This questions concerns the longitudinal aspect of the Equation of Time, also called the Equation of the Center. In some sources the equation looks like the following:
$nu - M = 2varepsilon sin M$ (1)
where $nu$ is the True Anomaly of the Sun's position from the Earth, $M$ is the Mean Anomaly, and $varepsilon$ is the eccentricity of the Earth's orbit (0.0167). $nu - M$ is the difference between the Sun's actual angle and the and the angle that would exist if the Earth's orbit were circular.
Other sources have a first-order approximation that looks like the following:
Time deviation (minutes) = $-7.655 sin d$ (2)
where d is the day of the year.
My difficulty is reconciling these two equations. None of the sources actually make this connection explicit. I assume that the difference has to do with converting angles and times, and I have tried various approaches to making the numbers work out, without avail. I would appreciate it if someone could tell me how the value of -7.655 minutes is derivable from $2 varepsilon$ and or point me at a resource that demonstrates the connection between them.
(Note I realize that both (1) and (2) are approximations. At this stage, I am trying to understand the situation in its simplest form before adding refinements.
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