Bessel’s method in study of solar eclipse influence on the ionosphere
Keywords:
ionosphere, solar eclipse, Bessel’s method, total electron content, TEC, eclipse phase, remote sensing, GPS, relative illuminance
Abstract
Relevance. A solar eclipse is a global disturbing factor that significantly changes the characteristics of the ionosphere. As is known, the ionosphere affects the propagation of radio waves of all ranges, that is, it affects the operation of navigation and radio astronomy systems, radars, telecommunications, and remote sensing of near-Earth space. Therefore, the study of the influence of solar eclipses on the ionosphere is an important task, which in general consists of astronomical and ionospheric parts of the work.
The purpose of this work is to present the elements of astronomical calculation methods developed for ionospheric research and to describe the results of using these methods to study the influence of solar eclipses on the ionosphere.
Methods and methodology. The methods are developed on the basis of the Bessel’s method, which makes it possible to significantly simplify calculations using the concept of the fundamental plane.
Results. Analytical relationships are obtained for the trace of the lunar shadow on the earth's surface, the eclipse phase, the magnitude of the obscuration, as well as the relative illuminance at the measurement point. Using the developed methods, GPS stations and satellite flights of the current constellation of satellites were optimally selected, the delay time of the main ionospheric response, which was approximately 30-40 minutes, and the relationship between the magnitude of the eclipse phase and the change in total electron content (TEC) were established. For eclipse phase 0.7, the TEC decrease was 3.5 TECU or 19%.
Conclusions. The developed methods make it possible to study the influence of solar eclipses on the ionosphere.
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References
1. Chapman S. The influence of a solar eclipse upon the upper atmospheric ionization. Monthly Not. Roy. Astron. Soc. 1932;92:413–420. https://doi.org/10.1093/mnras/92.5.413
2. Lewis I. M. Formulas for the ionosphere track in eclipses. The Astronomical J. 1940;49(1122):4–7. https://doi.org/10.1086/105607
3. Chernogor LF., Mylovanov YuB. Ionospheric Effects from the June 10, 2021 Solar Eclipse in the Polar Region. Kinematics and Physics of Celestial Bodies. 2022;38(4):29–52. https://doi.org/10.15407/kfnt2022.04.029 [In Ukrainian].
4. Chernogor LF, Mylovanov, YuB. Ionospheric Effects of the August 11, 2018, Solar Eclipse over the People’s Republic of China. Kinemat. Phys. Celest. Bodies. 2020;36(6):37–64. https://doi.org/10.15407/kfnt2020.06.037. [In Ukrainian].
5. Chernogor LF., Mylovanov YuB., Luo Y. Effects from the June 10, 2021 solar eclipse in the high-latitude ionosphere: results of GPS observations. Radio Phys. Radio Astron. 2022;27(2):93–109 https://doi.org/10.15407/rpra27.02.093. [In Ukrainian].
6. Chernogor LF, Mylovanov YuB, Dorokhov VL, Podnos VA, Tsymbal AM, Shevelev MB. TEC variations in equatorial ionosphere during June 21, 2020 solar eclipse. Visnyk of V.N. Karazin Kharkiv National University, series “Radio Physics and Electronics”. 2022;36:49–65. https://doi.org/10.26565/2311-0872-2022-36-04 [In Ukrainian].
7. Chernogor LF, Garmash KP. Ionospheric Processes during the Partial Solar Eclipse above Kharkiv on June 10, 2021. Kinematics and Physics of Celestial Bodies. 2022;38(2):3–22. https://doi.org/10.15407/kfnt2022.02.003. [In Ukrainian]
8. Chernogor LF, Garmash KP, Zhdanko YH, Leus SG, Luo Y. Features of ionospheric effects from the partial solar eclipse over the city of Kharkiv on 10 June 2021. Radio Phys. Radio Astron. 2021;26(4):326–343. https://doi.org/10.15407/rpra26.04.326 [In Ukrainian].
