As eclipse is a special type of Rosh Chodesh, we already have some liturgy and minhagim. Maybe there is no reason to announce rosh chodesh this week in shul in those places where it will be visible!
Following Chofetz Chaim ^, we can reflect on what eclipse represents. For example, it seems to be a very peculiar configuration of the solar system that even allows for eclipses (ekleípseon? eclepsim?): that moon trajectory is tilted such that it is sometimes goes into the same plane as earth and sun, and that sun and moon apparent sizes are close. Imagine how un-spectacular eclipse is on Jupiter – when every little moon transits in front of us and cover 5% of it. And if moon trajectory will be fully in the same plane as sun and earth, then would it be a monthly event? not so spectacular again …