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

How can one mathematically verify this?

So far:


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 $=0.05 \,\mathrm{s}$


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

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

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.


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:

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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