ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

APPARENT MOTION OF THE SUN AND MOON 149 Again if p/a=2e, what is the centre of the eccentric circle is the empty focus of the ellipse or that the ancient astronomers practically took the planets to be moving with uniform angular motion round the empty focus. This was not a bad approxi- mation. Also ES=r=EH approximately, ∴ r=a ( 1 - p/a cos θ ) but in the elliptic motion r=a (1-e cos θ).* Hence the error is not very considerable here also. This is the way in which the ancient astronomers, both Greek and Hindu, sought to explain the inequalities in the motion of the Sun and the Moon. In the case of the Moon, these astro- nomers took the coefficient 2e - e³/4 = 300' nearly; the modern value is 377' nearly. The reason for this has been pointed out to be that the Moon was observed correctly only at times of eclipses. At the eclipses of syzygies, the evection term of the Moon's equa- tion diminishes (numerically) the principal ecliptic term by about 76'. We have thus far explained the idea of planetary motion of the ancients under the eccentric circle costruction. The same, however, is explained under the epicyclic construction. Let AMP be the circular orbit of the Sun, having E the centre of the earth for the centre. (Fig. 16) Let the diameter AEP be the apse line. A the apogee and P the perigee. Let M be the mean position of the Sun in the orbit. With M as the centre, describe the epicycle UNS. Let EM cut the epicycle at N and U. Now the construction for finding S the apparent Sun is thus given:— Fig. 16 Make ∠UMS= ∠MEA, the arc US is measured clockwise whereas the arc A to M is measured counterclockwise. From this construction MS is parallel to EA. If EC be measured equal to MS, the radius of the epicycle, along EA to-

• Godfray's Astronomy, p. 149.