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ellipse in space.

orbit first : r = (p1)/(1+epsilon1*cos(theta1))

second orbit : r = (p2)/(1+epsilon2*cos(theta2))

the relation between two ellipse is some euler angles call them

first angle :a1

second angle :b1 (these three euler angles)

third angle :c1

(taking in account they have same focus :the sun)

? symbolic solution for this problem

? how solve this with approximation techniques.

what when orbit is not closed:hyperbole,parabole