Sky

With the configuration previously specified, in the V band the sky magnitude is 21.8 so:

$$M_{V}=21.8\Longrightarrow Z_{V}=7.4425\Longrightarrow F=6.87... ...} ~J\cdot s^{-1}\cdot m^{-2}\cdot \mu m^{-1}\cdot arcsec^{-2}$$

$$\displaystyle\left(\frac{F}{P}\right)_{Obj}=190.494940468~ph\cdot s^{-1}\cdot m^{-2}\cdot\mu m^{-1}\cdot arcsec^{-2}$$

Using the dispersion value $\Delta _{i}$, the telescope surface S, the exposure time T and the efficiency E as specified before, and taking in count theat the plate scale is 0.08 arcsecbin, we get

$$\Omega=0.0064~arcsec^{2}$$

So we get

$$N_{Sky}=\frac{F\cdot \Delta_{i}\cdot T\cdot E\cdot S\cdot\Omega}{P}= 29.7034950772\cdot~cnts\slash bin$$ (2.18)

The ETC for SUSI2 with the input parameter as specified above predicts N_ETC=30.22 cntsbin.