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A star was measured to have an apparent magnitude m=16 with S/N=10 integrated over a minute. What is the uncertainty in the measurement?

signal=flux*area*time

noise=sqrt(signal)=sqrt(fAt)

So, S/N=sqrt(fAt)

How can I find fA?

m=-2.5logfAt+K

16=-2.5log(fAt)+K

Hoping that K is arbitrary (please verify this), I choose K=0

Then 16=-2.5log(fAt)

So fA=3.98 e-7 J/s (units inconsequential)

So, uncertainty =6.3 e-4

??

HELP!

edit:

Or, I can get N=uncertainty=sqrt(S/10)=sqrtS <--- something VERY wrong here

signal=flux*area*time

noise=sqrt(signal)=sqrt(fAt)

So, S/N=sqrt(fAt)

How can I find fA?

m=-2.5logfAt+K

16=-2.5log(fAt)+K

Hoping that K is arbitrary (please verify this), I choose K=0

Then 16=-2.5log(fAt)

So fA=3.98 e-7 J/s (units inconsequential)

So, uncertainty =6.3 e-4

??

HELP!

edit:

Or, I can get N=uncertainty=sqrt(S/10)=sqrtS <--- something VERY wrong here

Last edited: