पञ्चसिद्धान्तिका (आचार्य वराहमिहिर - सूर्य, रोमक, पौलिश, वासिष्ठ एवं पितामह सिद्धान्त)

86 PAÑCASIDDHĀNTIKĀ IV. 15 the motion of bodies like the Sun, Moon, planets etc. Actually the stars are at widely different dis- tances from us and are moving in various directions at speeds of several miles per hour. But with all this they appear to be, and can be represented, as being fixed on a sphere, because of their enormous distances from us, so much so that we are practically viewing the same sphere as people several generations ago did. But the ancients believed that the stars were luminous bodies fixed on the under-surface of a sphere of radius only sixty times that of the orbit of the Sun (actually the earth) round the earth, with the centre of the sphere at the earth's centre. This sphere seems to be rotating about once a day, by the actual rotation of the earth, about once a day. Fig. IV. 4 On this sphere (Fig. 4) there is an important great-circle called the ecliptic (Krānti-vṛtta) (EC), marked by the twenty-seven asterisms, Aśvinī etc., on which the Sun (S) moves, (actually appears to move on account of the motion of the earth), completing a revolution once a year. The Moon and the planets move in orbits inclined to the ecliptic at small angles. Their longitudes are reckoned along the ecliptic from a fixed point called the first point of Meṣa or Aśvinī. Latitudes are measured on secondaries to the great circle, meeting at a point called the pole of the ecliptic (Kadamba). Another great circle called the Celestial Equator (AOB) cuts the ecliptic at r, called the First point of Aries or Vernal Equinox point, which, instead of being fixed, has a slow westward motion on the ecliptic. At the period of the authors of the first Siddhāntas, this point coincided with the first point of Meṣa, this being the reason why that particular point was taken by them for reckoning from. The angle between the two great circles (SrR) is called the Obliquity of the ecliptic. It was about 24° at the time of Varāhamihira, and now it is about 23° 27'. The declination (SR,) (Krānti) of a body like the Sun, is measured along the secondary passing through the body, (NPSRSP,) called the Declina- tion circle, all the secondaries meeting at the celestial poles, the poles of the stellar sphere, (SPNP), on the axis joining which the sphere apparently rotates. The declination is found by solving the spherical right angled triangle SrR. Spherical triangles were in general solved by the Hindu astronomers using the properties of plane right angled triangles formed by the sections of the sphere along the great circle arcs forming the spherical triangle (The