O Son !

these horizons. The true altitude is equal to the value of the
geocentric angle subtended by the celestial arc of true altitude.
The angular values of an infinite number of arcs of a variety of
lengths that are bounded by the sides of this angle and which are
parallel to the so-called celestial arc as well as to one another, are
equal to one another and to the true altitude. Every pair of straight
lines that describe the other altitudes originate from the point
where the plumb level of the place of observation intersects the
horizon. The plane passing through the centre of the earth
perpendicular to its axis is called the equatorial plane. The circle of
intersection of the equatorial plane with the Earth is called the
equator. The place and the direction of the equatorial plane and
those of the equatorial circle never change; they divide the Earth
into two equal hemispheres. The value of the arc of declination
between the Sun’s center and the equatorial plane represents the
Sun’s declination. The whiteness before the apparent sunrise on
the line of apparent horizon begins two degrees of altitude prior to
the redness; in other words, it begins when the Sun ascends to an
altitude of 19° below the apparent horizon. This is a fact stated in
a fatwâ [1] . Non-mujtahids do not have the right to change the fatwâ.
It has been reported in Ibn ’Âbidîn (Radd-ul-muhtâr) and in the
calendar by M.Ârif Bey that some ’ulamâ have said that it begins
when the Sun is a distance of 20° (from the apparent horizon).
However, acts of worship that are not performed in accordance
with the fatwâ are not sahîh (valid).
The Sun’s daily paths are circles on the (imaginary inner
surface of the) celestial sphere and which are parallel to one
another and to the equatorial plane. The planes of these circles are
(approximately) perpendicular to the earth’s axis and to the
meridian plane, and intersect the horizontal planes of a given
location obliquely, which means that the Sun’s daily path does not
intersect the line of apparent horizon at a right angle. The azimuth
circle through the Sun is perpendicular to the line of apparent
horizon. When the Sun’s centre is on the observer’s meridian, the
circle of declination going through its center and the location’s
azimuthal circle coexist, and its elevation is at its daily maximum
[1] Fatwâ is a conclusive explanation wherein an authorized Islamic
scholar answers Muslims’ questions. Conditions to be fulfilled to be an
authorized Islamic scholar are explained in our publications, Belief
and Islam, The Sunni Path, and Endless Bliss (chapter 33 of second
fascicle and chapter 10 of third fascicle).
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