## The halfway latitude in distance between the Equator and the North / South Poles.

WGS84 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.

This was calculated by me in the WGS84 ellipsoid of revolution or reference ellipsoid, using Charles Karney's "Online geodesic calculations using the GeodSolve utility": https://geographiclib.sourceforge.io/cgi-bin/GeodSolve "GeodSolve is accurate to about 15 nanometers (for the WGS84 ellipsoid)" or 0.000015 of a millimetre/millimeter or 0.00000059 of an inch. In emails to me from Charles Karney: "The accuracy of 15 nanometers that I quote is for paths up to half-way round the earth." "The accuracy for the Airy" [1830] "ellipsoid will be (very nearly) the same as for the WGS84 ellipsoid because the parameters are roughly the same."

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 north to the North Pole results in an ellipsoidal distance of 5017.021351334979 kilometres/kilometers or 3117.432538559176 international miles, similarly from 45° South to the South Pole. Precisely 45° N due south to the Equator results in 4984.944377977744 km or 3097.500831380826 international miles, similarly from precisely 45° S due 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 flattened at the poles. Therefore different degrees of latitude are not equal in distance, they are increasingly longer due north-south, the farther they are from the Equator.

For example in WGS84:

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

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

Only if the Earth were a perfect sphere, would halfway in distance between the Equator and a pole, be at precisely latitude 45° North or South.

Calculated in the WGS84 ellipsoid of revolution or reference ellipsoid, the surface at the Poles is 1 part in 298.257223563 or 21.3846857548 km or 13.2878276831 international miles closer to the Earth's centre/center, than at the surface at the Equator. In WGS84, the Equatorial circumference is 40075.016685578486 km or 24901.460896848956 international miles, and the Polar or meridional circumference is 40007.862917250892 km or 24859.733479760009 international miles. Therefore the Equatorial circumference in WGS84 is 67.153768327594 km or 41.727417088947 international 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 international miles, and from the Equator to a pole is 10001.965729312723 km or 6214.933369940002 international miles.

Calculation:

Equator to a Pole in WGS84 ellipsoidal distance= 10001965.729312723 metres/meters.

10001965.729312723 metres/meters ÷ 2 = 5000982.8646563615 metres/meters.

0° of latitude (Equator) due north or south for 5000982.8646563615 metres/meters in WGS84 ellipsoidal distance, results in a halfway latitude in distance of WGS84 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 south or north for 5000982.8646563615 metres/meters in WGS84 ellipsoidal distance, results in a halfway latitude in distance of WGS84 45° 08’ 39.5437411966” North or South / 45° 08.6590623532758’ N or S / 45.14431770588793° N or S.

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 international miles or 2700.3147217366963 nautical miles, to both the Equator and the North / South Pole.

WGS84 latitude 45° 08’ 39.5437411966” North / 45° 08.6590623532758’ N / 45.14431770588793° N is 16.038486678618 km or 9.965853589175 International miles farther north than precisely latitude 45° North. Similarly, WGS84 latitude 45° 08’ 39.5437411966” South / 45° 08.6590623532758’ S / 45.14431770588793° S is 16.038486678618 km or 9.965853589175 international miles farther south than latitude precisely 45° South. Computed in WGS84 ellipsoidal distance.

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 difference between halfway or midway computed in WGS84, and GRS80 ellipsoidal distance, in latitude (due north-south), is 0.078757 of a millimetre/millimeter or 0.003101 of an inch. The WGS84 latitude is 0.078757 mm or 0.003101 inches, farther north, than the GRS80 latitude. Incidentally the Earth's polar or meridional circumference computed in the GRS80 ellipsoid, is only 0.32906 mm or 0.01296 of an inch less, than that computed in the WGS84 ellipsoid.

