XMM-Newton Science Analysis System


eposcorr (eposcorr-3.13) [xmmsas_20230412_1735-21.0.0]

Some spherical geometry

eposcorr calculates angular distances directly using spherical trigonometry. In particular the following is used to calculate the angular distance, $\theta$, between two sources (labeled 1 and 2).

  $$\cos( \theta) = \sin(\delta_1) \sin(\delta_2) + \cos(\delta_1) \cos(\delta_2) cos(\Delta\alpha),$$ (9)

where $\delta$ refers to the declination of a source and $\Delta\alpha =\alpha_1 - \alpha_2$, the difference of the right ascension of the two sources.