Sky

With the configuration previously specified, in the B band the sky magnitude is 22.7 so:

$$M_{B}=22.7\Longrightarrow Z_{B}=7.1804\Longrightarrow F=5.49... ...} ~J\cdot s^{-1}\cdot m^{-2}\cdot \mu m^{-1}\cdot arcsec^{-2}$$

$$\displaystyle\left(\frac{F}{P}\right)_{Obj}=121.639165584\cdo... ...{3}~ph\cdot s^{-1}\cdot m^{-2}\cdot\mu m^{-1}\cdot arcsec^{-2}$$

Using the dispersion value $\Delta _{S}$, the telescope surface S, the exposure time T and the efficiency E as specified before, and taking in count that the plate scale is 0.2 arcsecpix and the slit width is 2 arcsec, we get

$$\Omega=0.4~arcsec^{2}$$

So we get

$$N_{Sky}=\frac{F\cdot \Delta_{S}\cdot T\cdot E\cdot S\cdot\Omega}{P}= 2.11543821788\cdot~cnts\slash bin$$ (2.14)

The ETC for FORS1 with the input parameter as specified above predicts N_ETC=2.1149 cntsbin.