The National Geodetic Survey's (USA) INVERSE ------ Interactively computes a single azimuth & distance https://www.ngs.noaa.gov/cgi-bin/Inv_Fwd/inverse2.prl, and FORWARD ---- Interactively computes a single geodetic position https://www.ngs.noaa.gov/cgi-bin/Inv_Fwd/forward2.prl, see also https://www.ngs.noaa.gov/TOOLS/Inv_Fwd/Inv_Fwd.html: assume that distances computed in the GRS80 (1980) ellipsoid, and the WGS84 (1984) ellipsoid are identical, "for the purpose of this application GRS80 and WGS84 are considered to be equivalent" "GRS80 / WGS84", however they actually compute in the GRS80 ellipsoid. Using National Geodetic Survey (USA) INVERSE Computation, and its FORWARD Computation: "Ellipsoid : GRS80 (NAD83) / WGS84", halfway in distance between the Equator and the North Pole computes as "LAT = 45 8 39.54374 North" (Latitude 45 degrees 8 minutes 39.54374 seconds North), which to this precision, is identical to that computed in the WGS84 ellipsoid, and to this precision, the same as WGS84 in position. "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 mm or 0.012154 of an inch.

Institut Géographique National (National Institute of Geographic Information), 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."

Steve Hilla, Geosciences Research Division Chief, NOAA (National Oceanic and Atmospheric Administration, 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)."

Joe Evjen a geodesist at NOAA (National Oceanic and Atmospheric Administration, USA, January 2018, to me:

"The U.S. National Geodetic Survey software INVERSE supports the value LAT = 45 8 39.54374 North

as provided and confirmed by others, when using the latest conventional ellipsoid, GRS80.

Output from INVERSE

Ellipsoid : GRS80 / WGS84 (NAD83)

Equatorial axis, a = 6378137.0000

Polar axis, b = 6356752.3141

Inverse flattening, 1/f = 298.25722210088

First Station : equator First Station : halfway

---------------- ----------------

LAT = 0 0 0.00000 North LAT = 45 8 39.54374 North

LON = 90 0 0.00000 West LON = 90 0 0.00000 West

Second Station : halfway Second Station : pole

---------------- ----------------

LAT = 45 8 39.54374 North LAT = 90 0 0.00000 North

LON = 90 0 0.00000 West LON = 90 0 0.00000 West

Forward azimuth FAZ = 0 0 0.0000 From North

Back azimuth BAZ = 180 0 0.0000 From North

Ellipsoidal distance S = 5000982.8645 m Ellipsoidal distance S = 5000982.8647 ".

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."

From "John Hamilton, a Geomatics Engineer with more than 30 years of experience in all types of Engineering Surveys who has has worked in all 50 US states, and on four continents": http://www.terrasurv.com/gpage.html December 2017 to me:

"But I concur with what is in your email as far as computing the 1/2-way distance. Of course, one could argue that halfway is angular, i.e. 45°00'00.00000"."

45° 08.6590623532758’ (45 degrees 8.6590623532758 minutes) North or South / 45.14431770588793° (45.14431770588793 degrees) North or South.

This was calculated by me in the WGS84 ellipsoid of revolution or reference ellipsoid, using Charles Karney's "Online geodesic calculations using the GeodSolve utility": https://geographiclib.sourceforge.io/cgi-bin/GeodSolve "GeodSolve is accurate to about 15 nanometers (for the WGS84 ellipsoid)" or 0.000015 of a millimetre/millimeter or 0.00000059 of an inch. In emails to me from Charles Karney: "The accuracy of 15 nanometers that I quote is for paths up to half-way round the earth." "The accuracy for the Airy" [1830] "ellipsoid will be (very nearly) the same as for the WGS84 ellipsoid because the parameters are roughly the same."

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 north to the North Pole results in an ellipsoidal distance of 5017.021351334979 kilometres/kilometers or 3117.432538559176 international miles, similarly from 45° South to the South Pole. Precisely 45° N due south to the Equator results in 4984.944377977744 km or 3097.500831380826 international miles, similarly from precisely 45° S due 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 flattened at the poles. Therefore different degrees of latitude are not equal in distance, they are increasingly longer due north-south, the farther they are from the Equator.

For example in WGS84:

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

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

Only if the Earth were a perfect sphere, would halfway in distance between the Equator and a pole, be at precisely latitude 45° North or South.

Calculated in the WGS84 ellipsoid of revolution or reference ellipsoid, the surface at the Poles is 1 part in 298.257223563 or 21.3846857548 km or 13.2878276831 international miles closer to the Earth's centre/center, than at the surface at the Equator. In WGS84, the Equatorial circumference is 40075.016685578486 km or 24901.460896848956 international miles, and the Polar or meridional circumference is 40007.862917250892 km or 24859.733479760009 international miles. Therefore the Equatorial circumference in WGS84 is 67.153768327594 km or 41.727417088947 international 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 international miles, and from the Equator to a pole is 10001.965729312723 km or 6214.933369940002 international miles.