9. Chernogor LF, Mylovanova LI, Mylovanov YuB, Tsymbal AM, Luo Y. Effects from the June 10, 2021 solar eclipse in the ionosphere over Kharkiv: results from ionosonde measurements. Visnyk of V.N. Karazin Kharkiv National University, series “Radio Physics and Electronics”. 2021;35:60–78. [In Ukrainian]. https://doi.org/10.26565/2311-0872-2021-35-06
10. Huang F., Li Q., Shen X., Xiong C., Yan R., Zhang S.‐R., et al. Ionospheric responses at low latitudes to the annular solar eclipse on 21 June 2020. J. Geophys. Res.: Space Phys. 2020;125:1–16, e2020JA028483. https://doi.org/10.1029/2020JA028483
11. Tsai H. F., Liu J. Y. Ionospheric total electron content response to solar eclipses. J. Geophys. Res. 1999;104(A6):12657–12668. https://doi.org/10.1029/1999JA900001
12. Zhang R., Le H., Li W., Ma H., Yang Y., Huang H., et al. Multiple technique observations of the ionospheric responses to the 21 June 2020 solar eclipse. Journal of Geophysical Research: Space Physics. 2020;125:1–15, e2020JA028450. https://doi.org/ 10.1029/2020JA028450
13. Gomez D. D. Ionospheric response to the December 14, 2020 total solar eclipse in South America. J. Geophys. Res.: Space Phys. 2021;126:1–14, e2021JA029537. https://doi.org/10.1029/2021JA029537
14. Aa E., Zhang S-R., Erickson P. J., Goncharenko L. P., Coster A. J., Jonah O. F., Lei J., Huang F., Dang T., Liu L. Coordinated ground-based and space-borne observations of ionospheric response to the annular solar eclipse on 26 December 2019. J. Geophys. Res.: Space Phys. 2020;125(11):1–17, e2020JA028296. https://doi.org/10.1029/2020JA028296
15. Cheng W., Xu W., Gu X., Wang S., Wang Q., Ni B., Lu Z., Xiao B., Meng X. A Comparative Study of VLF Transmitter Signal Measurements and Simulations during Two Solar Eclipse Events. Remote Sens. 2023;15 (3025):1–14. https://doi.org/10.3390/rs15123025
16. Harjosuwito J., Husin A., Dear V., Muhamad J., Faturahman A., Bahar A., Erlansyah, Syetiawan A., Pradipta R. Ionosonde and GPS total electron content observations during the 26 December 2019 annular solar eclipse over Indonesia. Ann. Geophys. 2023;41:147–172. https://doi.org/10.5194/angeo-41-147-2023
17. Verhulst T. G. W., Stankov S. M. The importance of the three-dimensional geometry of solar eclipses for analysis of the impact on the ionosphere. 2018 42nd COSPAR Scientific Assembly, Pasadena, California, USA, Abstract id. C1.1 79 18.
18. Verhulst T. G. W., Stankov S. M. Height dependency of solar eclipse effects: The ionospheric perspective. Journal of Geophysical Research: Space Physics. 2020;125:1–20, e2020JA028088. https://doi.org/10.1029/2020JA028088
19. Stankov S. M., Bergeot N., Berghmans D., Bolsée D., Bruyninx C., et al. Multi-instrument observations of the solar eclipse on 20 March 2015 and its effects on the ionosphere over Belgium and Europe. J. Space Weather Space Clim. 2017; 7(A19):1–23. https://doi.org/10.1051/swsc/2017017
20. Sun Y.-Y., Chen C.-H., Su X., Wang J., Yu T., Xu H.-R., Liu, J.-Y. Occurrence of nighttime irregularities and their scale evolution in the ionosphere due to the solar eclipse over East Asia on 21 June 2020. Journal of Geophysical Research: Space Physics. 2023;128:1–9. e2022JA030936. https://doi.org/10.1029/2022JA030936
21. Chauvenet W. Manual of Spherical and Practical Astronomy, 5-th ed. Vol.1. Philadelphia: J. B. Lippincott Co.; 1891. Reprinted 1960, New York: Dover Publications. 704 p.
