Flux from star  F_{∗}  (\frac{photons}{cm^{2} ∗ second})
Number of photons from star  N_{∗} = F_{∗} πR_{scope}^{2} t
Number of photons from background  N_{b} = F_{b} πR_{scope}^{2} t

Signal to noise ratio \frac{S}{N} ≃ \frac{N_{∗}}{\sqrt{N_{b}}}

\frac{F_{∗,Coma}}{F_{∗,Fornax}} = 10^{−0.2(3.8)} ≃ 0.17

F_{b,Coma} ≃ F_{b,Fornax}

\frac{F_{∗,Fornax} πR_{HST}^{2} t}{\sqrt{F_{b,Fornax} πR_{HST}^{2} t}} = \frac{(0.17 F_{∗,Fornax}) πR^{2} t}{\sqrt{F_{b,Fornax} πR^{2} t}}

R_{HST} = 0.17 R