Calculation:

Equator to a Pole in WGS84 ellipsoidal distance= 10001965.729312723 metres/meters.

10001965.729312723 metres/meters ÷ 2 = 5000982.8646563615 metres/meters.

0° of latitude (Equator) due north or south for 5000982.8646563615 metres/meters in WGS84 ellipsoidal distance, results in a halfway latitude in distance of WGS84 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 south or north for 5000982.8646563615 metres/meters in WGS84 ellipsoidal distance, results in a halfway latitude in distance of WGS84 45° 08’ 39.5437411966” North or South / 45° 08.6590623532758’ N or S / 45.14431770588793° N or S.

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 international miles or 2700.3147217366963 nautical miles, to both the Equator and the North / South Pole.

WGS84 latitude 45° 08’ 39.5437411966” North / 45° 08.6590623532758’ N / 45.14431770588793° N is 16.038486678618 km or 9.965853589175 International miles farther north than precisely latitude 45° North. Similarly, WGS84 latitude 45° 08’ 39.5437411966” South / 45° 08.6590623532758’ S / 45.14431770588793° S is 16.038486678618 km or 9.965853589175 international miles farther south than latitude precisely 45° South. Computed in WGS84 ellipsoidal distance.

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 difference between halfway or midway computed in WGS84, and GRS80 ellipsoidal distance, in latitude (due north-south), is 0.078757 of a millimetre/millimeter or 0.003101 of an inch. The WGS84 latitude is 0.078757 mm or 0.003101 inches, farther north, than the GRS80 latitude. Incidentally the Earth's polar or meridional circumference computed in the GRS80 ellipsoid, is only 0.32906 mm or 0.01296 of an inch less, than that computed in the WGS84 ellipsoid.

The National Geodetic Survey's (USA) INVERSE ------ Interactively computes a single azimuth & distance https://www.ngs.noaa.gov/cgi-bin/Inv_Fwd/inverse2.prl, and FORWARD ---- Interactively computes a single geodetic position https://www.ngs.noaa.gov/cgi-bin/Inv_Fwd/forward2.prl, see also https://www.ngs.noaa.gov/TOOLS/Inv_Fwd/Inv_Fwd.html: assume that distances computed in the GRS80 (1980) ellipsoid, and the WGS84 (1984) ellipsoid are identical, "for the purpose of this application GRS80 and WGS84 are considered to be equivalent" "GRS80 / WGS84", however they actually compute in the GRS80 ellipsoid. Using National Geodetic Survey (USA) INVERSE Computation, and its FORWARD Computation: "Ellipsoid : GRS80 (NAD83) / WGS84", halfway in distance between the Equator and the North Pole computes as "LAT = 45 8 39.54374 North" (Latitude 45 degrees 8 minutes 39.54374 seconds North), which to this precision, is identical to that computed in the WGS84 ellipsoid, and to this precision, the same as WGS84 in position. "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 mm or 0.012154 of an inch.

Institut Géographique National (National Institute of Geographic Information), 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."

Steve Hilla, Geosciences Research Division Chief, NOAA (National Oceanic and Atmospheric Administration, 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)."

Joe Evjen a geodesist at NOAA (National Oceanic and Atmospheric Administration, USA, January 2018, to me:

"The U.S. National Geodetic Survey software INVERSE supports the value LAT = 45 8 39.54374 North

as provided and confirmed by others, when using the latest conventional ellipsoid, GRS80.

Output from INVERSE

Ellipsoid : GRS80 / WGS84 (NAD83)

Equatorial axis, a = 6378137.0000

Polar axis, b = 6356752.3141

Inverse flattening, 1/f = 298.25722210088

First Station : equator First Station : halfway

---------------- ----------------

LAT = 0 0 0.00000 North LAT = 45 8 39.54374 North

LON = 90 0 0.00000 West LON = 90 0 0.00000 West

Second Station : halfway Second Station : pole

---------------- ----------------

LAT = 45 8 39.54374 North LAT = 90 0 0.00000 North

LON = 90 0 0.00000 West LON = 90 0 0.00000 West

Forward azimuth FAZ = 0 0 0.0000 From North

Back azimuth BAZ = 180 0 0.0000 From North

Ellipsoidal distance S = 5000982.8645 m Ellipsoidal distance S = 5000982.8647 ".

