Editing Approximation (section)

== Science ==
Approximation arises naturally in [[scientific experiment]]s. The predictions of a scientific theory can differ from actual measurements. This can be because there are factors in the real situation that are not included in the theory. For example, simple calculations may not include the effect of air resistance. Under these circumstances, the theory is an approximation to reality. Differences may also arise because of limitations in the measuring technique. In this case, the measurement is an approximation to the actual value.

The [[history of science]] shows that earlier theories and laws can be ''approximations'' to some deeper set of laws. Under the [[correspondence principle]], a new scientific theory should reproduce the results of older, well-established, theories in those domains where the old theories work.<ref>[https://www.britannica.com/EBchecked/topic/138678/correspondence-principle Correspondence principle] – ''[[Encyclopædia Britannica]]''</ref> The old theory becomes an approximation to the new theory.

Some problems in physics are too complex to solve by direct analysis, or progress could be limited by available analytical tools. Thus, even when the exact representation is known, an approximation may yield a sufficiently accurate solution while reducing the complexity of the problem significantly. [[Physicists]] often approximate the [[shape of the Earth]] as a [[sphere]] even though more accurate representations are possible, because many physical characteristics (e.g., [[gravity]]) are much easier to calculate for a sphere than for other shapes.

Approximation is also used to analyze the motion of several planets orbiting a star. This is extremely difficult due to the complex interactions of the planets' gravitational effects on each other.<ref>[http://plus.maths.org/content/mathematical-mysteries-three-body-problem The three body problem]</ref> An approximate solution is effected by performing [[iteration]]s. In the first iteration, the planets' gravitational interactions are ignored, and the star is assumed to be fixed. If a more precise solution is desired, another iteration is then performed, using the positions and motions of the planets as identified in the first iteration, but adding a first-order gravity interaction from each planet on the others. This process may be repeated until a satisfactorily precise solution is obtained.

The use of [[Perturbation theory|perturbations]] to correct for the errors can yield more accurate solutions. Simulations of the motions of the planets and the star also yields more accurate solutions.

The most common versions of [[philosophy of science]] accept that empirical [[measurement]]s are always ''approximations'' — they do not perfectly represent what is being measured.