If a body of unit mass is raised from the earth's surface to a height z in the atmosphere, the work that must be done against the earth's gravitational field is called its geopotential which is usually denoted by O and defined by the relation z
where the geopotential 0(0) at sea level is taken to be zero.
Due to the spheroidal shape of the earth and variation of the acceleration due to gravity, g, over the earth's surface, the surfaces of constant geopotential are not quite parallel to the surfaces of constant geometric height z above mean sea level which are called level surfaces. However, if we take a globally-averaged constant value of g at the earth's surface and call it g0 (= 9.81 m s~2), it is possible to define a geopotential height Z given by z
The difference between z and Z, however, is small and sometimes ignored and the height of a geopotential surface in geopotential metres (gpm) is taken to be equal to its height in geometric metres.
Continue reading here: Motion in the Earths Gravitational Field The Law of Central Forces
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