Back in June I wrote a story about the 45th parallel, which runs through New Hampshire. The state has two (two!) historical markers noting that you are halfway between the equator and the North Pole at that point. Except you’re not really because of geometry, as you can learn by reading my sterling prose.

I got an email today pointing me to a 2000 article in the Journal of the Royal Astronomical Society of Canada (http://adsabs.harvard.edu/full

Here is the article:

This is because the Earth is not a sphere, but an approximate ellipsoid of revolution (oblate spheroid), since it bulges at the Equator. Calculated WGS84 reference ellipsoid, the surface at the Poles is 1 part in 298.257223563 (21.3846857548 km or 13.2878276831 miles) closer to the Earth’s center, than at the surface at the Equator. In WGS84, the Equatorial circumference is 40075.016685578486 km or 24901.460896848956 miles, and the Polar or meridional circumference is 40007.862917250892 km or 24859.733479760009 miles. Therefore the Equatorial circumference in WGS84 is 67.153768327594 km or 41.727417088947 miles longer than the Polar or meridional circumference. From a Pole to a Pole the distance in WGS84 is 20003.931458625446 km or 12429.866739880005 miles, and from the Equator to a Pole is 10001.965729312723 km or 6214.933369940002 miles.

For example in WGS84:

Latitude 0° to 1° distance 110.574388557799 km or 68.707739649074 miles.

Latitude 89° to 90° distance 111.693864914200 km or 69.403350007332 miles.

Equator to a Pole in WGS84 = 10001965.729312723 meters.

10001965.729312723 meters ÷ 2 = 5000982.8646563615 meters.

0° of latitude due north or south for 5000982.8646563615 meters = WGS84 45° 08’ 39.5437411966” (45 degrees 8 minutes 39.5437411966 seconds) N or S / 45° 08.659062353275666’ (45 degrees 8.659062353278 minutes) N or S / 45.14431770588793° (45.14431770588793 degrees) N or S. Obviously also, from the North Pole the same distance due south, and from the South Pole the same distance due north. Therefore in the WGS84 ellipsoid, precisely midway between the Equator and the North / South Pole it is a distance of 5000.9828646563615 km or 3107.4666849700011 miles to both the Equator and the North / South Pole.

WGS84 latitude 45° 08’ 39.5437411966” North / 45° 08.659062353278’ N / 45.14431770588793° N is 16.038486678618 km or 9.965853589176 International miles farther north than latitude 45° North. Similarly, WGS84 latitude 45° 08’ 39.5437411966” South / 45° 08.659062353278’ S / 45.14431770588793° S is 16.038486678618 km or 9.965853589176 miles farther south than latitude 45° South.

**National Geodetic Survey (USA) INVERSE Computation, and its FORWARD Computation: “Ellipsoid : GRS80 / WGS84 (NAD83)”, halfway computes as “LAT = 45 8 39.54374 North” (Latitude 45 degrees 8 minutes 39.54374 seconds North), which to the same precision is identical to that computed in the WGS84**

**ellipsoid. “LAT = 45 8 39.54374 North” (45° 08’ 39.54374” N) is in latitude, i.e. due north-south, to a precision of 0.308707 of a millimeter or 0.012154 of an inch.**