ECLIPSES OF SUN

Data from Wikipedia and NASA (C)

 

A Sun eclipse happens when the Moon passes between the Earth and the Sun and so obscures totally or partially the vision of the Sun from our planet. This situation can only happen in the phase of new Moon, when the Moon and the Sun are in conjunction as seen from the Earth. The total eclipses are rare events, that happen only in some part of the globe in how much the totality verificates when the lunar shadow touches the earth surface.

 

 

 

TYPE OF ECLIPSES

 

They exist 4 type of solar eclipses :

 

Total, happens when the Sun is completely darkened from the Moon. The disc of the Moon covers that one of the Sun, with consequent strongly decrease of brightness; it can see only the crown that encircles our star. The line of totality on the Earth is a tightened wraps said path and only who is found in its inside will see the Sun totally eclipsed.

 

 

 

 

Annular, happens when the Sun and the Moon are aligned but the lunar disc is smaller than that solar one for via of the Moon near to the apogee or of the Earth to the perihelion. In such eclipses the Sun appears like an luminous ring that encircles the lunar disc.

 

 

 

Hybrid, happens when the eclipse is total and annular to second of the point of earth observation. They are extremely rare.

 

Partial, it happens when the Moon and the Sun arent perfectly aligned and only a part of the Sun comes darkened. This phenomenon generally is seen from a great part of the earths surface in the outskirtses of the totality zones or annlarity. Moreover some eclipses are exclusively partial when only a part of the lunar shadow intersects the earth surface.

 

 

The distance between Earth and Sun is approximately 400 times the Earth-Moon distance; the diameter of the Sun is approximately 400 times that lunar one. This analogy of relationships provokes that the Sun and the Moon as seen from the Earth have approximately the same angular diameter, half degree.

 

Since the orbit of the Moon around to the Earth is a elipse, therefore like that one of the Earth regarding the Sun, the apparent dimensions of Moon and Sun varies continuously. The magnitude of a eclipse is the relationship between the dimension appearing of the Moon and that one of the Sun during a eclipse. If the Moon is near the perigee its disc will appear enough large to cover the Sun and its photosfera, in such case the magnitude is greater of 1 and the eclipse is total. Viceversa if the Moon is near the apogee the eclipse will be annular and the magnitude inferior to 1. In the hybrid eclipses it oscillates around to 1.

 

Analogous in the periods in which the Earth it near the aphelion will take place more easy a total eclipse, if it near then perihelion an annular.

 

La definizione eclisse centrale spesso usata genericamente per totale, anulare o ibrida. Tuttavia non corretto, poich leclisse centrale solo quando la linea dellombra tocca la superficie terrestre. E possibile, ma raro, che una parte dellombra intersechi la Terra dando luogo ad uneclisse anulare o totale e che la linea non sia centrale (eclisse totale o anulare non-centrale).

 

The definition "central eclipse" is used generically for total, annular or hybrid. However it is not corrected, since the eclipse is cental only when the line of the shadow touches the earth surface. It is possible, but rare, that a part of the shadow intersects the Earth giving place to a annular eclipse or total and that the line is not centrals (total eclipse or non central annular).

 

The same term solar eclipse would be wrong in how much the passage of the lunar disc on that solar one is a occultation; a true eclipse is had when a body passes in the shadow of an other, typical the case of the Moon eclipses.

 

 

 

 

 

PREDICTIONS

 

The outline, not in scale, shows an alignment Sun-Earth-Moon during a solar eclipse. The black region to right of the Moon is its shadow, place in which the Sun is completely darkened. The small area that touches the Earth is where the eclipse is seen like total. The blue zone of the image that encircles the shadow is said penumbra, place in which the Sun is covered partially and it generates therefore partial eclipses.

 

 

 

 

 

The plan of the lunar orbit is tilted regarding that earthling of the ecliptic of 5. Because of that in the moment of the new Moon the Moon usually passes over or under the Sun. An eclipse can only happen when the new Moon is close to one of the points (sayings nodes) in which the lunar orbit intersects that earthling, the ecliptic.

 

As said over the lunar orbit is elliptic and the distance of the Moon from we varies of approximately 6% around to the medium value. Adding to this effect the variations of the earth orbit is clear that approximately 60% of the central eclipses are annular.

