The 2016-2100 total solar eclipse prediction by using Meeus Algorithm implemented on MATLAB
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Journal of Physics: Conference Series
PAPER • OPEN ACCESS
The 2016-2100 total solar eclipse prediction by using Meeus Algorithm
implemented on MATLAB
To cite this article: A Melati and S Hodijah 2016 J. Phys.: Conf. Ser. 771 012039
View the article online for updates and enhancements.
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International Symposium on Sun, Earth, and Life (ISSEL) IOP Publishing
Journal of Physics: Conference Series 771 (2016) 012039 doi:10.1088/1742-6596/771/1/012039
The 2016-2100 total solar eclipse prediction by using Meeus
Algorithm implemented on MATLAB
A Melati, S Hodijah
Physics Department, Faculty of Science and Technology, UIN Sunan Kalijaga
Yogyakarta, Jl. Maksda Adisucipto No. 1, Yogyakarta, Indonesia
E-mail: asih.melati@gmail.com
Abstract. The phenomenon of solar and lunar eclipses can be predicted where and when it will
happen. The Total Solar Eclipse (TSE) phenomenon on March 09th, 2016 became revival
astronomy science in Indonesia and provided public astronomy education. This research aims to
predict the total solar eclipse phenomenon from 2016 until 2100. We Used Besselian calculations
and Meeus algorithms implemented in MATLAB R2012b software. This methods combine with
VSOP087 and ELP2000-82 algorithm. As an example of simulation, TSE prediction on April
20th, 2042 has 0.2 seconds distinction of duration compared with NASA prediction. For the
whole data TSE from year of 2016 until 2100 we found 0.04-0.21 seconds differences compared
with NASA prediction.
1. Introduction
Total solar eclipse (TSE) is not a sign of human mortality and natality. As a matter of fact, it has a
predetermined time as the appearance of the hilal as said by Islamic phylosopher Shaykh al-Islam Ibn
Taimiyah. The eclipse on March 9th, 2016 was clearly visible in many parts in Indonesia, including
Central Sulawesi and Ternate. It was becomes special momentum and astronomy euphoria. The high
interest of public indicates that most of Indonesian people eager to learn astronomy. This euphoria was
different from TSE phenomenon in 1983 which enormous people were anxious. This research aims to
predict next TSE using Meeus Algorithm. Meeus Algoritm could predict maximum duration of TSE
[1][2]. We simulated TSE from year of 2016 until 2100 using MATLAB R2012b software.
2. TSE calculation based on Meeus Algorithm
To calculate or predict solar eclipse, we need to know Besselian Elements according to the date of the
solar eclipse. The Besselian elements of unification algorithms are VSOP87 (for the Sun) and ELP2000-
82 (for the Moon). The method was developed by Friedrich Wilhelm Bessel in 1842 and was repeatedly
refined since then. The basic idea of the method is that the Besselian elements describe the motion of
the lunar shadow on a suitably chosen, so called fundamental plane. The fundamental plane crosses the
centre of the Earth and is perpendicular to the axis of the shadow cone. The Besselian elements shown
in figure 1 below[3][5]. Where observer plane is an observer on the Earth's surface. L1 is a radius of the
penumbra cone in the fundamental plane, L2 is the radius of umbra cone in the fundamental plane, L1' is
the radius of penumbra cone in observer plane on the Earth's surface, L2' is the radius of umbra cone in
observer plane on the Earth's surface, f1 is angle between the penumbra cone and the shadow axis of
Moon's, f2 is angle between the umbra cone and the shadow axis of Moon's.
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution
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Published under licence by IOP Publishing Ltd 1
International Symposium on Sun, Earth, and Life (ISSEL) IOP Publishing
Journal of Physics: Conference Series 771 (2016) 012039 doi:10.1088/1742-6596/771/1/012039
Start
Input Data : Besselian
element based on date
and year TSE on 2016-
2100 No
Calculate Latitude, Longitude,
Azimuth and Altitude of Sun,
Radius Ratio between Moon
dan Sun, Path, Duration of solar
eclipse, and area
Error occur?
Yes or No?