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."

From "John Hamilton, a Geomatics Engineer with more than 30 years of experience in all types of Engineering Surveys who has has worked in all 50 US states, and on four continents": http://www.terrasurv.com/gpage.html December 2017 to me:

"But I concur with what is in your email as far as computing the 1/2-way distance. Of course, one could argue that halfway is angular, i.e. 45°00'00.00000"."

Latitude WGS84 45° 08’ 39.5437411966” North / 45° 6590623532758’ N / 45.14431770588793° N passes through the USA, Canada, France, Italy, Croatia, Bosnia Herzegovina, Serbia, Romania, Ukraine, Russia, Kazakhstan, Uzbekistan, Mongolia, China, Japan.

These are settlements, U.S. states, Canadian provinces, halfway in distance between the Equator and the North Pole, in the following countries:

Click on the blue text for the Wikipedia entries:

USA: Oregon; Woodburn, Molalla. Idaho: Salmon. Montana; Belfry. South Dakota: La Plant. Minnesota; Grove City, Pheasant Acres Golf Course, Lexington. Wisconsin; Medford, Antigo (City). Michigan; Menominee, East Jordan, Vanderbilt. New Hampshire: Coon Brook Bog "a Trout Pond in Pittsburg", Second Connecticut Lake more precisely its two largest islands. Maine; Stratton in Eustis.

Canada: Ontario; Baysville, Carleton Place, Osgoode, Lancaster - South Glengarry.

Quebec: Barrage-Hopkins - Coaticook. New Brunswick; Utopia - Upper Letang.

New Brunswick: Utopia, Chamcook Lake.

Nova Scotia; Fort Ellis, Stewiacke, East Stewiacke, Sherbrooke.

These are settlements, U.S. states, Canadian provinces, halfway in distance between the Equator and the North Pole, in the following countries:

Click on the blue text for the Wikipedia entries:

USA: Oregon; Woodburn, Molalla. Idaho: Salmon. Montana; Belfry. South Dakota: La Plant. Minnesota; Grove City, Pheasant Acres Golf Course, Lexington. Wisconsin; Medford, Antigo (City). Michigan; Menominee, East Jordan, Vanderbilt. New Hampshire: Coon Brook Bog "a Trout Pond in Pittsburg", Second Connecticut Lake more precisely its two largest islands. Maine; Stratton in Eustis.

Canada: Ontario; Baysville, Carleton Place, Osgoode, Lancaster - South Glengarry.

Quebec: Barrage-Hopkins - Coaticook. New Brunswick; Utopia - Upper Letang.

New Brunswick: Utopia, Chamcook Lake.

Nova Scotia; Fort Ellis, Stewiacke, East Stewiacke, Sherbrooke.

WGS84 / GRS80 45° 08’ 39.54374” N passing through Stewiacke, Nova Scotia (approximate).

France: Saint-Laurent-Médoc, Cottraud, Saint-Martin-de-Coux, Saint-Astier, Chanteroudilles, La Bachellerie, Cublac, La Rochette near Cublac, La Rivère de Mansac, Saint-Pantalèon-de-Larche, Brive-la-Gaillarde, Darsac, Saint Vincent, Yssingeaux, Arras-sur-Rhone, Les Fauries, Saint-Michel-sur-Savasse, Chatte, Grenoble suburb of Èchirolles.

Italy: Bussoleno, Zoei-Veretto grangia, Vindrolere, Bruzolo, Mappano, Settimo Torinese, Piana San Raffaele, Sessana, Casale Monferrato, Bivio Cava Manara, Mezzano Siccomario, Chignolo Po, Cremona, San Felice, Torre De' Picenardi, San Lorenzo De' Picenardi, Castellucchio, Mantua, Villimpenta, Roncanova, Maccacari, Spinimbecco, Borgoforte, Rottanova, Villaggio, Busonera, Santanna.

Croatia: Žminj, Oprisavci, Gradište, Otok.

Bosnia Herzegovina: Republika Srpska; Dobrljin, Gradiška, Brod.

