Astrophotography is a whole other bag of worms. It requires new techniques and new equipment if you really want to get into it. Good news: you no longer have to get out of bed early to catch a sunrise. Bad news: you have stand out in the cold in the middle of the night while fiddling with your camera in the dark.
There are a number of challenges one faces (other than the cold weather) when doing night sky photography.
a. You are shooting in MUCH lower light conditions than you face in other types of photography. Thus, gathering light will be your main concern
b. You will struggle with trying to focus on a subject that is millions of miles away
c. You will have to raise your ISO and shoot at long shutter speeds (noisy photos)
d. To top it off, you are trying to capture a moving object... slow moving but moving, nonetheless
e. If you want to include foreground subject interest to your composition, that will probably need to be captured in another shot with its own exposure settings and then combined in Photoshop. You may also have to learn light painting techniques
f. If you really get into it, you may have to purchase some new hardware & software and learn how to use it.
BUT, you can probably get started with the equipment you already own... a decent camera, wide angle lens, tripod and some warm clothes. After an outing or more, you can then decide if this is something you wish to pursue.
This all probably seems daunting, and you are about to say, "no way". But if you persevere, you will add some very nice photos to your portfolio.
Milky Way photography resources - pick out the best ones to shorten this list
Milky Way Post Processing resources - pick out the best ones to shorten this list
How to Post Process an Astro Image - 26 min
Moon photography resources - pick out the best ones to shorten this list
If you enjoy all of this, you can really go nuts and attempt to take photos of galaxies!