 

The lunar orbit intersects the ecliptic in the two nodes distant between they 180. The new Moon happens close to the nodes in two periods distant between they approximately 6 months, and therefore in these periods there will be at least a solar eclipse. Sometimes the new Moon happens enough near to a node in two consecutive months. This means that in that year there will be at least 2 solar eclipses, with a maximum of 5. However some of they will be only partial since the shadow passes over or under the earth poles.

 

During a central eclipse the lunar shadow (or the antishadow in the cases of annular eclipse) moves quickly from the west to east long the Earth. The Earth same rotates from the west to east but the shadow moves more and more fastly so that it seems that the eclipse is moved from the west to east on the earth surface.

 

The amplitude of path of totality varied in relation to the relative diameters of Sun and Moon. In the more favorable conditions, when a total eclipse happens very close to the perigee, the totality can extend for 250 km and the duration exceed the 7 minutes. Outside from the line of centrality will be looked in a widest zone like partial.

 

The solar total eclipses are rare events and although happen in average every 18 months esteem that in a point whichever of the Earth happen every 370 years in average. The duration of eclipse in a place whichever is a few minutes since the lunar shadow move to the speed of 1700 km/h. The totality never exceed 7m31s (second other sources 7m36s) and of usual it is the much short one (in a millenium less than 10 eclipses exceed the 7 minutes).

 

If one knows the date and the hour of a solar eclipse it is possible to foretell the successive ones by means of the use of the cycles. The most famous are the Saros and the Inex. The Saros, the most accurate, durates 6585,3 days, a little less than 18 years, and that means that after this period the eclipses are repeated practically in identical way. The more remarkable difference is a movement of 120 in longitude and a few in latitude. A cycle of Saros always begins with a partial eclipse in the polar regions then traslates on the globe with an series of totals and annular eclipses and ends in the opposite polar region. A Saros durates from 1226 to 1550 years and with 69-87 eclipse, of which 40-60 centrals.

 

Because of the tidial forces the lunar orbit goes away of approximately 3.8 cm to the year and esteem that in 600 million years the Earth-Moon distance will have grown of 23500 km, and consequently the Moon will not succeed to cover the Sun totally.

 

 

OBSERVATIONS

 

The direct observation of the Sun, also only for little second, cause permanent damn to the hairnet of the eyes causing also the blindness.

 

In normal conditions the Sun is therefore luminous that isnt the tendency to watch it. However during an eclipse, when great part of it is covering, is easier to watch it a long time. Ill-fatedly also in this situation they are serious risks, much more if binoculars or telescopes are used. They are absolutely necessary special glances or protections for the sight; the better way for its observation is the projection on a sheet.

 

Only exception is an observation during the short moments of totality since the solar brightness is so attenuated not to damage the eyes.

 

 

TECHNICAL NOTES

 

Said γ (gamma) the minimal distance from the axis of the shadow of the Moon to the center of the Earth, in unit of earth land equatorial radius

 

         if γ > 0 the axis passes to north of the center of the Earth and it is favorite for the observation the hemisphere north

         if γ < 0 the axis passes to south of the center of the Earth and it is favorite for the observation the hemisphere south

          

If |γ| < 0,9972 the eclipse is central, that is exists a line of central eclipse on the surface of the Earth

 

Saying u the radius of the cone of shadow of the Moon in the fundamental plan, that it is the plan that passes for the center of the Earth and is perpendicular to the axis of the shadow of the Moon

 

         if u < 0 the eclipse is total

         if u > 0,0047 the eclipse is annuar

         if 0 < u < 0,0047 the eclipse is annular or total-annular

 

In this last case saying ω = 0,00464√(1-γ)

 

         if u > ω the eclipse is annular

         if u < ω the eclipse is annular-total

 

The radius of the cone of shadow of the Moon in the fundamental plan is u+0,5460

 

         if |γ| is between 0,9972 and 1,5432+u the eclipse is non centrla is always partial

         if |γ| is between 0,9972 and 1,026 a part of the shadow cone can touch the Earth in the polar regions, but the axis of the cone does not touch the Earth

         if 0,9972 < |γ| < 0,9972+|u| the eclipse is non central total or annular; eclipse of this type is only one, on 9/4/2043

         if |γ| > 1,5432+u there arent visible eclipses from the earth surface

 

