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{\bf 29:61 General Astronomy\\
     Fall 2004\\
     Lecture 7 \ldots September 17,2004\\
     Eclipse Cycles and Precession}\\

{\em Just the facts, Ma'am}
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\noindent
$\bullet$ Synodic period of the Moon: $P_{syn}=29.5306$ days.\\
$\bullet$ Nodal period of the Moon: $P_{nod}=27.2122$

\noindent
$\bullet$ Condition for repetition of eclipses:
\begin{equation}
mP_{nod} = nP_{syn}
\end{equation}
with $m$,$n$ integers

$\bullet$ Angular momentum of an object (with mass m) moving with velocity $\vec{v}$ a distance $\vec{r}$ from the origin of a coordinate system:
\begin{equation}
\vec{L} = m \vec{r} \times \vec{v}
\end{equation}

$\bullet$ Definition of vector angular velocity $\vec{\omega}$, such that $|\omega| = \frac{d \theta}{dt}$,
\begin{equation}
\vec{\omega} = \frac{1}{r^2} \vec{r} \times \vec{v}
\end{equation}
Then, 
\begin{equation}
\vec{L} = r^2m \vec{\omega} = I \vec{\omega}
\end{equation}
With $I$ the {\em moment of inertia}.  

$\bullet$ Moment of inertia for uniform sphere of mass $M$ and radius $R$:
\begin{equation}
I = \frac{2}{5} M R^2
\end{equation}

$\bullet$ Definition of torque: causes change in angular momentum with time:
\begin{equation}
\vec{\tau} = \frac{d \vec{L}}{dt}
\end{equation}





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