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I would like to know how I can estimate the tangential and cross component of the galaxy's shear using Gnomonic projection of the right ascension and declination the galaxies relate to the center of galaxy cluster and estimate?

Edit. Shear is the second order moment of a galaxy's surface brightness. You can find more on the topic in the following wiki on weak lensing.

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  • $\begingroup$ Please elaborate what you mean by shear? When I read the title I thought about the shear in the galactic velocity fields and Oort's constants ... $\endgroup$
    – Walter
    Sep 5, 2014 at 9:59
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    $\begingroup$ @Walter shear is the second order moment of galaxy's surface brightness. You can find more exclusive explanation here $\endgroup$
    – Dalek
    Sep 5, 2014 at 10:26
  • $\begingroup$ I am not sure I understand what you are after: Do you mean you want to project the movement vectors of all galaxies in a galaxy cluster onto a plane which each galaxy then having a tangential and a radial component (the 3rd dimension we lost by projection), as well as a brightness. Once you have that, you want to somehow calculate the 2nd derivative of the brightness changes. Is this understanding correct? $\endgroup$
    – B--rian
    Mar 11, 2021 at 12:42
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    $\begingroup$ So you basically are asking how to derive the components of optical transfer matrix, in particular the off-diagonal components, of the media between us and the observed galaxy (assuming some kind of ideal galaxy forms the original undistorted image)? $\endgroup$ Mar 11, 2021 at 12:43
  • $\begingroup$ @planetmaker Your interpretation does probably make more sense :-) $\endgroup$
    – B--rian
    Mar 11, 2021 at 12:46

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