Determining the location of a place on planet Earth can be achieved knowing its geographical coordinates: latitude, longitude and altitude. In this work, since the considered model for the planet is a sphere, we are assuming that all points lie on the surface of the sphere, that is, have zero altitude.

The **latitude** of a location is the measure of the angle that the radius of the sphere passing through that place makes with the Equatorial line. Latitude varies between -90° (South Pole) and 90° (North Pole). Any point in the Equatorial line has latitude zero.

Another quantity that can be used instead of latitude is the **colatitude** of the place: measure of the angle that the radius passing through the North Pole makes with the radius passing through the given place, varying between 0°
(North Pole) and 180° (South Pole). Therefore, the Equatorial line is the set of points on the sphere with colatitude equal to 90°.

The **longitude** of a place is the angle that the meridian passing through that place makes with Greenwich's meridian. Longitude's absolute value varies between 0° and 180°: when the location is West of Greenwich's meridian, longitude is negative and, when the location is East of Greenwich's meridian, its longitude is positive.

On the following table, we present the latitudes and longitudes of some cities.

Oporto | Lisbon | Madrid | Paris | Rio de Janeiro | New York | Luanda | Tokyo | Sidney |
---|---|---|---|---|---|---|---|---|

41º9'N | 38°43'N | 40°25'N | 48°52'N | 22°55'S | 40°40'N | 8°49'S | 35°40'N | 33°52'S |

8°37'O | 9°8'O | 3°43'O | 2°20'E | 43°12'O | 73°56'O | 13°14'E | 139°46'E | 151°13'E |