Improving the use of geodetic, geocentric, and topocentric coordinate systems in meteor astronomy and related tasks
DOI:
https://doi.org/10.15407/knit2023.05.069Keywords:
calculation precision for kinematic parameters of meteors, geocentric coordinate system, geodetic coordinate system, meteor, meteor height calculation, meteor trajectory projection onto earth map, video observations of meteorsAbstract
The problem of using the geodetic, geocentric, and topocentric coordinate systems in video observations’ processing of meteors and other dynamical objects in Earth’s atmosphere is considered. For meteor heights in a range of 0…200 km and arbitrary Earth’s ellipsoid latitudes, the following values are calculated: the difference between geodetic and geocentric latitudes, the meridian arc length corresponding to this shift, and the difference between geocentric and geodetic altitudes above the Earth’s ellipsoid. The carried-out calculations allowed us to conclude that the geocentric coordinate system is optimal for the calculation of kinematic parameters of meteors and trajectory measurements of ballistic objects at all-range altitudes and long distances between observation points without using horizontal coordinate systems as intermediate ones. This coordinate system is also used in the computation of heliocentric orbit elements of meteoroids. It is noted that the transition from the geocentric to the geodetic coordinate system is necessary for mapping the projections of the meteor trajectory to search for their remnants — meteorites. The reason is related to the difference between them, which can reach 11 arcmin for objects located at an altitude of 100 km above the level of the Earth’s ellipsoid, which corresponds to the shift of 21 km. The difference between geocentric and geodetic altitudes is inessential and amounts to half a meter at an altitude of 100 km and slightly more than one meter at 200 km and can be neglected in meteor calculations and most ballistic tasks. These considerations formed the basis for our proposed alternative vector method for the inverse transition from geocentric to geodetic coordinates and the numerical solution of the corresponding equation. In order to decrease the calculation time for mass processing, it is recommended to change the numerical processing of the inverse task by fitting it with elementary functions. An example of fitting is given. It brings to the maximal deviation in latitude near one arcmin, which corresponds to approximately 35 meters. It is noted that such precision is satisfactory for meteor measurements, but for ballistic problems, the accuracy of fitting can be improved.References
Brown P.G., Assink J.D., Astiz L. and 30 more… A 500-kiloton airburst over Chelyabinsk and an enhanced hazard from small impactors. Nature, Vol. 503, Iss. 7475. P. 238-241 (2013).
https://doi.org/10.1038/nature12741
Gural P. The California All-sky Meteor Surveillance (CAMS) System. Proceedings of the IMC, Armagh, P. 28-31 (2010).
Jenniskens P., Gural P.S., Dynneson L., Grigsby B.J., Newman K.E., Borden M., Koop M., Holman D. CAMS: Cameras for Allsky Meteor Surveillance to establish minor meteor showers. Icarus,.216, P. 40-61 (2011).
https://doi.org/10.1016/j.icarus.2011.08.012
Kartashova A., Golubaev A., Mozgova A., Chuvashov I., Bolgova G., Glazachev D., Efremov V. Investigation of the Ozerki meteoroid parameters. Planetary and Space Science, 193. ID. 105034 (2020).
https://doi.org/10.1016/j.pss.2020.105034
Kozak P.M. Analysis of the methods and precision of determination of the equatorial coordinates in digital reducing of TV observations of meteors. Kinematics and Physics of Celestial bodies, Vol. 18, No. 5. P. 471-480 (2002).
Kozak P.M. A vector method for the determination of trajectory parameters and heliocentric orbit elements of a meteor in TV observations. Kinematics and Physics of Celestial bodies. Vol. 19. No 1. P. 62-76 (2003).
Kozak P., Stariy S. Determination of equatorial coordinates of bolide from observations with stationery low-sensitive home guard video camera. Bulletin of Taras Shevchenko National University of Kyiv. Astronomy, V. 62, No. 2. P. 6-10 (2021).
https://doi.org/10.17721/BTSNUA.2020.62.16-20
Kozak P., Rozhilo O., Kruchynenko V., Kazantsev A., Taranukha A. Results of processing of Leonids-2002 meteor storm TV observations in Kyiv. Advances in Space Research, Vol. 39. Iss. 4. P. 619 - 623 (2007).
https://doi.org/10.1016/j.asr.2005.08.014
Kozak P.M., Lapchuk V.P., Kozak L.V., Ivchenko V.M. Optimization of video camera disposition for the maximum calculation precision of coordinates of natural and artificial atmospheric objects in stereo observations. Kinematics and Physics of Celestial Bodies. Vol. 34. Iss. 6. P. 314 - 327 (2018).
https://doi.org/10.3103/S088459131806003X
Kozak P.M., Watanabe J. Meteors with extreme beginning heights from observations with high-sensitivity super-isocon TV systems. Mon. Not. R. Astron. Soc., Vol. 497. Iss. 4. P. 5550 - 5559 (2020).
https://doi.org/10.1093/mnras/staa2183
Kozak P.M., Watanabe J. Upward-moving low-light meteor - I. Observation results. Mon. Not. R. Astron. Soc., Vol. 467. Iss. 1. P. 793 - 801 (2017).
https://doi.org/10.1093/mnras/stx008
Kozak P.M., Zlochevskyi Y.E., Kozak L.V., Stariy S.V. Problems of videorecords processing of bright bolides and falling space vehicle remnants detected with the low-sensitive home video cameras in bad observational conditions. Space Science and Technology, Vol. 27, No. 6. P. 85-97 (2021).
https://doi.org/10.15407/knit2021.06.085
Moritz H. Fundamental geodetic constant. Proc. of the IAG XVII Gen. Assembly IUGG/IAG. - Canberra, 34 p. (1979).
Serapinas B.B. Geodetic bases of maps: Tutorial. Publishing of Moscow State University. 2001. 133 p.