Serbia: Stara Bingula, Sakula.

Romania: Buzau, Teregova, Rusca, Dumbraven, Horzu, Cuca, Pausesti-Maglasi, Bujoreni, Olteni, Curtea de Arges, Retevoie, Furnico, Trestioare, Lipa, Plopu.

Russia: Mikhaylovsk, Tamanskiy, Bolshoy Raznokol, Troitskaya, Vitaminkombinat, Krasnogvardenskoye, Nekrasovskaya.

Kazakhstan: KOHBIP.

China: Kala Fangzicun, Yuanwangcun, Songyuan, Tuanjie, Jinshengcun, Wulan Bada Administrative Village.

Latitude WGS84 45° 08’ 39.5437411966” South / 45° 08.6590623532758’ S /45.14431770588793° S, halfway in distance between the Equator and the South Pole, passes through Chile, Argentina, New Zealand.

New Zealand: The latitude is arrived at, when entering Reidston, Waitaki District, Otago (south-west of Oamaru) from the north.

Of course the problem with a monument or a sign, is for example, from Ordnance Survey Great Britain https://www.ordnancesurvey.co.uk/docs/support/guide-coordinate-systems-great-britain.pdf : "note that the axes of the WGS84 Cartesian system, and hence all lines of latitude and longitude in the WGS84 datum, are not stationary with respect to any particular country. Due to tectonic plate motion, different parts of the world move relative to each other with velocities of the order of ten centimetres per year. The International Reference Meridian and Pole, and hence the WGS84 datum, are stationary with respect to the average of all these motions. But this means they are in motion relative to any particular region or country. In Britain, all WGS84 latitudes and longitudes are changing at a constant rate of about 2.5 centimetres per year in a north-easterly direction. Over the course of a decade or so, this effect becomes noticeable in large-scale mapping. Some parts of the world (for example Hawaii and Australia) are moving at up to one metre per decade relative to WGS84."

The circumference of latitude WGS84 45° 08’ 39.5437411966” North and South / 45° 08.6590623532758’ N and S / 45.14431770588793° N and S, is 28313.513848132750 km or 17593.201856242512 international miles or 15288.074432037122 nautical miles.

At WGS84 45° 08’ 39.5437411966” North and South / 45° 08.6590623532758’ N and S / 45.14431770588793° N and S, the area of the Earth closer to the Equator is 360,771,696.223667 km² or 139,294,730.652977 square international miles, and the area closer to the poles is 149,293,925.500422 km² or 57,642,706.892988 square international miles.

The area of the Earth in WGS84 is 510,065,621.724089 km² or 196,937,437.545965 square international miles. Therefore at these latitudes 70.73% of the Earth's area is closer to the Equator, and 29.27% is closer to the poles.

Incidentally the Latitude for halfway in area between the Equator and the poles, i.e. an equal amount of area above and below this latitude between the Equator and a pole: 30.1112517186482574° to 30.1112517186482579° North or South / 30° 06.675103118895474’ N or S to 30° 06.675103118895444’ N or S / 30° 06’ 40.50618713372664” N or S to 30° 06’ 40.50618713372844” N or S. Circumference 34696.251666589664 km or 21559.251264235405 international miles.

Calculated in the WGS84 ellipsoid, using Charles Karney's "geodesic polygon calculations using the Planimeter utility": https://geographiclib.sourceforge.io/cgi-bin/Planimeter "The result for the area is accurate to about 0.1 m² per vertex."

This article explains halfway between the Equator and the North Pole, far better than I can:

Journal of the Royal Astronomical Society of Canada, April 2000 edition, "Midway from Equator to the North Pole".

"Since there are many different reference ellipsoids, the precise latitude of a feature on the surface is not unique: this is stressed in the ISO standard which states that "without the full specification of the coordinate reference system, coordinates (that is latitude and longitude) are ambiguous at best and meaningless at worst"."

"Latitude and longitude are commonly used to refer to a specific location on the surface of the Earth. It is important to keep in mind that latitude and longitude are always specified in terms of a datum. The latitude and longitude of your current position are different for different datums."

"For reasons that are a mixture of valid science and historical accident, there is no one agreed ‘latitude and longitude’ coordinate system." "The result is that different systems of latitude and longitude in common use today can disagree on the coordinates of a point by more than 200 metres. For any application where an error of this size would be significant, it’s important to know which system is being used and exactly how it is defined."

