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

206 PAÑCASIDDHĀNTIKĀ IX.9 In the same way, the maximum of the Moon’s equation of the centre is 120' × 2.467 + (120' × 2.467 − 250) ÷ 235 = 296' + .3' = 296' .3. This too was determined by analysis of syzygies at the occurrence of eclipses. According to modern astronomy, the mean of the maximum equation of the centre of the Moon at true syzygies is 297'.3, a difference of only one minute! (At mean syzygies it is 303'.5). Epicyclic theory We shall now proceed to explain the epicyclic theory of planetary motion, used by this Siddhānta, and show how it works, by relating it to the modern theory, which latter is as follows: The earth and the other planets like Mercury etc. move round the Sun in eclipses, with the Sun at one of the two foci. The point nearest to the Sun on the ellipse is the perihelion, and the most distant, aphelion, which, from the point of view of the earth, are called the perigee and apogee, respectively. In the same manner, the Moon moves in an eclipse round the earth at one focus. This fact relating to the planets was first discovered by the European astronomer Kepler and is called Kepler’s First Law of planetary motion. The line joining the Sun and the planet (or the earth and the Moon), called the radius vector, sweeps equal areas in equal time. This is Kepler’s Second Law of planetary motion. From this it can be readily inferred that the motion of the planet is swiftest at perihelion (or perigee for the Moon) and lowest at aphelion. Kepler’s Third Law, that the square of the periodic time of the planets round the Sun is proportionate to the cube of the distance, is not wanted for our purpose here. The celebrated astronomer, Newton, showed that all the three laws follow from his Theory of Universal Gravitation, that all bodies attract one another with a force proportionate to their masses, and inversely proportionate to the square of the distance between them. But ancient Indian astronomers held the view that the earth is the centre round which the Moon, Sun and planets move. All the motion is in circles, and uniform. To explain the non-uniformity of the apparent motion caused by the equation of the centre, it was assumed that these bodies moved in circles called epicycles, (manda-vṛttas), the centres of which moved in circles round the earth as centre. In the case of the star-planets, another set of epicycles called epicycles of conjunction or śīghra-vṛttas were assumed, the effect of which is to convert helio-centric positions into geocentric. As the observers are on the earth, it is geocentric positions that are wanted, and therefore given, whether by Hindu astronomy or by modern western astronomy. The inaccuracy in the positions given by the former is due to unawareness of the elliptic motion and the inability to observe accu- rately for want of adequate instruments, with the result that small errors in the constants accumu- lated in course or time, to give large errors. It has been said that whether the heliocentric theory is adopted or the geocentric theory, the result in so far as this goes, is the same. Then, it may be asked, is it not better to adopt the geocentric theory which agrees with our perception? No. There is a clinching proof for the motion of the earth round the Sun, in the phenomenon of aberration which makes the Sun and star planets appear to be a little in advance of their real positions, the quantity being so small that very accurate measure- ment is required to find it, capable only by modern instruments. The heliocentric theory is also simpler, and satisfies the requirement of least assumption. Adhering to only circular motion, so satisfying to their minds, the ancients had to get the equa- tion of the centre, caused by the motion on the ellipse. They sought to achieve it in two ways, by using epicycles, as indicated already, or excentric circles, or both. How the ex-centric is used for the purpose is explained as follows: