A fisheye camera lens is used for a wide range of activities in different fields: Astronomers use a fisheye camera lens to project the night sky onto a dome in an observatory. They also project other weather phenomena onto the dome to provide a good experience for people. Flight simulators at aviation schools use fisheye camera lenses to immerse pilots in a simulated/training environment. Astronomers use fisheye lenses to obtain light pollution data and observe cloud formations. Computer graphic designers use fisheye lenses to create environment maps for rendering 3D images and virtual panoramas. Weather stations use fisheye camera lenses to monitor and share current sky conditions. They can also share previous weather conditions along with climate indicators such as temperature, humidity, rainfall, and wind. Photographers and videographers use fisheye camera lenses to create backgrounds in their work. It also allows them to get as close as possible to the subject and capture action shots.
With so many options available, choosing a lens for astrophotography seems quite daunting. Trust me, it's not an easy task. Astrophotography is like the ultimate test for optical quality of a lens because point light sources are the most challenging to capture, and stars are point light sources. Every lens has optical aberrations, and astrophotographers always want a lens with minimal optical defects. Ideally, you need a lens that has no chromatic aberration or coma. Almost all wide-angle lenses are affected by coma, some more severely than others. Except for lunar and solar astrophotography, you will be photographing very dim objects and will need low-aperture lenses. Lenses with apertures of f/2.8 or lower are more suitable for astrophotography.
Circular fisheye camera lenses are quite limited because you can't play around with composition too much. In most cases, in astrophotography, fisheye camera lenses are used to shoot directly upwards and include the entire sky in one frame. They are excellent choices for capturing the Milky Way or very active aurora storms as they cover the entire sky when the lights cover the whole sky. Circular fisheye camera lenses are also great for showing the orientation of the entire sky during a total solar eclipse. They can also be used for capturing meteor showers, especially shooting fireballs streaking across the sky. Note that most other meteors will appear short and not very impressive in a fisheye lens. You need bright and long-lasting fireballs to make the final image truly impressive.