<P> The first published reference to the Earth's size appeared around 350 BC, when Aristotle reported in his book On the Heavens that mathematicians had guessed the circumference of the Earth to be 400,000 stadia . Scholars have interpreted Aristotle's figure to be anywhere from highly accurate to almost double the true value . The first known scientific measurement and calculation of the radius of the Earth was performed by Eratosthenes in about 240 BC . Estimates of the accuracy of Eratosthenes's measurement range from 0.5% to 17% . For both Aristotle and Eratosthenes, uncertainty in the accuracy of their estimates is due to modern uncertainty over which stadion length they meant . </P> <P> Earth's rotation, internal density variations, and external tidal forces cause its shape to deviate systematically from a perfect sphere . Local topography increases the variance, resulting in a surface of profound complexity . Our descriptions of Earth's surface must be simpler than reality in order to be tractable . Hence, we create models to approximate characteristics of Earth's surface, generally relying on the simplest model that suits the need . </P> <P> Each of the models in common use involve some notion of the geometric radius . Strictly speaking, spheres are the only solids to have radii, but broader uses of the term radius are common in many fields, including those dealing with models of Earth . The following is a partial list of models of Earth's surface, ordered from exact to more approximate: </P> <Ul> <Li> The actual surface of Earth </Li> <Li> The geoid, defined by mean sea level at each point on the real surface </Li> <Li> A spheroid, also called an ellipsoid of revolution, geocentric to model the entire Earth, or else geodetic for regional work </Li> <Li> A sphere </Li> </Ul>

What is the diameter of the earth at the equator