I tried a different approach to verify Mengy's measurements. I aimed my ship directly downward and hovered over various points of interest, recording the planetary coordinates of each one. I also double checked several of these measurements in my SRV and they were all a match within ~0.0002 degrees, so I think the technique is reliable.
http://i.imgur.com/1YnQBI1.jpg
Using those coordinates along with the radius of the planet, we can then calculate distances between points without having to worry about things like where the "center" of a parked ship is considered to be. So we start by dividing the planet's circumference by 360 to find the linear surface distance per degree:
Code:
radius = 1122 kilometers
circumference = PI * 2 * 1122 ~= 7049.7339 kilometers
arclength = 7049.7339 * 1000 / 360 ~= 19582.5942 meters per degree
Next, we can compute the "distance" in degrees between any two coordinate pairs and use the conversion factor above to translate that into the linear distance in meters. Technically we're working in spherical coordinates which would complicate such calculations, but since we're working over such a small area I think we can treat our coordinates as if they were cartesian. So let's try verifying the distance from the center (peak) of the north pyramid to the center of the large circle:
Code:
arc = ((-31.7804 - -31.7865)^2 + (-128.9001 - -128.9236)^2)^0.5 degrees
arc = (0.0061^2 + 0.0235^2)^0.5 degrees
arc = (0.00058946)^0.5 degrees
arc ~= 0.02427880 degrees
distance = 0.02427880 * 19582.5942 ~= 475.44 meters
Not what I expected. But maybe there's too much imprecision in our measurements; the planet radius is rounded to the nearest kilometer, and our coordinates are probably only accurate to ~0.0005 degrees. Just to be on the safe side, let's subtract 1km of radius and round our coordinates to 0.001 degree in such a way so as to minimize the calculated distance, in order to establish a lower bound:
Code:
radius = 1121 kilometers
circumference = PI * 2 * 1121 ~= 7043.4508 kilometers
arclength = 7043.4508 * 1000 / 360 ~= 19565.1409 meters per degree
arc = ((-31.781 - -31.786)^2 + (-128.901 - -128.923)^2)^0.5 degrees
arc = (0.005^2 + 0.022^2)^0.5 degrees
arc = (0.000509)^0.5 degrees
arc ~= 0.02256103 degrees
distance = 0.02256103 * 19565.1409 ~= 441.41 meters
Oh dear. Even allowing for a very wide margin of error, the shortest that distance could be according to this surveying method is almost 73 meters further than Mengy's measurement -- an error of almost 20%.
Of course it's possible that there's some additional confounding factor that invalidates the assumptions of this survey; the planet might not be perfectly spherical, or the published radius might be incorrect. But I think it's worth double checking, perhaps by having two commanders in SRVs try to repeating Mengy's measurements; SRVs being much smaller than ships might reduce one potential source of error.
