\section{Effective temperature of the sun}
\par
To determine the effective temperature of the sun at 21 cm, we allowed
the sun to drift through our telescope. This produced a power curve
that followed the characterstic Bessel function of a circular
arpeture.  We also calibrated our telescope using a noise diode, which
filled the antenna with a signal equivalent to that of a black body at
150 K. In both cases, we plotted the power at the telescope antenna
verses time.
\par 
Using the output from the noise diode as a reference, we found that the
height of the power curve corresponded to an effective temperature of
469 K, with an error of about 9 K.  This value,
however, does not take into account the fact that the solid angle of
the sun is far less than the solid angle of the telesope.  To correct
this, we measured the full width at half power of the power curve. The
value of 1376 seconds we obtained, is about 1.6\% of 24 hours. Thus,
the beam angle of the telescope is about 1.6\% of $360\deg$, or
about $5.7\deg$ with an error of $0.3\deg$. The well-known value
of the linear angle subtended by the sun is $.5\deg$.
\par
We must multiply our value for the temperature of the sun by the
ratio of the solid angle of the telescope to that of the sun.  Since
the solid angle is proportional to the square of the linear angle,
this correction factor becomes:

\begin{equation}
 c = \left( \frac{\sin\theta_{b}}{\sin\theta_\sun}\right)^{2}. 
\label{corr}
\end{equation}

where $ \theta_{b} $ is the beam angle of the telescope.  After
applying this correction factor, we calculate the effective
temperature of the sun to be about 60,000 K, with an error of about
10\%.  In \cite{sun}, we find that this temperature is consistent with
predicted values in the range of frequencies we are studying.
