luminosity and flux

[StephenPrivitera]

L=A[sig]T4
f=L/A=[sig]T4
Where does time come into these equations?

If one telescope of a known diameter can reach a certain magnitude, it is easy to find what magnitude a different telescope of known magnitude can reach. But if a telescope integrating over 10s can reach a certain magnitude, how can we determine what magnitude the same telescope will reach integrating over 1hr?

Also, what does it mean for something to have a spectral resolution of 5?

[Nereid]

Where does time come into these equations?
What are the units of [sig]?
But if a telescope integrating over 10s can reach a certain magnitude, how can we determine what magnitude the same telescope will reach integrating over 1hr?
Assuming you're still way above sky noise, presumably.
If one star has a magnitude of 5, and another 10, what is the ratio of the energy received, in unit time, by the same telescope?
How many seconds are there in an hour?