22. Buchanan S. B. The mathematical theory of eclipses. Philadelphia and London: J. B. Lippincott Company; 1904. 292 p.
23. Smart W. M. Textbook on spherical astronomy, 6th ed. Cambridge: Cambridge University Press; 1977. 443 p.
24. Ball R. A Treatise On Spherical Astronomy. London: Cambridge University Press; 1908. 506 p.
25. Williams W. Jr. Prediction and Analysis of Solar Eclipse Circumstances. National Technical Information Service Technical Report NTIS No. AD726626, Springfield, Virginia; 1971. 131 p.
26. Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac. London: H. M. Nautical Almanac Office; 1974. 547 p.
27. Seidelmann P. K., editor. Explanatory Supplement to the Astronomical Almanac. California: University Science Books; 1992. 752 p.
28. Urban S. E., Seidelmann P. K., editors. Explanatory Supplement to the Astronomical Almanac, 3d ed. Mill Valley, California: University Science Books; 2013. 768 p.
29. Meeus J., Grosjean C. C., Vanderleen W. Canon of Solar Eclipses. New York: Pergamon Press; 1966. 750 p.
30. Espenak F. Fifty Year Canon of Solar Eclipses: 1986–2035. Cambridge, Massachusetts: Sky Publishing Corp.; 1987. 278 p.
31. Espenak F., Meeus J. Five Millennium Catalog of Solar Eclipses: –1999 to +3000 (2000 BCE to 3000 CE). Revised NASA/TP-2009-214174; 2009. 278 p.
32. Meeus J. Elements of Solar Eclipses 1951–2200. Virginia, USA: Willmann Bell; 1989. 105 p.
33. Littmann M., Espenak F., Willcox K. Totality. Eclipses of the Sun, 3rd ed. Oxford, New York: Oxford University Press; 2008. 358 p.
34. Steele J. M. Observations and Predictions of Eclipse Times by Early Astronomers. Springer-Science+Business Media. 2000. 321 p.
35. https://www.iausofa.org
36. Meeus J. Astronomical Algorithms second edition. Virginia, USA: Willmann Bell; 1998. 477 p.
37. Meeus J. Mathematical Astronomy Morsels. Richmond, Virginia: Willmann-Bell; 1997. 379 p.
38. Meeus J. More Mathematical Astronomy Morsels. Richmond, Virginia: Willmann-Bell; 2002. 429 p.
39. Meeus J. Mathematical Astronomy Morsels III. Richmond, Virginia: Willmann-Bell; 2004. 374 p.
40. Meeus J. Mathematical Astronomy Morsels IV. Richmond, Virginia: Willmann-Bell; 2007. 373 p.
41. Meeus J. Mathematical Astronomy Morsels V. Richmond, Virginia: Willmann-Bell; 2009. 373 p.
42. Montenbruck O., Pfleger T. Astronomy on the Personal Computer. 4th, Completely Revised Edition. New York: Springer; 2000. 300 p.
43. Duffett-Smith P. Astronomy with your Personal Computer, 2nd ed. New York: Cambridge University Press; 1997. 259 p.
44. Duffett-Smith P., Zwart J. Practical Astronomy with your Calculator or Spreadsheet, 4th еd. New York: Cambridge University Press; 2012. 216 p.
45. https://eclipse.gsfc.nasa.gov/
46. https://www.eclipsewise.com/
47. Mahooti M. Standards of Fundamental Astronomy. MATLAB Central File Exchange. Retrieved June 30, 2023. https://www.mathworks.com/matlabcentral/fileexchange/74523-standards-of-fundamental-astronomy
48. Eagle D. A MATLAB Implementation of Elements of Solar Eclipses. MATLAB Central File Exchange. Retrieved June 30, 2023. https://www.mathworks.com/matlabcentral/fileexchange/71132-a-matlab-implementation-of-elements-of-solar-eclipses
49. Mahooti M. Solar Eclipse. MATLAB Central File Exchange. Retrieved June 30, 2023. https://www.mathworks.com/matlabcentral/fileexchange/55279-solar-eclipse
50. Mahooti M. Local Circumstances of a Solar Eclipse. MATLAB Central File Exchange. Retrieved June 30. 2023. https://www.mathworks.com/matlabcentral/fileexchange/55609-local-circumstances-of-a-solar-eclipse
51. Carton W. H. C. The speed of the lunar shadow on Earth during solar eclipses. J. Br. Astron. Assoc. 2011;121(2):105–108.
52. Pasachoff J. M., Fraknoi A. Resource Letter OSE-1: Observing Solar Eclipses. American Journal of Physics. 2017;85(7); 485–494. http://dx.doi.org/10.1119/1.4985062
53. Zillman M. P. Astronomy Resources on the Internet 2022. 2022;:1–28. http://www.AstronomyResources.info/
54. https://www.eclipsewise.com/solar/SEprime/2001-2100/SE2022Oct25Pprime.html
55. Moore P., Rees R. Patrick Moore’s Data Book of Astronomy. New York: Cambridge University Press; 2011. 576 p.
2. Lewis I. M. Formulas for the ionosphere track in eclipses. The Astronomical J. 1940;49(1122):4–7. https://doi.org/10.1086/105607
3. Chernogor LF., Mylovanov YuB. Ionospheric Effects from the June 10, 2021 Solar Eclipse in the Polar Region. Kinematics and Physics of Celestial Bodies. 2022;38(4):29–52. https://doi.org/10.15407/kfnt2022.04.029 [In Ukrainian].
4. Chernogor LF, Mylovanov, YuB. Ionospheric Effects of the August 11, 2018, Solar Eclipse over the People’s Republic of China. Kinemat. Phys. Celest. Bodies. 2020;36(6):37–64. https://doi.org/10.15407/kfnt2020.06.037. [In Ukrainian].
5. Chernogor LF., Mylovanov YuB., Luo Y. Effects from the June 10, 2021 solar eclipse in the high-latitude ionosphere: results of GPS observations. Radio Phys. Radio Astron. 2022;27(2):93–109 https://doi.org/10.15407/rpra27.02.093. [In Ukrainian].
6. Chernogor LF, Mylovanov YuB, Dorokhov VL, Podnos VA, Tsymbal AM, Shevelev MB. TEC variations in equatorial ionosphere during June 21, 2020 solar eclipse. Visnyk of V.N. Karazin Kharkiv National University, series “Radio Physics and Electronics”. 2022;36:49–65. https://doi.org/10.26565/2311-0872-2022-36-04 [In Ukrainian].
7. Chernogor LF, Garmash KP. Ionospheric Processes during the Partial Solar Eclipse above Kharkiv on June 10, 2021. Kinematics and Physics of Celestial Bodies. 2022;38(2):3–22. https://doi.org/10.15407/kfnt2022.02.003. [In Ukrainian]
8. Chernogor LF, Garmash KP, Zhdanko YH, Leus SG, Luo Y. Features of ionospheric effects from the partial solar eclipse over the city of Kharkiv on 10 June 2021. Radio Phys. Radio Astron. 2021;26(4):326–343. https://doi.org/10.15407/rpra26.04.326 [In Ukrainian].
9. Chernogor LF, Mylovanova LI, Mylovanov YuB, Tsymbal AM, Luo Y. Effects from the June 10, 2021 solar eclipse in the ionosphere over Kharkiv: results from ionosonde measurements. Visnyk of V.N. Karazin Kharkiv National University, series “Radio Physics and Electronics”. 2021;35:60–78. [In Ukrainian]. https://doi.org/10.26565/2311-0872-2021-35-06
10. Huang F., Li Q., Shen X., Xiong C., Yan R., Zhang S.‐R., et al. Ionospheric responses at low latitudes to the annular solar eclipse on 21 June 2020. J. Geophys. Res.: Space Phys. 2020;125:1–16, e2020JA028483. https://doi.org/10.1029/2020JA028483
11. Tsai H. F., Liu J. Y. Ionospheric total electron content response to solar eclipses. J. Geophys. Res. 1999;104(A6):12657–12668. https://doi.org/10.1029/1999JA900001
12. Zhang R., Le H., Li W., Ma H., Yang Y., Huang H., et al. Multiple technique observations of the ionospheric responses to the 21 June 2020 solar eclipse. Journal of Geophysical Research: Space Physics. 2020;125:1–15, e2020JA028450. https://doi.org/ 10.1029/2020JA028450
13. Gomez D. D. Ionospheric response to the December 14, 2020 total solar eclipse in South America. J. Geophys. Res.: Space Phys. 2021;126:1–14, e2021JA029537. https://doi.org/10.1029/2021JA029537
