Imagine we have a sphere. And inside the sphere there are two points. Now we have an arc that is connecting these two points and it is said that arc that goes through the center of the sphere is the shortest distance between two points. For example a plane flying from point a to point b has to go little bit north/south for the shortest distance.
I asked my colleagues about this problem and all of them replied: Oh, I just solved some numerical problems and I totally understand it.
I solved a quite of them myself, but I still doesn't understand why.
I would really appreciate an explanation.
Answer
Please refer to: https://en.wikipedia.org/wiki/Great-circle_distance
In astronomy, it should be treated as the orthodromic distance, since you are talking about planets. As the link above has pointed out, this orthodromic distance is the shortest distance between two points on the surface of a sphere, measured along the surface of the sphere (as opposed to a straight line through the sphere's interior, which you thought). It is also called the great-circle distance.
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