सिद्धान्तशिरोमणि: गणिताध्याय (भास्कराचार्य - ग्रहगणित, मध्यमाधिकार व स्पष्टाधिकार सटीक)

363
Comm. In figure 71, the eclipsing body is just con-
tacting the eclipsed body. Taking the case of a lunar
eclipse, the latitude then of the Moon is evidently P+r
ie. β=P+r holds good at the moment of first con-
tact. (C) is the cross-section of the shadow-cone at the
lunar orbit and (M) is the Moon.
(fig. 72), CB+AM-CM=CB+AB+
BM-CM=AB+(CB+BM)-CM=
AB+CM-CM=AB
∴ P+r-β=AB=Sthagita. Thus
Sthagita gives the portion of the
diameter of the eclipsed body which
is shadowed. The eclipsed body is
termed the Chādya, the eclipsing
body as the Chādaka and P+r as
the Manaikya-ardha ie. half the
sum ofthe diameters of the eclipsing
and eclipsed bodies.
Fig. 72
When the Sthagita exceeds the diameter of the
eclipsed body the eclipse is evidently total ie., when
P+r-β>2r ie. P-r>β.
Verse 12. Duration of the eclipse and duration of
its totality.
Sthiti-Khanda = √(P+r)²-β² × 60 = ½ Duration of
—————————————— the eclipse
m₁-s₁
Marda-Khanda = √(P-r)²-β² × 60 = ½ Duration of
—————————————— totality
m₁-s₁
where P is the radius of the shadow-cone, r the radius of
the Moon's disc, β its latitude taken to be constant during
the eclipse, m₁ and s₁ the daily motions of the Moon and
Sun respectively.
Comm. (1) The time between the moment of first
contact and the middle of the eclipse or the moment of