Closest distance between two conics (ellipse,hyp.,par.) (1 Viewer)

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I have question for you,How calculate closest distance between two
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
I have the same type of problem and I am looking for a formula for the distance between two quadratic figures in [tex]\Re^n[/tex] but I haven't seen it anywhere.

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