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Fix index
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Signed-off-by: Marcello Seri <[email protected]>
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mseri committed Jul 23, 2024
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Expand Up @@ -234,7 +234,7 @@ \chapter*{Preface}
This is a scalar quantity that, as we will see, measures its resistance to changes in its state of motion, also known as \emphidx{inertia}.

\begin{tcolorbox}[title=Newton's second law of motion]
\index{Newton ! second law}
\index{Newton!second law}
There exist \emphidx{frames of reference}, that is, systems of coordinates, in which the motion of the particle is described by a differential equation involving the forces $\vb*{F}$ acting on the point particle, its mass $m$ and its acceleration as follows
\begin{equation}\label{eq:newton}
\vb* F = m \ddot{\vb*{x}}.
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In this model of the solar system, with the Sun fixed at the origin, we will describe the Earth by a point particle of mass $m$ whose position (and motion) is described by a vector $\vb*{x}\in\mathbb{R}^3$.

Due to our choice of coordinates, the gravitational attraction of the Sun acts in the direction of $-\vb*{x}(t)$.
\emph{Newton's law of universal gravitation} \index{Newton ! universal gravitation} says that such a force is proportional to
\emph{Newton's law of universal gravitation} \index{Newton!universal gravitation} says that such a force is proportional to
\begin{equation}
\frac{GmM}{\|\vb*{0}-\vb*{x}\|^2} = \frac{GmM}{\|\vb*{x}\|^2},
\end{equation}
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