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

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In summary, the conversation discusses calculating the closest distance between two ellipses in space using the equations for the orbits and the relationship between the two ellipses. The question is posed about finding a symbolic solution and using approximation techniques, and the possibility of the orbits not being closed is also mentioned. Another person mentions a similar problem of finding the distance between two quadratic figures in n-dimensional space.
  • #1
petra
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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
 
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  • #2
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.
 

1. What is the formula for finding the closest distance between two conics?

The formula for finding the closest distance between two conics (ellipse, hyperbola, or parabola) is given by the distance formula:
d = √((x2-x1)^2 + (y2-y1)^2)

2. How do I determine which conics are closest to each other?

To determine which conics are closest to each other, you can calculate the distance between the centers of the conics using the formula mentioned above. The conics with the shortest distance between their centers will be the closest to each other.

3. Can the closest distance between two conics be negative?

No, the closest distance between two conics cannot be negative. The distance between two points is always a positive value, therefore the closest distance between two conics will also be a positive value.

4. How do I find the closest distance between an ellipse and a parabola?

To find the closest distance between an ellipse and a parabola, you can first determine the closest distance between the centers of the two conics. Then, you can use the distance formula to find the distance between a point on the ellipse and a point on the parabola. Finally, you can subtract the radii of the two conics from this distance to get the shortest distance between the two curves.

5. Is there a graphical method for finding the closest distance between two conics?

Yes, there is a graphical method for finding the closest distance between two conics. You can plot the two conics on a graph and visually identify the points where the two curves are closest to each other. Then, you can use the distance formula to calculate the exact distance between these points. However, this method may not always be accurate and it is recommended to use the formula for a more precise result.

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