"Because Earth deviates significantly from a perfect ellipsoid, the ellipsoid that best approximates its shape varies region by region across the world. Clarke 1866, and North American Datum of 1927 with it, were surveyed to best suit North America as a whole." "As satellite geodesy and remote sensing technology reached high precision and were made available for civilian applications, it became feasible to acquire information referred to a single global ellipsoid. This is because satellites naturally deal with Earth as a monolithic body. Therefore, the GRS 80 ellipsoid was developed for best approximating the Earth as a whole, and it became the foundation for the North American Datum of 1983. Though GRS 80 and its close relative, WGS 84, are generally not the best fit for any given region, a need for the closest fit largely evaporates when a global survey is combined with computers, databases, and software able to compensate for local conditions."

"Datums may be global, meaning that they represent the whole earth, or they may be local, meaning that they represent an ellipsoid best-fit to only a portion of the earth."

"Because the ellipsoid shape doesn’t fit the Earth perfectly, there are lots of different ellipsoids in use, some of which are designed to best fit the whole Earth, and some to best fit just one region. For instance, the coordinate system used with the Global Positioning System (GPS) uses an ellipsoid called GRS80 (Geodetic Reference System 1980) which is designed to best-fit the whole Earth."

Currently the best fit ellipsoids of revolution or reference ellipsoids, for the whole Earth / geoid as a whole, that have latitude-longitude based on them, are the WGS84 (World Geodetic System 1984) ellipsoid, and the GRS80 (Geodetic Reference System 1980) ellipsoid. Therefore it makes sense to use latitude based on the WGS84 ellipsoid or the GRS80 ellipsoid, for the halfway in distance latitude. Computed in the Airy 1830 (Ordnance Survey Great Britain) local ellipsoid, the Earth's equatorial circumference would be 3.604 km or 2.239 miles less, than computed in the WGS84 / GRS80 ellipsoid, and the Earth's polar or meridional circumference 3.359 km or 2.087 miles less. Furthermore computed in the Clarke 1866 local ellipsoid (North American Datum of 1927, acronym NAD27), the distance from the Equator to the North Pole is 77.686 metres/meters or 85 yards or 255 feet less, than in the WGS84 / GRS80 global ellipsoid. Therefore using a local datum such as NAD27 (Clarke 1866 ellipsoid) for halfway, does not make sense. The current datum for the USA, and Canada, is NAD83, acronym for North American Datum of 1983, which is based on the GRS80 ellipsoid. Though NAD83 will be replaced in North America by NATRF2022, acronym for North American Terrestrial Reference Frame of 2022, in 2022, but NATRF2022 will retain the GRS80 ellipsoid. GRS80 is civilian and has replaced local ellipsoids in many countries, whereas WGS84 is run by the United States Department of Defense. However WGS84 is used by handheld navigation grade, commercial grade, consumer grade GPSr / GNSSr; automotive navigation systems; smartphones; navigation systems for aircraft, ships; Google Earth; Wikipedia etc. Whereas GRS80 is used by Survey-Grade GNSS receivers for accurate and precise surveying, i.e. GRS80 is used by surveyors, surveying & mapping organizations.

France: Saint-Laurent-Médoc, Cottraud, Saint-Martin-de-Coux, Saint-Astier, Chanteroudilles, La Bachellerie, Cublac, La Rochette near Cublac, La Rivère de Mansac, Saint-Pantalèon-de-Larche, Brive-la-Gaillarde, Darsac, Saint Vincent, Yssingeaux, Arras-sur-Rhone, Les Fauries, Saint-Michel-sur-Savasse, Chatte, Grenoble suburb of Èchirolles.

Italy: Bussoleno, Zoei-Veretto grangia, Vindrolere, Bruzolo, Mappano, Settimo Torinese, Piana San Raffaele, Sessana, Casale Monferrato, Bivio Cava Manara, Mezzano Siccomario, Chignolo Po, Cremona, San Felice, Torre De' Picenardi, San Lorenzo De' Picenardi, Castellucchio, Mantua, Villimpenta, Roncanova, Maccacari, Spinimbecco, Borgoforte, Rottanova, Villaggio, Busonera, Santanna.

