\vfill\break
\section{Velocity corrections}
\label{corrections}

The stars in the galactic disk do not revolve around the galactic
center completely uniformly: each star's orbit differs by a little
from the average behavior.  The fact that Sun has a certain ``drift''
velocity relative to the rotation of the galactic disk must be taken
into account in calculations of the velocity of interstellar hydrogen.

The velocity can be determined by observation of nearby stars; for our
calculations, we used the data from \cite{allen}. The velocity is
19.7~km/sec, pointing toward $239.9\deg$ galactic longitude, $31.4\deg$
galactic latitude.

\begin{figure}[ht]
\begin{center}
\leavevmode
\epsfxsize=0.5\hsize
\epsfbox{/mit/bert/Class/JuniorLab/paper/correction.eps}
\end{center}
\caption{Calculation of the velocity correction}
\end{figure}

If our antenna is pointing towards a point on the galactic equator at
some galactic longitude $\Theta$, the magnitude of the projection of
the Sun's drift velocity onto the line of sight will be
$$\Delta v_S = 20{\rm km\over sec} \cdot\cos(31.4\deg)\cos(239.9\deg-\Theta)$$
(the first cosine for projection into the galactic plane, the second
for projection in the correct longitudinal direction).

Another correction we must take into account here is the one for
Earth's rotation.  Earth's orbital speed is 30~km/sec, i.e., {\em
more} than the drift of the Sun relative to the neighboring stars.
The direction of Earth's motion varies seasonally.  Since the Earth's
orbit is nearly circular, we can assume that Earth's motion is
perpendicular to the position of the Sun relative to Earth, which ban
be found in ephemeris tables; we obtained it from the telescope-controlling
program on the PC instead.  The direction for the end of October, when
we took our data, points toward $22.5\deg$ galactic longituide,
$25\deg$ latitude.  The projection onto line of sight is, like above:
$$\Delta v_E = 25{\rm km\over sec}
\cdot\cos(25\deg)\cos(22.5\deg-\Theta)$$

The corrected velocity along the line of sight is obtained by
subtracting these two corrections from the mesured velocity:

$$ V' = V - \Delta v_S - \Delta v_E $$
