Geocentric model the coordinate system in order to predict the motions of planetary bodies, though doing so may make calculations easier to perform or interpret. A geocentric coordinate system can be more convenient when dealing only with bodies mostly influenced by the gravity of the Earth (such as artificial satellites and the Moon), or when calculating what the sky will look like when viewed from Earth (as opposed to an imaginary observer looking down on the entire solar system, where a different coordinate system might be more convenient). The Ptolemaic model of the solar system held sway into the early modern age;
Aristarchus of Samos to Aristarchus, "On the Sizes and Distances of the Sun and Moon", is based on a geocentric world view. It has historically been read as stating that the angle subtended by the Sun's diameter is two degrees, but Archimedes states in "The Sand Reckoner" that Aristarchus had a value of ½ degree, which is much closer to the actual average value of 32' or 0.53 degrees. The discrepancy may come from a misinterpretation of what unit of measure was meant by a certain Greek term in the text of Aristarchus. Aristarchus claimed that at half moon (first or last quarter