Exoplanetary Transit Spectroscopic Modeling

Design and construct a physical analog model to simulate the light curve degradation of a star during planetary transit, accounting for limb darkening effects and potential starspot interference. You must calibrate your model to distinguish between planetary transit and intrinsic stellar variability signatures using a light-sensitive diode and a varying opacity mask. Finally, provide a mathematical derivation that correlates your experimental signal-to-noise ratio with the projected exoplanetary radius.