Croatia: Žminj, Oprisavci, Gradište, Otok.

Bosnia Herzegovina: Republika Srpska; Dobrljin, Gradiška, Brod.

Serbia: Stara Bingula, Sakula.

Romania: Buzau, Teregova, Rusca, Dumbraven, Horzu, Cuca, Pausesti-Maglasi, Bujoreni, Olteni, Curtea de Arges, Retevoie, Furnico, Trestioare, Lipa, Plopu.

Russia: Mikhaylovsk, Tamanskiy, Bolshoy Raznokol, Troitskaya, Vitaminkombinat, Krasnogvardenskoye, Nekrasovskaya.

Kazakhstan: KOHBIP.

China: Kala Fangzicun, Yuanwangcun, Songyuan, Tuanjie, Jinshengcun, Wulan Bada Administrative Village.

Latitude WGS84 45° 08’ 39.5437411966” South / 45° 08.6590623532758’ S /45.14431770588793° S, halfway in distance between the Equator and the South Pole, passes through Chile, Argentina, New Zealand.

New Zealand: The latitude is arrived at, when entering Reidston, Waitaki District, Otago (south-west of Oamaru) from the north.

Of course the problem with a monument or a sign, is for example, from Ordnance Survey Great Britain https://www.ordnancesurvey.co.uk/docs/support/guide-coordinate-systems-great-britain.pdf : "note that the axes of the WGS84 Cartesian system, and hence all lines of latitude and longitude in the WGS84 datum, are not stationary with respect to any particular country. Due to tectonic plate motion, different parts of the world move relative to each other with velocities of the order of ten centimetres per year. The International Reference Meridian and Pole, and hence the WGS84 datum, are stationary with respect to the average of all these motions. But this means they are in motion relative to any particular region or country. In Britain, all WGS84 latitudes and longitudes are changing at a constant rate of about 2.5 centimetres per year in a north-easterly direction. Over the course of a decade or so, this effect becomes noticeable in large-scale mapping. Some parts of the world (for example Hawaii and Australia) are moving at up to one metre per decade relative to WGS84."

The circumference of latitude WGS84 45° 08’ 39.5437411966” North and South / 45° 08.6590623532758’ N and S / 45.14431770588793° N and S, is 28313.513848132750 km or 17593.201856242512 international miles or 15288.074432037122 nautical miles.

At WGS84 45° 08’ 39.5437411966” North and South / 45° 08.6590623532758’ N and S / 45.14431770588793° N and S, the area of the Earth closer to the Equator is 360,771,696.223667 km² or 139,294,730.652977 square international miles, and the area closer to the poles is 149,293,925.500422 km² or 57,642,706.892988 square international miles.

The area of the Earth in WGS84 is 510,065,621.724089 km² or 196,937,437.545965 square international miles. Therefore at these latitudes 70.73% of the Earth's area is closer to the Equator, and 29.27% is closer to the poles.

Incidentally the Latitude for halfway in area between the Equator and the poles, i.e. an equal amount of area above and below this latitude between the Equator and a pole: 30.1112517186482574° to 30.1112517186482579° North or South / 30° 06.675103118895474’ N or S to 30° 06.675103118895444’ N or S / 30° 06’ 40.50618713372664” N or S to 30° 06’ 40.50618713372844” N or S. Circumference 34696.251666589664 km or 21559.251264235405 international miles.

Calculated in the WGS84 ellipsoid, using Charles Karney's "geodesic polygon calculations using the Planimeter utility": https://geographiclib.sourceforge.io/cgi-bin/Planimeter "The result for the area is accurate to about 0.1 m² per vertex."

This article explains halfway between the Equator and the North Pole, far better than I can:

Journal of the Royal Astronomical Society of Canada, April 2000 edition, "Midway from Equator to the North Pole".

**The ellipsoid used is GRS1975. Though****to my knowledge, no one knows accurately and precisely where any particular GRS1975 latitude-longitude is positioned on Earth.****Examples:**

Mario Bérubé, Team Leader, Geodetic Survey Division, Natural Resources Canada in September 2013: "I am not familiar with GRS1975."Mario Bérubé, Team Leader, Geodetic Survey Division, Natural Resources Canada in September 2013: "I am not familiar with GRS1975."

