Computing the heavens   -   De sterrenhemel voor Nederland en België

## How to compute the magnitude and obscurity of a solar eclipse

I assume here that you have computed the moment of closest approach of the solar and lunar disc for a certain observer, so that the moment of maximum eclipse is defined and you have topocentric positional data for both objects. I therefore assume that you can calculate the distance between the centres of the two discs (Δ) and their radii: rs and rm.

The magnitude of a partial eclipse is equal to the fraction of the solar diameter that is covered by the Moon and given by:

mag = (rs + rm - Δ) / (2 rs)

For an annular eclipse (and I suppose this could also apply to a total solar eclipse), the magnitude is simply:

mag = rm / rs

The obscurity of a partial eclipse is defined by the fraction of the solar surface (rather than diameter) covered by the Moon. To compute it, one needs the following relations:

cos A = (rs2 - rm2 + Δ2) / (2 rs rm)

cos B = (rs2 + rm2 - Δ2) / (2 rs Δ)

C = π - A - B

D = rm / rs

obs = (D2 C + A - D sin B)/π

For a central eclipse (annular or total), A and B above are not defined, and the obscurity is simply given by:

obs = max(D2, 1)

Computing the heavens   -   De sterrenhemel voor Nederland en België