[Tex/LaTex] An Extremely Long Equation with Fraction

equations

I don't know what to do in order to fit this equation in the document, because it's so long.
Help will be very appreciated, and also if someone have any idea how to simplify this equation it's will be very helpful. 

\documentclass[12pt]{article}
\begin{document}
\begin{equation} a(t) =
\frac{6.67384\times 10^{-11}\times 5.972\times 10^{24}}
{ \left[149.6\sin (\frac{3\pi t}{47\times 10^6})-0.908
\left( 2.5\times 10^{-8} t^2 + 9.479 \times 10^{-6}(t+
\left| t-379.189\right| -379.189)\right)\right]^2+
\left[149.638 - 0.418(2.5\times 10^{-8} t^2 + 9.479
\times 10^{-6}(t+\left| t-379.189\right| -379.189))- 149.6 \cos
\left( \frac{3\pi t}{47\times 10^6}
\right)\right]^2+ 0.0002831}
\end{equation}
\end{document}

Best Answer

How about

enter image description here

(You are obviously free to come up with snazzier symbols than "B", "C", and "D".)

\documentclass[12pt]{article}
\usepackage{mathtools}
\begin{document}
Let
\begin{equation} 
a(t) =
\frac{6.67384\cdot 10^{-11}\cdot 5.972\cdot 10^{24}}{B}
\end{equation}
where
\begin{align*}
B&= \bigl[149.6\sin C-0.908D \bigr]^2\\
&\quad+ \bigl[149.638 - 0.418D- 149.6 \cos C\bigr]^2 + 0.0002831\,,\\
C &= 3\pi t/(47\cdot 10^6)
\shortintertext{and}
D &= 2.5\cdot 10^{-8} t^2 + 9.479 \cdot 10^{-6}\bigl(t+
\lvert t-379.189\rvert -379.189\bigr)
\end{align*}
\end{document}
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