Find the minimal distance between any point on the sphere

In summary, the minimal distance on a sphere is the shortest distance between any two points on the surface of the sphere. It is calculated using the Great Circle Distance formula and is always a positive value. The size of the sphere does affect the minimal distance, with larger spheres having longer distances. The minimal distance on a sphere is used in various real-world applications, such as navigation, satellite communication, and geospatial analysis. It takes into account the curvature of the Earth to determine the shortest distance between two locations on its surface.
  • #1
helix999
32
0
How can we find the minimal distance between any point on the sphere whose centre is 2,1,3 and radius is 1 and any point on the sphere centred at -3,2,4 and radius is 4?


is there any formula for finding this minimum distance ?
 
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  • #2


find the distance between the centres, and subtract the sum of radii of the spheres...
 
  • #3


thnx aniketp...that was helpful...i got my answer
 
  • #4


no problem, but i hope you understood WHY this works.
 
  • #5


well...yes...i have a math exam tomorrow...have to finish a LOT of things
 

Related to Find the minimal distance between any point on the sphere

1. What is the definition of minimal distance on a sphere?

The minimal distance between any two points on a sphere is the shortest distance along the surface of the sphere between those two points.

2. How is the minimal distance calculated on a sphere?

The minimal distance on a sphere is calculated using the Great Circle Distance formula, which takes into account the radius of the sphere and the angles between the two points.

3. Can the minimal distance on a sphere be negative?

No, the minimal distance on a sphere is always a positive value. Negative distances are not possible on a sphere because it is a closed surface with no inside or outside.

4. Is the minimal distance on a sphere affected by the size of the sphere?

Yes, the minimal distance on a sphere is affected by the size of the sphere. A larger sphere will have a longer minimal distance between two points compared to a smaller sphere with the same two points.

5. How is the minimal distance on a sphere used in real-world applications?

The minimal distance on a sphere is used in many real-world applications, such as navigation systems, satellite communication, and geospatial analysis. It helps in determining the shortest distance between two locations on the Earth's surface, taking into account the curvature of the Earth.

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