What are the parallels halfway between the equator and the poles?

Answer 1

The latitudes half way between the equator and poles are at 60 N & S At these latitudes the circumference is half of that at the equator.

The Earth's circumference at the Equator is approx. 24,000 miles. At latitudes 60 N & S the circumference is 12,000 miles.

At the poles N & S, latitude 90 N & S, the circumference is '0' (zero) ; a dot point.

Taking an angular value for half way at 45 o N & S , the circumference is approximately 17,000 miles.

Answer 2

Equidistant in distance between the Equator and North/South Pole: Calculated in the WGS84 ellipsoid, 45° 08’ 39.5437411966” (45 degrees 8 minutes 39.5437411966 seconds) North or South / 45° 08.6590623532758’ (45 degrees 8.6590623532758 minutes) North or South / 45.14431770588793° (45.14431770588793 degrees) North or South.

Calculation:

Equator to a Pole in WGS84 ellipsoidal distance = 10,001,965.729312723 metres/meters (6,214.933369940002 international miles).

10,001,965.729312723 metres/meters ÷ 2 = 5,000,982.8646563615 metres/meters (3,107.4666849700011 international miles).

0° of latitude (Equator) due true north or south for 5,000,982.8646563615 metres/meters in WGS84 ellipsoidal distance, results in a halfway latitude in distance of 45° 08’ 39.5437411966” North or South / 45° 08.6590623532758’ N or S / 45.14431770588793° N or S.

90° North or South of latitude (North or South Pole) due true south or north for 5,000,982.8646563615 metres/meters in WGS84 ellipsoidal distance, results in a halfway latitude in distance of 45° 08’ 39.5437411966” North or South / 45° 08.6590623532758’ N or S / 45.14431770588793° N or S.

Calculated in the WGS84 ellipsoid, 45° 08’ 39.5437411966” North/South or 45° 08.6590623532758’ N/S or 45.14431770588793° N/S is 16.038486678618 km or 9.965853589175 International miles further north/south than precisely latitude 45° North/South.

In the GRS80 (1980) ellipsoid of revolution or reference ellipsoid, halfway or midway in distance between the Equator and a pole computes as 45° 08’ 39.5437437477” North or South / 45° 08.6590623957954’ North or South / 45.14431770659659° North or South. The halfway latitude for both the WGS84 ellipsoid and the GRS80 ellipsoid are equal at the precision of 45° 08’ 39.54374” N/S. Furthermore, calculated in both the WGS84 ellipsoid and the GRS80 ellipsoid, 45° 08’ 39.54374” N/S in latitude (i.e. due true north-south) is to a precision of 0.308707 mm or 0.0121538 of an inch.

Institut Géographique National (National Institute of Geographic Information), Paris, France, December 2017 to me: "Indeed we confirm that the latitude of the point that is equidistant from the equator and the north pole (considering the shortest route on the surface of the IAG-GRS80 ellipsoid) is 45°08’39.54374” ".

Professor Richard B. Langley, Geodetic Research Laboratory, Dept. of Geodesy and Geomatics Engineering, University of New Brunswick, Fredericton, Canada, December 2017 to me: "according to one piece of software at my disposal (which I believe has the geodesy correct), I get 45° 8' 39.54374" using the GRS80/WGS84 ellipsoid."

Mario Bérubé, Team Leader, Geodetic Survey Division, Natural Resources Canada, September 2013: "Your computations of halfway latitude on WGS84 and GRS1975 using the Vincenty method are correct. The latest realization of ITRF, ITRF2008 is using the GRS80 ellipsoid. It is very close to WGS84."

Steve Hilla, Geosciences Research Division Chief, National Geodetic Survey, NOS, NOAA, Silver Spring, Maryland, USA, January 2018, to me: "I hope you will find interesting the attached pages taken from a publication called Geometric Geodesy - Part 1, by Prof. Richard H. Rapp. On pages 36-40 is a discussion of how to compute lengths along a Meridian Arc. Using Equation (3.114) and the GRS80 constants in (3.118), I wrote a short program (also included) to compute the distance from the equator to a point at Latitude 45-08-39.54374 N. Using this Latitude, I get a distance that is indeed half the distance from the equator to the pole (to a tenth of a millimeter)."

45° of latitude is obviously halfway in latitude between the Equator at 0° and poles at 90°. However, it is not halfway in ellipsoidal distance. In WGS84, precisely 45° North due true north to the North Pole results in an ellipsoidal distance of 5,017.021351334979 km or 3,117.432538559176 international miles; similarly from precisely 45° South due true south to the South Pole. Precisely 45° N due true south to the Equator results in 4,984.944377977744 km or 3,097.500831380826 international miles; similarly from precisely 45° S due true north to the Equator. Therefore, in WGS84, precisely 45° North / 45° South is 32.076973357235 km or 19.931707178350 international miles closer to the Equator, than to the North / South Pole.

This is because the Earth is not a perfect sphere, but an approximate oblate spheroid; since it bulges at the Equator and is flattened at the poles. Therefore, different degrees of latitude are not equal in distance, they are increasingly longer due north-south, the further they are from the Equator.

Answer 3

The latitudes half way between the equator and poles are at 60 N & S At these latitudes the circumference is half of that at the equator.

The Earth's circumference at the Equator is approx. 24,000 miles. At latitudes 60 N & S the circumference is 12,000 miles.

At the poles N & S, latitude 90 N & S, the circumference is '0' (zero) ; a dot point.

Taking an angular value for half way at 45 o N & S , the circumference is approximately 17,000 miles.

Answer 4

Answer #1:

I believe you mean the Tropics of Cancer and Capricorn, but they are not half way (ie 45 degrees north and south) they are 23° 26′ 16″ N and S respectively.

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Answer #2:

I believe you mean the parallels halfway between the equator and the poles,

since that's the way you worded the question.

They are the parallels of 45° North latitude and 45° South latitude.