An observer uses the B and V filters to obtain four exposures of the same field at different air masses: two B exposures at air masses 1.05 and 2.13, and two V exposures at air masses 1.10 and 2.48. Four stars in this field are photometric standards. Their standard magnitudes given in the table below, as are the instru are mental magnitudes in each frame. |(B- V b(2) v1) b(1) v(2) V Air mass 2.48 1.05 2.13 1.10 Star A 12.01 10.687 8.778 -0.07 9.853 9.427 Star B 0.36 9.739 12.44 10.693 11.479 9.160 0.69 8.873 Star C 11.462 12.19 10.759 9.425 Star D 1.15 12.89 11.898 12.547 9.522 10.002 (a) Compute the extinction coefficients for the instrumental system: k,, k", k^, and kf". Hint: at each air mass, Equation (10.10) holds. Write an equation for the differ- at the two air masses (e. g. ence between the magnitudes equation for b(2) - an b(1)). Examination of this equation will suggest a method for computing the coefficients. You may find it helpful to enter the data from the table into a spreadsheet in performing the computations
(b) Compute the instrumental magnitudes of each star at zero air mass