Minimum distance between ellipses

In summary, the conversation discusses the problem of computing the minimum distance between two non-interacting bodies on elliptical orbits. The problem can be addressed numerically using a conjugate gradient method, but there is a question about whether an analytical approach exists that could simplify the problem and speed up computation. The question has been posted on the Celestial Mechanics Forum with no response yet. There is also a clarification that the problem involves two ellipses in 3D with one shared focus.
  • #1
Coelum
97
32
Forum,
I'm addressing the problem of computing the minimum possible distance between two non-interacting bodies on elliptical orbits. From a general point of view, it looks like a minimization problem of a function of two variables, e.g. in the domain [0,2*pi)*[0,2*pi). This problem can be numerically addressed in a standard fashion, e.g. by a conjugate gradient method. But I wonder if an analytical approach exists that can simplify the problem - maybe reducing it to unidimensional - and significantly speed-up the computation.
I have posted the some question on the Celestial Mechanics Forum - no reply so far.
 
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  • #2
If the path is ellptical, wouldn't it just be a straight line representing the minor axis of the ellipse?
 
  • #3
I guess I've not been clear enough: I'm dealing with two ellipses (e.g., representing the paths of two minor planets around the sun) in 3D. Of course, you may assume that they share one of the foci.
 

FAQ: Minimum distance between ellipses

1. What is the minimum distance between two ellipses?

The minimum distance between two ellipses is the shortest distance between any two points on the two ellipses. It can be calculated using mathematical equations and varies depending on the size, shape, and orientation of the ellipses.

2. How is the minimum distance between ellipses calculated?

The minimum distance between ellipses can be calculated using mathematical formulas such as the distance between two points and the distance between a point and an ellipse. These formulas take into account the coordinates and radii of the ellipses to determine the minimum distance.

3. Can the minimum distance between ellipses be negative?

No, the minimum distance between ellipses cannot be negative. It is always a positive value because it represents the distance between two objects and cannot be less than zero.

4. What factors affect the minimum distance between ellipses?

The size, shape, and orientation of the ellipses are the main factors that affect the minimum distance between them. The larger the ellipses, the greater the minimum distance will be. Similarly, the more elongated or tilted the ellipses are, the larger the minimum distance will be.

5. Is there a way to find the minimum distance between ellipses without using equations?

No, the minimum distance between ellipses cannot be determined without using equations. However, there are computer programs and software that can calculate it for you, making it easier and more efficient to find the minimum distance between ellipses.

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