14. Aa E., Zhang S-R., Erickson P. J., Goncharenko L. P., Coster A. J., Jonah O. F., Lei J., Huang F., Dang T., Liu L. Coordinated ground-based and space-borne observations of ionospheric response to the annular solar eclipse on 26 December 2019. J. Geophys. Res.: Space Phys. 2020;125(11):1–17, e2020JA028296. https://doi.org/10.1029/2020JA028296
15. Cheng W., Xu W., Gu X., Wang S., Wang Q., Ni B., Lu Z., Xiao B., Meng X. A Comparative Study of VLF Transmitter Signal Measurements and Simulations during Two Solar Eclipse Events. Remote Sens. 2023;15 (3025):1–14. https://doi.org/10.3390/rs15123025
16. Harjosuwito J., Husin A., Dear V., Muhamad J., Faturahman A., Bahar A., Erlansyah, Syetiawan A., Pradipta R. Ionosonde and GPS total electron content observations during the 26 December 2019 annular solar eclipse over Indonesia. Ann. Geophys. 2023;41:147–172. https://doi.org/10.5194/angeo-41-147-2023
17. Verhulst T. G. W., Stankov S. M. The importance of the three-dimensional geometry of solar eclipses for analysis of the impact on the ionosphere. 2018 42nd COSPAR Scientific Assembly, Pasadena, California, USA, Abstract id. C1.1 79 18.
18. Verhulst T. G. W., Stankov S. M. Height dependency of solar eclipse effects: The ionospheric perspective. Journal of Geophysical Research: Space Physics. 2020;125:1–20, e2020JA028088. https://doi.org/10.1029/2020JA028088
19. Stankov S. M., Bergeot N., Berghmans D., Bolsée D., Bruyninx C., et al. Multi-instrument observations of the solar eclipse on 20 March 2015 and its effects on the ionosphere over Belgium and Europe. J. Space Weather Space Clim. 2017; 7(A19):1–23. https://doi.org/10.1051/swsc/2017017
20. Sun Y.-Y., Chen C.-H., Su X., Wang J., Yu T., Xu H.-R., Liu, J.-Y. Occurrence of nighttime irregularities and their scale evolution in the ionosphere due to the solar eclipse over East Asia on 21 June 2020. Journal of Geophysical Research: Space Physics. 2023;128:1–9. e2022JA030936. https://doi.org/10.1029/2022JA030936
21. Chauvenet W. Manual of Spherical and Practical Astronomy, 5-th ed. Vol.1. Philadelphia: J. B. Lippincott Co.; 1891. Reprinted 1960, New York: Dover Publications. 704 p.
22. Buchanan S. B. The mathematical theory of eclipses. Philadelphia and London: J. B. Lippincott Company; 1904. 292 p.
23. Smart W. M. Textbook on spherical astronomy, 6th ed. Cambridge: Cambridge University Press; 1977. 443 p.
24. Ball R. A Treatise On Spherical Astronomy. London: Cambridge University Press; 1908. 506 p.
25. Williams W. Jr. Prediction and Analysis of Solar Eclipse Circumstances. National Technical Information Service Technical Report NTIS No. AD726626, Springfield, Virginia; 1971. 131 p.
26. Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac. London: H. M. Nautical Almanac Office; 1974. 547 p.
27. Seidelmann P. K., editor. Explanatory Supplement to the Astronomical Almanac. California: University Science Books; 1992. 752 p.
28. Urban S. E., Seidelmann P. K., editors. Explanatory Supplement to the Astronomical Almanac, 3d ed. Mill Valley, California: University Science Books; 2013. 768 p.
29. Meeus J., Grosjean C. C., Vanderleen W. Canon of Solar Eclipses. New York: Pergamon Press; 1966. 750 p.
30. Espenak F. Fifty Year Canon of Solar Eclipses: 1986–2035. Cambridge, Massachusetts: Sky Publishing Corp.; 1987. 278 p.
