There isn't a specific term for someone who studies eclipses. However, depending on the focus of their study, you could call them:

* Astronomer: This is the most general term for someone who studies celestial objects and phenomena, including eclipses.

* Solar Physicist: If their focus is on the Sun and its activity related to eclipses, this is a more specific term.

* Astrophysicist: This term encompasses a broader range of celestial phenomena, but they may study eclipses as part of their research.

* Eclipsologist: While not a commonly used term, it's technically accurate and may be used in informal contexts.

Ultimately, the best term to use depends on the specific context and the person's area of expertise.