Output Data : Latitude,
Longitude, Azimuth and
Altitude of Sun, Radius Ratio
between Moon dan Sun, Path,
Duration of solar eclipse, and
area
Result
analyzing
Conclusion
End
Figure 1. Description Figure 2.Flow chart of TSE predictions.
Besselian element in the from
of image
(http://www.gautschy.ch/~rita/
archast/solec/solec.html).
In the case of a central eclipse, the type of the eclipse can be determined by the following rules: if u
< 0, the eclipse is total; if u > +0.0047, it is annular; if u is between 0 and +0.0047, the eclipse is either
annular or annular-total. u represents radius of the Moon’s umbral cone in the fundamental plane. In the
latter case, the ambiguity is removed as follow
0, 00464 1 2 > 0 (1)
If u < , the eclipse is annular-total; otherwise it is the annular one. In the case of a partial solar eclipse,
the greatest magnitude is attained at the point of the surface of the Earth which comes closest to the axis
of shadow. The magnitude of the eclipse at that point is
1,5433 u
0,5461 2u (2)
2
International Symposium on Sun, Earth, and Life (ISSEL) IOP Publishing
Journal of Physics: Conference Series 771 (2016) 012039 doi:10.1088/1742-6596/771/1/012039
represents the least distance from the axis of the Moon’s shadow to the center of the Earth, in units of
the equatorial radius of the Earth [4].
3. Methods
Prediction steps of a total solar eclipse are presented in the form of a flow chart shown figure 2.
4. Result and discussion
Based on our TSE predictions there are ± 68 total solar eclipse that will occur from year of 2016 to 2100
(see figure 3, prediction of the total solar eclipse on April 20th, 2042) using Besselian element illustrated
on Table.1
Table 1. Besselian Element for TSE on April 20th, 2042[5]
Figure 3. Simulation TSE Predictions Display on April 20th, 2042 Using MATLAB Software
Figure 4. Graph Geographic Region or position through which the Total Solar Eclipse on April 20th,
2042.
3International Symposium on Sun, Earth, and Life (ISSEL) IOP Publishing
Journal of Physics: Conference Series 771 (2016) 012039 doi:10.1088/1742-6596/771/1/012039
Figure 5. Geographic Region or position through which the Total Solar Eclipse on April 20th, 2042.
Figure 4 and 5 shows TSE coverage on 20 April 2042. The TSE will be observed in Indian Ocean,
then across Jambi town and southern Sumatra, Java Sea, Bangka and Belitung Island, Java Sea, the city
of Pontianak, West Kalimantan, then across Malaysia, South China Sea, Brunei, Sabah-Malaysia, the
Philippines and ended up in the North Pacific Ocean. The longest duration of totality based on the
algorithm is 4 minutes 51 seconds.
All of the obtained TSE are different compared with NASA prediction. NASA prediction will have
0.2 seconds longer duration than our research. Based on the results that have been obtained, simulation
TSE predictions with Besselian method combined with VSOP87 (for the Sun) and ELP2000-82 (for the
Moon) algorithms on MATLAB software could be used as reference for the next total solar eclipse
predictions until 2100[4]. Our results show 0.04-0.21 seconds longer duration of totality
compared with the results from NASA [6]
Acknowlegment
We would like to thank Astronic Study Club Sunan Kalijaga Islamic State University for support this
research, Dr Rinto Anugraha lecturer Physics Department Gajah Mada University and Anggara Dwi
for helping operate several label programming.
References
[1] Lewis Isabel M 1931 American Astronomical Society 6 265 – 266
[2] Meeus J 2003 J. British Astronomical Association 113 (6): 343-348
[3] Gautschy R 2012 Canon of Solar Eclipse from 2501 BC to 1000 AD (Swiss: Swiss National
Science Foundation)
[4] Meeus J 1998 Astronomical Algorthms second edition (Virginia, USA: Willmann Bell) p 379-
388
[5] Meeus J 1989 Elements of Solar Eclipses 1951-2200 (Virginia, USA: Willmann Bell) p 150
[6] Espenak F and Meeus J 2009 Five Millenium Catalog of Solar Eclipses: -1999 to +3000 (2000
BCE to 3000 CE)-Revised NASA/TP-2009-214174 p. A-164
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