31. Espenak F., Meeus J. Five Millennium Catalog of Solar Eclipses: –1999 to +3000 (2000 BCE to 3000 CE). Revised NASA/TP-2009-214174; 2009. 278 p.
32. Meeus J. Elements of Solar Eclipses 1951–2200. Virginia, USA: Willmann Bell; 1989. 105 p.
33. Littmann M., Espenak F., Willcox K. Totality. Eclipses of the Sun, 3rd ed. Oxford, New York: Oxford University Press; 2008. 358 p.
34. Steele J. M. Observations and Predictions of Eclipse Times by Early Astronomers. Springer-Science+Business Media. 2000. 321 p.
35. https://www.iausofa.org
36. Meeus J. Astronomical Algorithms second edition. Virginia, USA: Willmann Bell; 1998. 477 p.
37. Meeus J. Mathematical Astronomy Morsels. Richmond, Virginia: Willmann-Bell; 1997. 379 p.
38. Meeus J. More Mathematical Astronomy Morsels. Richmond, Virginia: Willmann-Bell; 2002. 429 p.
39. Meeus J. Mathematical Astronomy Morsels III. Richmond, Virginia: Willmann-Bell; 2004. 374 p.
40. Meeus J. Mathematical Astronomy Morsels IV. Richmond, Virginia: Willmann-Bell; 2007. 373 p.
41. Meeus J. Mathematical Astronomy Morsels V. Richmond, Virginia: Willmann-Bell; 2009. 373 p.
42. Montenbruck O., Pfleger T. Astronomy on the Personal Computer. 4th, Completely Revised Edition. New York: Springer; 2000. 300 p.
43. Duffett-Smith P. Astronomy with your Personal Computer, 2nd ed. New York: Cambridge University Press; 1997. 259 p.
44. Duffett-Smith P., Zwart J. Practical Astronomy with your Calculator or Spreadsheet, 4th еd. New York: Cambridge University Press; 2012. 216 p.
45. https://eclipse.gsfc.nasa.gov/
46. https://www.eclipsewise.com/
47. Mahooti M. Standards of Fundamental Astronomy. MATLAB Central File Exchange. Retrieved June 30, 2023. https://www.mathworks.com/matlabcentral/fileexchange/74523-standards-of-fundamental-astronomy
48. Eagle D. A MATLAB Implementation of Elements of Solar Eclipses. MATLAB Central File Exchange. Retrieved June 30, 2023. https://www.mathworks.com/matlabcentral/fileexchange/71132-a-matlab-implementation-of-elements-of-solar-eclipses
49. Mahooti M. Solar Eclipse. MATLAB Central File Exchange. Retrieved June 30, 2023. https://www.mathworks.com/matlabcentral/fileexchange/55279-solar-eclipse
50. Mahooti M. Local Circumstances of a Solar Eclipse. MATLAB Central File Exchange. Retrieved June 30. 2023. https://www.mathworks.com/matlabcentral/fileexchange/55609-local-circumstances-of-a-solar-eclipse
51. Carton W. H. C. The speed of the lunar shadow on Earth during solar eclipses. J. Br. Astron. Assoc. 2011;121(2):105–108.
52. Pasachoff J. M., Fraknoi A. Resource Letter OSE-1: Observing Solar Eclipses. American Journal of Physics. 2017;85(7); 485–494. http://dx.doi.org/10.1119/1.4985062
53. Zillman M. P. Astronomy Resources on the Internet 2022. 2022;:1–28. http://www.AstronomyResources.info/
54. https://www.eclipsewise.com/solar/SEprime/2001-2100/SE2022Oct25Pprime.html
55. Moore P., Rees R. Patrick Moore’s Data Book of Astronomy. New York: Cambridge University Press; 2011. 576 p.
Published
2023-11-02
Cited
How to Cite
Милованов, Ю. Б., & Dorokhov, V. L. (2023). Bessel’s method in study of solar eclipse influence on the ionosphere. Visnyk of V.N. Karazin Kharkiv National University, Series “Radio Physics and Electronics”, (39), 36-59. https://doi.org/10.26565/2311-0872-2023-39-04
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Original Article
