In Indian Astronomy, the great Jupiter – Saturn perturbation, is calculated using the formula given below.
The Kali year, ky, is calculated and 4660 is deducted from it to get the kyb, the kali year balance. Its Bhujamsa,x is calculated using the Equation of Bhuja and then its Bhujajya ( Sin x ) is calculated to get the value of Manda Phala, a.
Mathematically, it can be written as
Y, (Year of Birth) + 3102 = ky, the Kali Year of Birth
kyb ( kali year balance ) = ( ky – 4660 )
x = kyb*360/918
b, bhujajya = sin(x)
Since the duration is 918 years and perturbation amplitude is 1187 seconds,
Manda Phala, a = sin(x) * 1187
( Example – My year of birth is 1955. Add 3102 and we get 5057. Less 4660 is 397. 397*360/918 is 155.6 and its Bhujamsa is 25 degrees roughly ( 180-155). So Sin (25 ) is 0.41. Manda Phala, therefore is 0.41*1187 seconds or Vikalas. )
This value, Manda Phala, a is added to Jupiter’s mean longitude, if Jove’s long is less than 180 and subtracted if Jove’s long is greater than 180.
In the West, this discovery is attributed to Laplace. The duration of the perturbation of 918 years is known as Laplace period. Its amplitude of .332 degrees is similar to the Indian value of 1187 seconds.
Laplace gives the equation 2 nj – 5 ns, bringing to light the 5:2 Resonance in the orbits of the two celestial giants. 2 revolutions of Saturn = 5 revolutions of Jupiter = 60 years !