In the case of partial eclipses the maximum magnitude in the better place of visibility on the Earth, that it is more close to the axis of the shadow is

 

1,5433+u-|γ|

------------

0,5421+2u

 

 

CURIOSITY

 

As saying the maximum possible number of eclipse in a year is 7:

 

5 solar + 2 lunar, on 1805,1935,2206 (4 on 5 are partial)

4 solar + 3 lunar

3 solar + 4 lunar

2 solar + 5 lunar on 1879, 2132

 

In some cases all the eclipses in a year can be partial, 2 on 2 in 1996, 3 on 3 in 2018, 4 on 4 in 2000

 

The maximum number of solar eclipses in a year is 2, on 1973

The maximum number of annular eclipses in a year is 2

The maximum number of solar total+annular eclipses in a year is 3, 1489, 1666, 3192

 

 

Usually the hybrid eclipses are totals in the beginning moments, then they annular and finally they return totals. The eclipse of 3 November 2013 it will be an exception, will begin like total, after 15 second ones it will become annular and such it will remain until the end.

 

2 consecutive eclipses cannot be both only total

2 consecutive eclipses can be both hybrid, ex. 23/12/1908 e 7/06/1909

 

The smallest partial eclipse of Sun of this century will have magnitude 0,005, on 24/10/2098. A more small will happen on 23/08/2883 with magnitude 0.001.

 

Between the year 0 to 4000 d.C. only 33 total eclipses of Sun exceed the 7 minutes, of which nobody in this century.

 

If 2 successive new moon give place to a solar eclipses in nearly all the cases they are both partial and visible from opposite hemispheres.

 

The intersection of the cone of shadow with the fundamental plan creates a small circumference whose the maximum is 3% of the Earth. In the case of the penumbra it is between the 53 and 58%.

 

Between the year 0 and 4000 d.C. only 33 total eclipses of Sun exceed the 7 minutes, of which nobody in this century. The next eclisse over 7 minutes will happen on 16 July 2186 and will last 7m29s.

 

In our century only 11 eclipses will exceed 5 minuteren, the longest on 22 July 2009 with 6m40s.

 

The maximum duration of a annular eclipse is 12m30s.

 

Between the year 0 and 3000 d.C. only 7 annular eclipses exceed 12 minutes, of which nobody in our millenium. The greater in XXI century will be on 15 January 2010 with 11m11s, on 26 January 2028 with 10m31s and on 5 February 2046 with 9m46s.

 

Two successive solar eclipses generally are separated from 6 lunations, much more rarely from 5 or less. When they be distant only 1 lunation the phenomenon calls Duo. In 20 and 21 century there are 31 Duos. Last in the 2000 (1 july/31 July) and next one in 2011 (1 june/1 July). Rare are the duos in the same month, the next one in December 2206 (1 and 30). Of the 2 eclipses one happens before that Moon catches up the node, the following after, therefore the eclipses will be visible from opposite hemispheres. Nearly all are partial, only 15 cases between the 2000 a.C. and 3000d.C. are a total and a partial. The next one in the 2195. No case of annularity.

 

The christmas eclipses are much rare, in our single millenium 13, of which 4 totals, 3 annulars and 6 partial ones, the next one in 2038.

 

Rare also the eclipses on 29 February, from year 0 to 3000d.C. only the 8 cases, the next one in 2044.

 

The eclipse with the longest line than totality exceeds the 15300 km. In the last 2000 years only 2 cases, 19 March 573 and on 25 september 1745. The longest of this millennium on 18 March 2360 with 15291 km.

 

TYPE OF ECLIPSES

 

 

TYPE I

 

The entire lunar penumbra passes on the Earth, exists therefore a centrality line. The eclipse can be annular, total or hybrid.

 

 

 

 

In all the points of the curve DUM' the eclipse begins at daybreak, an observer sees all the eclipse. In all the points of the curve DQM' the eclipse it ends at daybreak, an observer will not see nothing. In all the points of the curve DG'M' the maximum of the eclisse happens at daybreak. In the region DG'M'V the Sun rises eclipsed and it will look the maximum of eclisse and the end. In the region DQM' G' the Sun rises eclipsed, but the end will be only the end. In all the points of the curve LVR' the eclipe ends to the sunset, an observer sees however all the eclipse. In all the points of the curve LTR' the eclipe begins to the sunset, an observer does not see nothing. In all the points of the curve LH'R' the maximum happens to the sunset. In the region LVR'H' the o Sun set eclipsed, will look the beginning and the maximum. In the region LH'R'T the o Sun set eclipsed, will look only the beginning of the eclipse. In the region LVR'M'U all the eclisse will be visible, from the first one to the last contact. The line G'H' is the totality line. In the places on the curves DL and M'R' the Moon touches the Sun, the eclipse is partial with magnitudine 0,000.

