Authors: Alexis Zaganidis
In the present article, we derive an analytic formula of the Apparent Daytime Length Ratio with respect to the Earth's orbit angle $alpha(t)$ between the orbital position of the Earth's perigee and the orbital position of the Earth at a given $t$, with respect to the latitude, with respect to the Earth's axial tilt $epsilon$ and with respect to the solar apparent diameter $theta_{AS}$. That formula is simplified a lot under the approximation of a punctual Sun ($theta_{AS}=0$) and we name it the Punctual Daytime Length Ratio. The first steps for the derivation of the Apparent Daytime Length Ratio is to consider the parametric curve on the Earth's surface satisfying a tangent sunlight with respect to the parametric angle $theta$, the Sunlight obliquity angle $Omega$ (the equatorial declination of the Sun) and with respect to a solar apparent diameter $theta_{AS}$. The second part of the present article is about the precise numerical derivation of the Zenith Time Angle and the precise numerical derivation of the Equation Of Time in the following both cases : at the Meridian Plane $S_{JS}$ parallel to the sunlight at the exact time of the June Solstice, and at the Meridian Plane $S_{ME}$ parallel to the sunlight at the exact time of the March Equinox. For both Zenith Time angles and for both Equations Of Time, there is a tiny latitude dependency/variation of $17$ seconds.
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[v1] 2023-10-12 13:00:00
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