstances
of the eclipse in question. For more information contact Fred Espenak, NASA / GSFC, Code 693,
Greenbelt, MD 20771 (USA) or via e-mail: [email protected]
31