 

Are of type I the eclipses on 24 october 1995 and 21 june 2020.

 

 

 

 

 

 

TYPE II

 

Only a part of the lunar penumbra passes over the Earth, therefore a centrality line exists and the eclipse it can be total, annular or hybrid.

 

 

 

The visibility conditions are the same ones of type I, but the curves that delimit rising and the sunset of the Sun arent separated but they form an 8, the curve M'QWVR'TWU. On arc WUM' the eclipse begins to the dawn. In region WQM'U the Sun rises eclipsed. On arc WTR' the eclipse begins to the sunset. In area WTR' V the sun sets eclipsed. In area WUM' R'V the eclipse is visible entire. The curve M'G'H'R' is the line of "maximum eclipse on the horizon". The curve G'UVH' is the totality line.

 

Are of type II the eclipses on 1 august 2008, 11 august 1999 and 10 june 2021

 

 

 

 

 

 

 

 

 

 

 

 

TYPE III

 

Less of the half of the lunar penumbra passes on the Earth and the cone of shadow or its extension does not touch it. The eclipse is partial.

 

 

 

 

The visibility regions are same of type II, except that does not exist the centrality line. The maximum magnitude of the eclipse happens in Y' not far away from W. Y' is in fact the point on the earth surface more near to the axis of the shadow.

 

Are of type III the eclipses on 12 october 1996 and 4 january 2011.

 

The eclipses type I, II e III are the most frequent.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TIPO IV

 

The entire lunar penumbra passes on the Earth, however the limit north (or south) of the penumbra touches the Earth from the same part regarding the meridian centers them (DL regarding NS in figure).

 

 

 

 

In the point D the eclipse begins at daybreak, in L ends at daybreak. The limit north DL often is an arc much small. The curves of beginning and ending with the Sun on the horizon are separated, but one of they is distorted and forms an 8. On the arc DUM' the eclipse begins at daybreak. On the arc DQM' the eclipse ends at daybreak. On the curve R' VW the eclipse ends to the sunset of the Sun. On the curve WaL' the eclipse ends at daybreak. On the curve R'TW the eclipse begins to the sunset. On the curve WbL' the eclipse begins at daybreak. In the area WaL'b the Sun rises eclipsed. In area WVRT the Sun set eclipsed. The limit south of the eclipse is the curve M'R', the centrality line the curve G' H', and there are the classic 2 curves of "maximum on the horizon": on DG'M' the maximum it happens at daybreak, on W'H'R' to the sunset. The area WaL'b can be also on the first curve, neighbor to D, or in M' or R', but not on two curves at the same time.

 

In some cases 2 consecutive eclipses are of type IV.

 

In the first figure saying ψ the angle between NS and GH, will be an eclipse of type IV if

 

0,997 sin ψ < |γ| + u < 0,997

 

It is of type IV the eclipse on 7 march 1970 and on 29 march 2006.

 

 

 

 

 

TYPE V

 

This type of eclipse happens when the central line touches the Earth from the same part regarding the central meridian.

 

 

 

In this case the central line begins and ends at daybreak. G and H are both in area NMS. Obviously G and H could be also in area NRS and in this case the central line begins and ends to the sunset of the sun. In any case the W node is not between G' and H'. In no case the eclipse will be visible to noon, or before or after.

 

So that happens a eclisse of type V must be taken place

 

0,997 sin ψ < |γ| < 0,997 with ψ like up.

 

Will be of type V the eclipses on 7 february 2008 and 30 march 2033.

 

 

 

 

 

 

 

 

 

 

 

TYPE VI

 

This type of eclipse happens when only a small part of the cone of penumbra of the Moon touches the Earth.

