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Hipparcus said the faintest magnitude of a star the human eye can see is 6.

How can one mathematically verify this?

So far:

Assumptions:

Human eye receives $1000 \,\mathrm{photons/(cm^2 \, Angstrom)}$

Human eye pupil area $=0.5 \,\mathrm{cm^2}$

Passband bandwitdh in the eye is $2000 \,\mathrm{Angstrom}$

integration time $=0.05 \,\mathrm{s}$

Calculations:

$n_\text{photons}=\text{flux}\times \text{area}\times \text{integration time}$

$\text{flux}=1000/{0.5\times 0.05}=40000 \text{photons/seconds Angstrom}$

How can I proceed from here?

Should i get data from a known star to use it to determine the magnitude?

Any hints or advice will be deeply appreciated.

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closed as off-topic by rob May 27 '18 at 19:27

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – rob
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ Hello! Please don't re-ask closed questions. $\endgroup$ – rob May 27 '18 at 19:28
  • $\begingroup$ I showed effort to work through the question and I asked if I should pursue a specific direction. And the answer, if given would have applied to several other problems and as this particular calculation has no easily find-able sources I believe it is in the best interest of the community to keep this question open. But your call... $\endgroup$ – user3636673 May 27 '18 at 22:41
  • $\begingroup$ @JDOe You might like to raise this issue in Physics Chat. $\endgroup$ – rob May 28 '18 at 16:35