There is of course some relation to the apparent position of the sun. But the apparent position of the moon at the moment of sunset is of much bigger importance. Please note that the moon’s orbit is significantly inclined with respect to the plane in which the Earth circles around the sun. So it may happen that the moon will set much more to the north or to the south of the actual sunset point. Additionally, the effects of the year’s seasons will add to this effect. So there might be some months when the extremes of these effects will cumulate, and other months when they will cancel each other out.
Please imagine the following scenarios:
1. It is winter in the northern hemisphere and the moon’s declination (height above the celestial equator) is minor than the sun’s: In this case the southern hemisphere is favoured for observing the crescent, and the apex of the Hilal sighting curve will be in very southern latitudes.
2. It is summer in the northern hemisphere and the moon’s declination (height above the celestial equator) is major than the sun’s: In this case the northern hemisphere is favoured for observing the crescent, and the apex of the Hilal sighting curve will be in very northern latitudes.
3. It is winter in the northern hemisphere and the moon’s declination (height above the celestial equator) is major than the sun’s: In this case the apex of the Hilal sighting curve will be close to the equator.
4. It is summer in the northern hemisphere and the moon’s declination (height above the celestial equator) is minor than the sun’s: In this case the apex of the Hilal sighting curve will be close to the equator, too. So far, so good. Now some long-time effects have to be considered, too. The moon’s orbit is not constant, instead it is “tumbling around” and it is also changing its inclination with respect to the plane in which the Earth circles around the sun. So there will be several years when the first of the above scenarios will prevail. After some years this will slowly change and another scenario will prevail, and so on. After a period of around 18.6 years, this “tumbling around” has once completed and the whole will repeat again in a similar fashion. Sorry, this is only a very “raw” explanation, but I hope that it will make clear why the apex of the visibility parabola may be found at very extreme latitudes in some years, and also very close to the equator during other years. By the way, this is also a contra-argument against ittihâdu l-matâli`, and even a contra-argument against using observation data from the same meridian n the southern hemisphere for the northern hemisphere (and vice-versa). Observation conditions on the same meridian in the southern hemisphere will in almost all cases vary greatly from observation conditions in the northern emisphere.
Please imagine the following scenarios:
1. It is winter in the northern hemisphere and the moon’s declination (height above the celestial equator) is minor than the sun’s: In this case the southern hemisphere is favoured for observing the crescent, and the apex of the Hilal sighting curve will be in very southern latitudes.
2. It is summer in the northern hemisphere and the moon’s declination (height above the celestial equator) is major than the sun’s: In this case the northern hemisphere is favoured for observing the crescent, and the apex of the Hilal sighting curve will be in very northern latitudes.
3. It is winter in the northern hemisphere and the moon’s declination (height above the celestial equator) is major than the sun’s: In this case the apex of the Hilal sighting curve will be close to the equator.
4. It is summer in the northern hemisphere and the moon’s declination (height above the celestial equator) is minor than the sun’s: In this case the apex of the Hilal sighting curve will be close to the equator, too. So far, so good. Now some long-time effects have to be considered, too. The moon’s orbit is not constant, instead it is “tumbling around” and it is also changing its inclination with respect to the plane in which the Earth circles around the sun. So there will be several years when the first of the above scenarios will prevail. After some years this will slowly change and another scenario will prevail, and so on. After a period of around 18.6 years, this “tumbling around” has once completed and the whole will repeat again in a similar fashion. Sorry, this is only a very “raw” explanation, but I hope that it will make clear why the apex of the visibility parabola may be found at very extreme latitudes in some years, and also very close to the equator during other years. By the way, this is also a contra-argument against ittihâdu l-matâli`, and even a contra-argument against using observation data from the same meridian n the southern hemisphere for the northern hemisphere (and vice-versa). Observation conditions on the same meridian in the southern hemisphere will in almost all cases vary greatly from observation conditions in the northern emisphere.
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