Midway from Equator to the North Pole

Recently, there was a small controversy in the Nova Scotia media about the correct location of a monument near Stewiacke, Nova Scotia. In the 1930's, the marker was erected to indicate one place in Nova Scotia that is midway between the North Pole and the Equator. That marker is north of the 45th parallel and some people felt that it was at the wrong place. geocentric latitude

The controversy occurs because the midway point can be defined in a couple of ways. The first and simplest definition is a point on the 45th parallel. This latitude is halfway between the equator at 0 N latitude and the North Pole at 90 N latitude in angle only. The other method is to use the distance along the surface of the Earth between the two limits. If the Earth were a perfect sphere, then 45 N latitude would also be midpoint as specified by this method.

The Earth is, in reality, an oblate spheroid because the Earth's rotation cause it to bulge at its equator and flatten at its poles. The local latitude is determined by the angle between a plumb bob and the equatorial plane of the Earth. A plumb bob hangs perpendicular to the surface. As you can see in the image below, the plumb bob in this case does not point at the center of the Earth. If that latitude were 45 N, then the location of that point on the Earth will be closer to the equator than the North Pole.
angles on spheroid distance and angle diagram

The distance along the surface of the Earth for a given change in latitude varies with the latitude. Near the North Pole, the Earth's curvature is small than near the equator. As a result, the distance require to change latitude by one degree at the North Pole is larger than that distance to change by the same latitude near the equator. This is because the radius of surface at he poles is large than the same radius at the equator.

The Observer's Handbook gives the relationship to calculate the distance required to change 1 degree of latitude at any latitude.
(see p28 Observer's Handbook 2004, Ed. Rajiv Gupta, The Royal Astronomical Society of Canada)

Distance in kilometres between 1 degree latitude = 111.13295 - 0.55982 km cosine(2 x latitude)+ 0.00117 cosine(4 x latitude)

The distance from the Equator to a pole is 90 x 111,132.95 m = 10,001,966 metres
To be halfway between the equator and the pole you must be 5,000,983 metres from the equator (or the pole).

A summing of the distances for each degree of latitude allows one to calculate the fraction of the distance between the equator and pole for every degree of latitude. The results are shown in the graph below for just the latitudes near 45 N. Note that 1/2 way is not at 45 N but slight north of that parallel. Half way is determined to be at about 45 deg 8.76 min of latitude.

Below is a map of central Nova Scotia showing 45 N latitude as well as the parallel (45 9'N) on which you will be half way between the Equator and the North Pole. Some local communities that lie on or near that line are Harbourville and Sheffield Mills. The line is just north of the town of Canning.

Note: The exact distance between lines of latitude depends on the modelling of the shape of the Earth. The one used here is the one adopted by the International Astronomical Union in 1976 (GRS1975). It uses a mean radius of the Earth as 6378.140 km and a flattening of the spheroid of 1/298.2570.

Most GPS units use the WGS84 datum which is slightly different. The Earth's mean radius is 6378.137 km and the flattening is 1/298.257223563

Another webpage on this subject: http://www.uwgb.edu/dutchs/geolwisc/geostops/halfway.htm

END: May 12, 1996
Revised: Nov 2004
Assembled by Larry Bogan from information provided by Sherman Williams