**Handheld navigation-grade GPSr /GNNSr have a choice of many datums, and therefore many ellipsoids, but GRS1975 is not one of them. WGS84 is the****latitude-longitude coordinate****system, that is by far the most commonly used by handheld navigation-grade GPSr /GNNSr**.**Furthermore in western countries, survey-grade GNSS receivers use the GRS80 (1980) ellipsoid.**"Since there are many different reference ellipsoids, the precise latitude of a feature on the surface is not unique: this is stressed in the ISO standard which states that "without the full specification of the coordinate reference system, coordinates (that is latitude and longitude) are ambiguous at best and meaningless at worst"."

"Latitude and longitude are commonly used to refer to a specific location on the surface of the Earth. It is important to keep in mind that latitude and longitude are always specified in terms of a datum. The latitude and longitude of your current position are different for different datums."

"For reasons that are a mixture of valid science and historical accident, there is no one agreed ‘latitude and longitude’ coordinate system." "The result is that different systems of latitude and longitude in common use today can disagree on the coordinates of a point by more than 200 metres. For any application where an error of this size would be significant, it’s important to know which system is being used and exactly how it is defined."

"Because Earth deviates significantly from a perfect ellipsoid, the ellipsoid that best approximates its shape varies region by region across the world. Clarke 1866, and North American Datum of 1927 with it, were surveyed to best suit North America as a whole." "As satellite geodesy and remote sensing technology reached high precision and were made available for civilian applications, it became feasible to acquire information referred to a single global ellipsoid. This is because satellites naturally deal with Earth as a monolithic body. Therefore, the GRS 80 ellipsoid was developed for best approximating the Earth as a whole, and it became the foundation for the North American Datum of 1983. Though GRS 80 and its close relative, WGS 84, are generally not the best fit for any given region, a need for the closest fit largely evaporates when a global survey is combined with computers, databases, and software able to compensate for local conditions."

"Datums may be global, meaning that they represent the whole earth, or they may be local, meaning that they represent an ellipsoid best-fit to only a portion of the earth."

"Because the ellipsoid shape doesn’t fit the Earth perfectly, there are lots of different ellipsoids in use, some of which are designed to best fit the whole Earth, and some to best fit just one region. For instance, the coordinate system used with the Global Positioning System (GPS) uses an ellipsoid called GRS80 (Geodetic Reference System 1980) which is designed to best-fit the whole Earth."

Currently the best fit ellipsoids of revolution or reference ellipsoids, for the whole Earth / geoid as a whole, that have latitude-longitude based on them, are the WGS84 (World Geodetic System 1984) ellipsoid, and the GRS80 (Geodetic Reference System 1980) ellipsoid. Therefore it makes sense to use latitude based on the WGS84 ellipsoid or the GRS80 ellipsoid, for the halfway in distance latitude. Computed in the Airy 1830 (Ordnance Survey Great Britain) local ellipsoid, the Earth's equatorial circumference would be 3.604 km or 2.239 miles less, than computed in the WGS84 / GRS80 ellipsoid, and the Earth's polar or meridional circumference 3.359 km or 2.087 miles less. Furthermore computed in the Clarke 1866 local ellipsoid (North American Datum of 1927, acronym NAD27), the distance from the Equator to the North Pole is 77.686 metres/meters or 85 yards or 255 feet less, than in the WGS84 / GRS80 global ellipsoid. Therefore using a local datum such as NAD27 (Clarke 1866 ellipsoid) for halfway, does not make sense. The current datum for the USA, and Canada, is NAD83, acronym for North American Datum of 1983, which is based on the GRS80 ellipsoid. Though NAD83 will be replaced in North America by NATRF2022, acronym for North American Terrestrial Reference Frame of 2022, in 2022, but NATRF2022 will retain the GRS80 ellipsoid. GRS80 is civilian and has replaced local ellipsoids in many countries, whereas WGS84 is run by the United States Department of Defense. However WGS84 is used by handheld navigation grade, commercial grade, consumer grade GPSr / GNSSr; automotive navigation systems; smartphones; navigation systems for aircraft, ships; Google Earth; Wikipedia etc. Whereas GRS80 is used by Survey-Grade GNSS receivers for accurate and precise surveying, i.e. GRS80 is used by surveyors, surveying & mapping organizations.