You are happy with the distances between California and Japan, so if I asked you what is the distance between say San Francisco airport (SFO) and Tokyo airport (HND), what is this figure? Where did your information come from? Why do you trust this source? If for some reason you can't give me that specific figure, then give me an alternative trustworthy figure (plus source) for any two places in California and Japan.
Follow up question, can you explain how you check that distance on Bing maps? i.e. can you talk me through how I would do that. Obviously I could use the "red pin" method, but you have some doubts about that, so how else can this be done?
You can fly nonstop from LA to Tokyo in like 10-11 hours.
If you know what type of plane you are on you can estimate the top speed of the plane with information online.
In addition I know a couple of people who work on planes who have corroborated the speed information about the planes found online.
In addition each plane is equipped with something that can measure speed.
If you are in a large passenger plane and not allowed into the cockpit to see the speedometer you can ask a flight attendant what your cruising speed is.
You take your miles per hour speed estimate and multiply the number of hours spent flying to come up with a distance estimate.
You can do the same for shipping times although I've never taken a ship to Japan. I trust that hundreds of thousands of people who have done international shipping have done this.
I take my hat off to you. You've built an entire belief system based on a staggeringly varied set of criteria for your standards of evidence.
You won't believe a shred of evidence from the official Bing documentation because anybody could have written or changed it, whereas in reality it is likely that only a few dozen people in the world will have the necessary security permissions to permit that and they will all be subject to scrutiny from their peers and line managers, so the likelihood that this documentation is anything other than what Microsoft intend it to to be is non-existent. Which leaves you with two possibilities, either it is correct or Microsoft are deliberately lying to you for "reasons".
By that standard, you can't ever believe anything anyone has ever written anywhere because anyone could have written it or changed it.
But when it comes to the distance from LA to Tokyo, you can just get the necessary information to work it out online or from a couple of people you know or you just ask a flight attendant (so where do they get their information from?). This is your standard of evidence gathering now is it?
You claim a non-stop flight time between 10 and 11 hours between the two airports. I just checked flightradar24 and quickly found a couple of examples, one was just over 11 hours, the other 9 hours 15. They both use a Boeing 777 which has a cruise speed in the range mach 0.84-0.89. Now cruise speed varies with altitude and temperature and ATC may assign a common speed for separation in busy periods, so the aircraft might not be able to fly the speed they ideally want, but lets work some approximate figures out.
Cruising at 40,000 feet, mach 0.84 equates to 554mph and with a 9 hour 15 flight time, that gives a distance of 5,125 miles.
Cruising at 30,000 feet, mach 0.86 equates to 583pmh and with an 11 hour flight time, that gives a distance of 6,413 miles.
So that's 5,769 miles +/- 644 miles, i.e. +/- 11%
Plus or minus eleven percent! That's a level of accuracy you're comfortable with? The answer is certainly correct, the actual distance is 5487 miles, so well inside the range just calculated.
Now lets have a look at Bing maps. You've used this for 15 years, never knew it had a distance measuring tool ("red pin"). Took me all of 5 minutes to discover that and I'm not a Bing user.
You start off saying you trust Bing maps, now you've backtracked somewhat and you trust just the driving and walking distances. Out of interest, how do you measure walking distances, surely not with a GPS device? But Bing maps covers the whole world, most of which is covered in water, so what you are really saying is you trust Bing maps for the 30% of the earth which is dry land, but only the bits which have marked roads or tracks you can measure.
You claim without offering any evidence whatsoever that Bing maps distances (i.e. the ones you trust) are based on real world distances which include taking elevation into account. Where do you get this from?
I can't speak for Bing, since it is closed source, however in OpenStreetMap, roads are defined via paths joining nodes, so A to B to C etc. and the nodes are defined in terms of their latitude and longitude. Elevation is not defined although you could theoretically get elevation data from other sources. Various people have asked how these route distances are calculated and the consensus seems to be that using Haversine or Vincenty between pairs of nodes and totalling these values along a route is quite satisfactory as elevation changes make little difference. I haven't checked the code to see if this is actually how it's done and I'm not going to bother doing so.
My guess is that Bing may well use Haversine in just this way for their driving and walking distances. But unlike you, I'm not prepared to just come up with an idea and take it on board without investigation, so lets have a look. How about for starters we find a really nice long and very straight road and compare the driving/walking distance with the "red pin" distance. How about this one:
https://www.bing.com/maps?osid=c39ac59f-9e2f-4ba1-b226-09a9c1384f66&cp=24.764682~50.511889&lvl=9&v=2&sV=2&form=S00027. Bing says it's a 256km drive across Saudi Arabia. The "red pin" distance is ... 256km. Exactly the same.
OK, so far, but this road has no significant elevation changes, so how about
https://www.bing.com/maps?osid=6651a272-f4ac-4f9b-8874-70ff9bcacbc0&cp=37.752553~-122.41805&lvl=15&v=2&sV=2&form=S00027. A 10.6km walk up and down the hills of your old favourite, San Francisco. Plenty of elevation changes there. Guess what, the "red pin" distance is ... 10.6km.
Of course none of this proves anything about how Bing actually goes about calculating driving or walking distances, but it certainly suggests that simply using the "red pin" method to calculate each segment of a path is giving the same answers.
And we've already established to everyone's satisfaction apart from yours that "red pin" is Haversine and Haversine is based solely on spherical trigonometry.