Geocentric model explanation in terms of the Earth's revolution about the sun. In 1838, astronomer Friedrich Wilhelm Bessel measured the parallax of the star 61 Cygni successfully, and disproved Ptolemy's claim that parallax motion did not exist. This finally confirmed the assumptions made by Copernicus, providing accurate, dependable scientific observations, and conclusively displaying how distant stars are from Earth. A geocentric frame is useful for many everyday activities and most laboratory experiments, but is a less appropriate choice for solar system mechanics and space travel. While a heliocentric frame is most useful in those cases, galactic and extragalactic astronomy is easier if
Central limit theorem possible values. The law of large numbers as well as the central limit theorem are partial solutions to a general problem: "What is the limiting behaviour of as approaches infinity?" In mathematical analysis, asymptotic series are one of the most popular tools employed to approach such questions. Suppose we have an asymptotic expansion of : Dividing both parts by and taking the limit will produce , the coefficient of the highest-order term in the expansion, which represents the rate at which changes in its leading term. Informally, one can say: " grows approximately as ". Taking the difference between and