Equator

An equator is an imaginary circle on the surface of a  rotating sphere. As any three-dimensional object, a sphere rotates around a line through its mass center; this line is known as rotation axis. In absence of external torques, a rotation axis is fixed in space. The two places where the rotation axis intersects the surface of the sphere are the poles (the North Pole and the South Pole). The equator is defined as the intersection (a circle) of the surface of the sphere with a plane (the equatorial plane) that passes through the center of the sphere and is orthogonal to its rotation axis. The equator is a great circle, its center coincides with the center of the sphere. Clearly the equator is midway between the poles and divides the sphere exactly into two halves, the Northern and Southern hemisphere, hence the name (lit. "equal maker"). Note that usually the term hemispheres denotes the  surface of the half-sphere, not the half-sphere itself.

Earth
The Earth is the sphere to which the concept of equator is applied most widely. On Earth the equator services as a reference for geographical coordinates. It is the zero of latitude, i.e., the equator has by definition zero degrees (0°) latitude, the North Pole has by definition ninety degrees latitude (90°N) and the South Pole has latitude 90°S.

The equator is 40&thinsp;076.592 kilometers long. The linear velocity (with respect to an inertial system fixed to the Sun) resulting from the rotation of the earth (with its angular period of 24 hours) is highest on the equator and is about 40&thinsp;076/24 &asymp; 1670 kilometer per hour. Obviously, the linear velocity on the poles is zero.

The length of a degree of longitude on the equator (and therewith the circumference of the Earth at the equator) was first determined around 1740 by a French expedition to Peru. Scientific members were Pierre Bouguer, Charles Marie de La Condamine, and the leader of the expedition,Louis Godin.

An important circle on the Northern hemisphere (not a great circle) is the Tropic of Capricorn. This is the latitude where the Sun seems exactly overhead once a year—at the summer solstice (around June 21). In 2010 it was at 23º 26′ 17″ north of the equator (the Earth axis "wobbles" somewhat due to external torques so that the latitude varies a little in time). The Arctic circle is the polar circle 90°&minus;23º 26′ 17″ &asymp; 66° 34′ north of the equator. It is the northern most latitude on Earth that just sees the sun rise and immediately set at the winter solstice (around December 22). On the Southern hemisphere these circles are called the Tropic of Capricorn and the Antarctic circle, respectively.

The area with the equator right in the middle, between the Tropic of Cancer and the Tropic of Capricorn, sees the Sun exactly overhead (at 90°) twice a year and in other periods under an angle that deviates at most 46° from overhead position. Hence this area on Earth receives a large amount of Solar energy all through the solar year and is consequently on average the hottest region on Earth. This region around the equator (the "Tropics") hardly experiences any seasons.

Sky
An other important sphere is the stellar circle (in antiquity known as heavenly sphere). Its equatorial plane coincides with Earth's equatorial plane and divides the sky into a Northern and Southern sky.