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: 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) |