Just a day ago, I was browsing r/geography, as one usually does when bored, and stumbled upon a post about the closest embassy to its home country. Then I saw this comment by u/DontPoopInMyPantsPlz:
On the other hand, the embassy of Spain in New Zealand is the contender for the furthest embassy.
I figured this would be a fun problem to get a definitive answer to by writing a simple Python script for.
I used the Wikipedia page for List of National Capitals to compile a list of all capitals in the world, and then used the Wikipedia page for each individual capital to get its coordinates. Note that the Wikipedia page contains territories and also states whose sovereignty is not recognized by all other nations -- the significance of this sentence will become apparent later. I just used Wikipedia's list of capitals for this post, though I elected to ignore Tokelau because it doesn't have a central capital.
Once I got a list of all capitals, I used the Haversine formula to calculate the distance between the two capital cities. The Haversine formula isn't guaranteed to be more than 0.5% accurate, a fact which conveniently requires citation on Wikipedia. So, for all the distances that fell within 0.5% of the top result, I used Vincenty's formulae to verify the result. Then, I went down the list and saw what two nations actually have mutual diplomatic missions.
Now, I understand that consulates exist and that embassies aren't necessarily in the (de facto) capitals, but I wasn't going to make this too hard on myself.
After running my script, here are the top five results for the two farthest capitals.
It shouldn't surprise you that all of these capital cities are almost antipodes of each other. Assuming a smooth Earth, the farthest two points on Earth can be is 20038 km. That means that the distance between Taipei and Asunción is a staggering 99.52% of the maximum possible distance.
Luckily enough for us, Taiwan and Paraguay do have embassies to each other located in Taipei and Asunción. If we use the exact coordinates for their embassies, we get a distance of 19934 km. I got curious and looked up flights from Asunción to Taipei. The flight will take around 45 hours and will have two stops. Their diplomats better ask for first-class accommodations or else they will certainly not enjoy this arduous journey.
Unsurprisingly the Pitcairn Islands neither sends nor receives any diplomatic missions. So second place belongs to Spain and New Zealand. Indeed, u/DontPoopInMyPantsPlz was only slightly wrong. Upon getting these results, I logged back on Reddit to comment about my findings, only to discover that AI had beaten me by a few hours. At least I had fun typing in coordinates for 243 capitals.
Feel free to contact me at aryan.abed[at]pm.me