 

 

 

 

 

 

 

 

 

In such situation the curve of the limit north (or south) begins or ends at daybreak (or to the sunset). In no case the eclipse he is visible to noon since the straight MR is always in a part regarding the central meridian NS. For all the places in the oval M'QR'T the Sun sets still eclipsed. On the curve M'TR' the eclipse begins to the sunset. On the curve M'QR' the eclipse ends to the sunset. On the curve M'Y R' the maximum of the eclipse happens to the sunset. Therefore in the region M'Y'R'Q it will look the beginning and the maximum of eclipse but the not end, in the region M'Y'R'T will look only the beginning. The maximum magnitude of the eclipse is visible in the Y' point.

 

So that happens a eclisse of type VI must be taken place

 

0,997 sin ψ < |γ| - L < 0,997 with ψ like up.

 

The eclipse will be always partial with the maximum magnitude 0,25 and visible in the polar regions.

 

Will be of type VI the eclipses on 15 july 2083 and on 24 october 2098.

 

 

 

 

 

 

TYPE VII

 

This type of eclipse happens when only a part of the cone of shadow of the Moon touches the Earth. The eclipses areannular or total (not central)

 

 

The area in which the eclipse is visible is a small semicircle. The visibility conditions are like in type III. The totality region is delimited from the curve of "maximum on the horizon". In the case in figure an observer in the small semicircle can see the beginning of the partial phase and the totality, but not the end of the eclipse. If the small semicircle it were on the curve M'W it would see instead the maximum and the end but not the beginning. If the small semicircle it coincided with the W point happens a strange event: the eclipse it begins with the Sun under the horizon, it can see the phase of maximum, and the end of the eclipse happens with the Sun under the horizon, like 17 December 2104.

 

An eclipse of type VII was on il 31 may 2003 and will be another on 29 april 2014.

 

 

 

NOTES ON THE SOLAR ECLIPSES

 

The medium frequency of a total eclipse of Sun for a data point on the Earth is of 375 years.

The medium frequency of an annular eclipse of Sun for a data a point on the Earth is of 224 years.

The medium frequency of a total or annular eclipse of Sun for a data point on the Earth is of 140 years.

 

There are nations in which a total eclipse does not happen from centuries:

 

         Tahiti, 10 april 1698

         Seychelles, 2 july 1647

         Bermuda, 30 august 1532

         Israele, 9 july 1488

         Vaticano, 1 january 1386

         Malta, 12 august 603

         Madeira, 4 may 292

 

And many will have to wait for centuries:

 

         Falkland, 23 october 2348

         Danimarca, 2 september 2426

         Madeira, 18 september 2620

         Tahiti, 2 march 2910

 

Considering the period from 1401 to 3000 it discovers that there are places in which in less than 7 years happen 3 total solar eclipses:

 

mare di Java, 1434-1437-1438

Messico, 1796,1799,1803

Filippine, 1814,1817,1821

Oceano Indiano, 1849,1854,1856

Oceano Indiano, 2194,2197,2201

 

In a place of the pacific Ocean from the 2447 will be looked 4 total eclipses in only 4 year!

 

But the record is 5 total eclipses in 32 years.

 

During a solar eclipse often some planets are looked near the Sun; from 1900 to 2100 in only 3 cases the planets will be within 1 from the Sun, of which the next event on 26 December 2057.

 

Rare also the occultation of planet from part of the eclipsed Sun, only one from year 0 to 3000, on 14 May 2105.

 

If we consider the duration of an eclipse from the moment of the first contact to the moment of the last contact, independently from the totality, annularity or partiality, the time can exceed the 4 hours. The longer event happened on 14 December 1955 with 4h26m30s, next on 15 January 2010 with 4h13m.

 

The wider path of totality: in the arc of 3 millenia, there are 14 cases in which it is wider than 800 km, the maximum on 24 May 1248 with 1216 km, next on 21/02/2213.

 

The wider path of annularity, always from year 0 to 3000: 13 cases in which it is wider than 1000 km, the maximum on 12 November 1547 with 1546 km.

 

In rare cases they can be many successive eclipses of which no partial one, example, 6 eclipses, from the 21/6/2001 comprised: 14/12/2001, 16/06/2002, 4/12/2002, 31/05/2003, 23/11/2003.

 

In 348 they have been quite 7 consecutive eclipses and from the 30/4/2041 they will be 12!