Not sure if this helps, but in RL celnav the Sun and Moon are considered to be rising or setting when their "upper limb" (the top) is just on the horizon. This occurs when the bodies are actually 0°50' below the horizon. This is because atmospheric refraction* at the horizon amounts to about 34' and the semi-diameter (half of the diameter) is about 16'. Add those together and when the center of the body is calculated to be at an altitude of -0°50', the upper limb should just be touching the horizon.
*Refraction can be calculated using the formula -0.0167°/tan(H+7.32/(H+4.32)) ...where H = altitude in decimal degrees.
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