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Imagine you and your friend are on a huge sphere like the moon (radius r). You start at two oposite sides of the sphere and you move with a constant speed (v) yet in a completely random way (not the best example, but somehow like molecules). How long does it take until you and your friend meet eachother (the distance between you becomes less than d? And what about this question in just 2 dimensions (2 points moving on a circle)?

Interesting to know would also be a function that shows the probability of both friends having met eachother after a certain amount of time has passed. ( p(t) = ...)

I know that my question is similar to this problem: "Fastest way to meet, without communication, on a sphere?" but I couldn't find the answer to my question in the comments.

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Joba
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    Look at: http://math.stackexchange.com/questions/1214022/fastest-way-to-meet-without-communication-on-a-sphere/1218124#1218124 – Emilio Novati May 31 '15 at 19:34
  • It is a similar but yet different question since it's not about moving randomly but rather about finding the most efficient solution. And the case of both players moving randomly isn't covered. – Joba May 31 '15 at 19:36
  • What does movement with constant speed in a random direction mean? Can we imagine straight line (resp. geodetic) movement with a new direction chosen at random after every interval $\Delta t$, and then use the limit $\Delta t\to 0$? – MvG Jun 01 '15 at 07:18
  • Yes, that is exactly what I meant – Joba Jun 01 '15 at 07:26

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