How to compute the magnitude and obscurity of a solar eclipseI 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: r_{s} and r_{m}.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 = (r_{s} + r_{m} - Δ) / (2 r_{s}) For an annular eclipse (and I suppose this could also apply to a total solar eclipse), the magnitude is simply: mag = r_{m} / r_{s} 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 = (r_{s}^{2} - r_{m}^{2} + Δ^{2}) / (2 r_{s} r_{m}) cos B = (r_{s}^{2} + r_{m}^{2} - Δ^{2}) / (2 r_{s} Δ) C = π - A - B D = r_{m} / r_{s} obs = (D^{2} 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(D^{2}, 1) |