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which is the universal variable formulation of Kepler's Equation. This equation can now be solved numerically using a [[root-finding algorithm]] such as [[Newton's method]] or [[Laguerre's method]] or a given time <math>t</math> to yield <math>s</math>, which in turn is used to compute the [[f and g functions]]:
:<math>\begin{align}
f(s) & = 1 - \left(\frac \mu {r_0}\right) s^2 c_2(\alpha s^2), \\
g(s) & = t - t_0 - \mu s^3c_3(\alpha s^2), \\
\frac{df}{dt} & = -\left(\frac{\mu}{r r_0}\right)s c_1(\alpha s^2), \\
\frac{dg}{dt} & = 1 - \left(\frac{\mu}{r}\right)s^2c_2(\alpha s^2)
\end{align}</math>
The values of the f and g functions determine the position of the body at the time <math>t</math>.
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