Scientific Indian Astronomical Findings Of Aryabhatta

[JANASENA]

ECCENTRIC CIRCLE CONSTRUCTION

 

 

It was known that the planets move uniformly in circles round the Earth. If the motion appeared to be variable, it was due to the fact that the centres of such circles (ie; the eccentric circles) didnot coincide with the centre of earth. To illustrate the point (in the figure) 'E' represent the centre of the earth and the APM represent the sun's circular orbit or concentric; let A and P be the apogee and the perigee respectively. From EA, cut off EC equal to the radius of the sun's epicycle. With C as the centre and with the radius equal to EA, describe the eccentric A'P'S, cutting PA and PA produced at P' and A'. Here A' and P' are real apogee and perigee of the suns's orbit. Let PM and P'S be any two equal arcs measured from P and P'. The idea is that on the mean planet M and apparent sun is S move simultaneously from P and P' in the counter clockwise direction along the concentric and eccentric circles respectively. They move with the same angular motion and arrive simultaneously at M and S. In the figure below EM and CS are parellel and equal and hence MS is equal and parallel to EC. Let SH be drawn perpendicular to EM the angle PEM is the mean anomaly and the angle P'ES the true anomaly; the angle SEM is the equation of the center and is the readily seen to be + from P' to A' and - from A' to P'. thus as regards the character of the equation, the eccentric circle is quite right. We now turn to examine how far it is true as to the amount. 

Let the angle SEM be denoted by E and the angle PEM=the angle P'CS=teeta.

In the case of the sun, if the value of p be correctly taken, the error in the co-sfficient of the second term becomes +3'; similarly, in the case of the moon the corresponding error becomes + 8'. Again, if p/a=2e, the centre of the eccentric circle is the empty focus of the ellipse; (ie) the ancient astronomers assumed the planets to be moving with uniform regular motion round the empty focus. this was not a bad approximation. 
Also, ES=r=EH approximately.
Therefore r=a(1-p/a*cos teeta).
But in elliptic motion r=a(1-e cos teeta)

Hence the error is not very considerable here either. This is the way in which the ancient astronomers, both Greek and Indian, sought to explain the inequalities in the motion of the sun and the moon. In the case of the moon, these astronomers took the co-sfficient 2e-e^3/4=300' nearly; the modern value of it is 377' nearly. The reasons for this is that the moon was observed correctly only at the times of eclipses. during the eclipses or syzygis the evection term of the moon's equation diminishes(numericaly) the principal elliptic term by 76'

 

 

 

[JANASENA]

to be honest antha chadivina okkamukka ardham kala . can anyone expalin me in manual language ? 

[ChampakDas]

planets earth chutu thirugutuntayi...if they did all the time and if you take the contours of all of them you should see only one circle but wasn't like that...obtain contours were different enduku different ani explanation echadu em udni aada

[JANASENA]

planets earth chutu thirugutuntayi...if they did all the time and if you take the contours of all of them you should see only one circle but wasn't like that...obtain contours were different enduku different ani explanation echadu em udni aada

 

 

[ChampakDas]

ite em cheyali

 

[vadapav]

to be honest antha chadivina okkamukka ardham kala . can anyone expalin me in manual language ? 

[Maximus]