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In relation to the image above, although the topic relates to math, how can I visualise the situation described in the final equation presented, i.e., the declinations, ascensions, solar and lunar radii. A diagram would be of great help.

  • $\begingroup$ A solar eclipse happens when the point on Earth where you are, the center of the Moon, and the center of the Sun, fall on one straight line. The equation is just saying "the angle between the sun/moon (from your point of view) has to be small". $\endgroup$ – Fattie Jul 11 '16 at 14:08

For a small region not far from the equator, an equirectangular projection will do. If you want celestial north to be up, declination should increase from bottom to top, and right ascension should increase from right to left. To correct the aspect ratio, scale the RA axis by cos(dec). Then the sun and moon are circles of the respective angular radii, without the RA scale factor.

In the equation for $z$, $\Delta$ is the declination of the sun, $\delta$ is the declination of the moon, and $a$ is the difference in their right ascensions.

visualization of partial solar eclipse

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