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{\bf 29:61 General Astronomy\\
     Fall 2004\\
     Lecture 7 \ldots September 15,2004\\
     The Orbit of the Moon and Eclipses}\\

{\em Just the facts, Ma'am}
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\noindent
$\bullet$ The altitude angle of a celestial object at transit is 
\begin{equation}
Al = \bar{\lambda} + \delta
\end{equation}
where $\delta$ is the declination of the object, and $\bar{\lambda}$ is the complement of the latitude.

\noindent
$\bullet$ The average inclination of the Moon's orbit to the plane of the ecliptic,
$\iota = 5^{\circ} 08^{'}$.  

\noindent
$\bullet$ The average angular diameter of the Sun as seen from Earth,
$\theta = 32^{'}$.  

\noindent
$\bullet$ The maximum distance $l$  in back of an object in which an umbral eclipse of the Sun will be seen  is 
\begin{equation}
l = \frac{d}{2\tan [\theta/2]}
\end{equation}
where $d$ is the diameter of the object, and $\theta$ is the angular diameter of the Sun at that point (32 arcminutes at the orbit of the Earth). 



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