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The locus of all points of zero latitude ... sometimes also known as the "Equator" ... is the longest parallel of constant latitude. It's length is the equatorial circumference of the earth ... roughly 24,900 miles (40,073 km) .
The parallel of zero latitude on the earth is usually referred to as the earth's 'equator'.
The 49th parallel north is a latitudinal circle on the Earth that is 49 degrees above the Earth's equator. This imaginary line is used as the border between the United States and Canada.
The Equator divides the Earth into the Northern Hemisphere and the Southern Hemisphere. Lines of latitude are parallel to the Equator both to the north and to the south.
"Parallel to the earth" is a somewhat messy phrase used to describe something that stays the same distance above the earth's surface. Of course since the earth's surface is curved, this means that whatever the 'something' is, it also must be curved. Here are a couple of examples: 1). During certain atmospheric conditions (K = infinite), a radio signal launched horizontally propagates 'parallel to the earth', and exactly follows the earth's curvature. 2). Geostationary communications satellites ... like the ones that private homes use those little dishes to receive TV from ... are in circular orbits over the earth's equator. They revolve around the earth once in 24 hours, on paths that are 'parallel to the earth'.