How does astronomy relate to meteorology?
My initial thought is that there is no relation, however since astronomy includes our Sun and Moon I have revised that thought to say that meteorology depends heavily on astronomy.
The Moon has an effect on atmospheric pressure in much the same way it affects tides. This is not a huge impact on meteorology at all but technically it does relate to meteorology.
The Sun, on the other hand, is where ALL the energy that drives the weather of the Earth. Any changes in the Sun's activity will directly impact the weather and climate of the Earth.