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Planetary Planning

Fortunately, you have a model that is capable of calculating the fuel storage requirements, as long as you know the average distance between points on the surface of the planet.

Additionally, the model does not require the Geodesic distance (i.e. the distance betwen poles would be the diameter, and not the length of the arc).

You can assume that the planet is a perfect sphere. What is the distance between two points on the planet?

Note: for simplicity, use the radius of the planet as the distance unit.

Hint A Monte Carlo approach for this problem may be helpful to get an idea of the result. To do this, use that the multivariate normal distribution is spherically symmetric: if X, Y, Z have a normal distribution respectively, (X, Y, Z)/|(X, Y, Z)| has uniform distribution over the sphere.