Topocentric Correction Explained

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Updated February 14, 2004

Topocentric Correction Explained

Results collected with Sky Scan's modest arc of four simple radio telescopes, has been used as a first point of observational reference by a leading meteoricist in interpreting what really happened vs. what was predicted for Leonids 2002. In his first note to us, Dr. Rob McNaught stated:

"After applying the topocentric correction (the peak time varies by a few minutes depending on your location on the Earth), the following geocentric peak times are derived for the two peaks. These geocentric peak times can then be compared with predictions."

The topocentric correction simply accounts for the fact the observer is approximately one Earth radius at position angle XYZ from the theoretical geocentric point (Earth's centre) used in predictions, which can be figured using relatively straightforward math and reduced to minutes and seconds (of time, that is).

In a subsequent e-mail exchange with the accommodating Dr. McNaught, who is with the Research School of Astronomy and Astrophysics, Australian National University, the writer (McCurdy) learned that while I had correctly surmised the leading (eastern) edge of Earth would encounter the sheet early, this is of rather lesser importance than latitude, more specifically ecliptic latitude, in which calculation an entirely different coordinate grid is applied to Earth than that to which we are accustomed. According to Dr. McNaught, these corrections can be as much as 11 minutes, early for stations in the south (in ecliptic terms) and late in the north. This is because the extreme points (the poles) are offset to the ecliptic by one Earth-radius, and the meteoroid stream is tilted (by 163 degrees) relative to the ecliptic. Whatever the new numbers, however, Edmonton was at that moment in time as firmly placed in the northwest as ever, resulting in a net time lag in both dimensions as the peak 'traveled' from the Earth's centre to our fair city. (McCurdy: late, as usual.)

This is not so different from time differences in observations of dynamic events like eclipses and occultations which travel a path along Earth's surface. In this case, a theoretical plane has traveled through Earth.

Ultimately, the calculations of when the peak of the meteoroid stream would have encountered Earth's centre will be compared to the predictions. Differences between the two will be rigorously assessed, with an improved theoretical model the inevitable result. But a crucial step in this path will have been the collection of solid data. Primitive radio observatories can apparently accomplish this objective, at least if there are several of them and they support each other's results to the degree that the Sky Scan array did.

 

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We gratefully acknowledge the financial support of the 

Edmonton Centre of the Royal Astronomical Society of Canada, Department of Physics (University of Alberta)

and the

Natural Sciences and Engineering Research Council of Canada

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