How to Calculate Planet Perturbation

Find the mass of the planet you want to calculate perturbation for. Label this "m1." For example, let's say you want to calculate the perturbation of Saturn's orbit. The mass of Saturn is 5.6846 x 10^26 kg, so m1 will be 5.6846 x 10^26 kg.

Find the mass of the sun. Label this "m2." The mass of the sun is 1.9891 x 10^30 kg, making m2 = 1.9891 x 10^30 kg.

Find the distance between the planet and the sun. Label this "r." Continuing with our example, the distance between the sun and Saturn is between 837 and 934 million miles, So r is equal to all values between 837 and 943 million miles.

Insert the above values into Newton's gravitational force formula, F = G [(m1 x m2)/ r^2], using 6.674 x 10^-11 N (m/kg)^2 for G (the constant of gravity). For our example, the formula will look like this:
F = 6.674 x 10^-11 N (m/kg)^2 [(5.6846×10^26 kg x 1.9891 x 1030 kg)/ 8.37x10^8 miles]
and
F = 6.674 x 10^-11 N (m/kg)^2 [(5.6846×10^26 kg x 1.9891 x 1030 kg)/ 9.34x10^8 miles].

Solve the equation to determine the perturbation value for your planet. The perturbation will be the values between the answer for the first equation and the answer for the second. For our example,
6.674 x 10^-11 (11.3072 x 10^56/8.37 x 10^8) = 9.016 x 10^37 m/kg^2
6.674 x 10^-11 (11.3072 x 10^56/9.34 x 10^8) = 8.0797 x 10^37 m/kg^2.

Thus, the perturbation of the standard orbit of Saturn is between 8.0797 x 10^37 m/kg^2 and 9.016 x 10^37 m/kg^2.