Latitude exact relationship of parallels and meridians with horizontal and vertical: both are complicated curves. On the sphere the normal passes through the centre and the latitude () is therefore equal to the angle subtended at the centre by the meridian arc from the equator to the point concerned. If the meridian distance is denoted by then where denotes the mean radius of the Earth. is equal to . No higher accuracy is appropriate for since higher-precision results necessitate an ellipsoid model. With this value for the meridian length of 1 degree of latitude on the sphere is (60.0 nautical miles).
Celestial equator south), the celestial equator tilts towards the opposite horizon. The celestial equator is defined to be infinitely distant (since it is on the celestial sphere); thus, the ends of the semicircle always intersect the horizon due east and due west, regardless of the observer's position on Earth. (At the poles, the celestial equator coincides with the astronomical horizon.) At all latitudes, the celestial equator is a uniform arc or circle because the observer is only finitely far from the plane of the celestial equator, but infinitely far from the celestial equator itself. Astronomical objects near the celestial equator appear above