Editing Equation of time (section)

=== Secular change ===

The difference between the MICA and {{math|Δ''t''}} results was checked every 5&nbsp;years over the range from 1960 to 2040. In every instance the maximum absolute error was less than 3&nbsp;s; the largest difference, 2.91&nbsp;s, occurred on 22&nbsp;May 1965 (day&nbsp;141). However, in order to achieve this level of accuracy over this range of years it is necessary to account for the secular change in the orbital parameters with time. The equations that describe this variation are:{{r|Duffett-Smith|p=86}}{{r|Hughes+|p=1531,1535}}
:<math>\begin{align}
e &= 1.6709 \times 10^{-2} - 4.193 \times 10^{-5}\left(\frac{D}{36\,525}\right) - 1.26\times 10^{-7}\left(\frac{D}{36525}\right)^2 \\
\varepsilon &= 23.4393-0.013\left(\frac{D}{36\,525}\right) - 2\times 10^{-7}\left(\frac{D}{36\,525}\right)^2 + 5\times 10^{-7}\left(\frac{D}{36\,525}\right)^3\mbox{ degrees} \\
\lambda_\mathrm{p} &= 282.938\,07 + 1.7195\left(\frac{D}{36\,525}\right) + 3.025\times 10^{-4}\left(\frac{D}{36\,525}\right)^2\mbox{ degrees}
\end{align}</math>
According to these relations, in 100&nbsp;years ({{math|''D''}}&nbsp;=&nbsp;{{val|36525}}), {{math|''λ''<sub>p</sub>}} increases by about 0.5% (1.7°), {{math|''e''}} decreases by about 0.25%, and {{math|''ε''}} decreases by about 0.05%.

As a result, the number of calculations required for any of the higher-order approximations of the equation of time requires a computer to complete them, if one wants to achieve their inherent accuracy over a wide range of time. In this event it is no more difficult to evaluate {{math|Δ''t''}} using a computer than any of its approximations.

In all this note that {{math|Δ''t<sub>ey</sub>''}} as written above is easy to evaluate, even with a calculator, is accurate enough (better than 1&nbsp;minute over the 80-year range) for correcting sundials, and has the nice physical explanation as the sum of two terms, one due to obliquity and the other to eccentricity that was used previously in the article. This is not true either for {{math|Δ''t''}} considered as a function of {{math|''M''}} or for any of its higher-order approximations.