Approximately how many times brighter is Venus at its peak magnitude compared to Sirius?
Answer
40 times brighter
The difference in apparent magnitude between Venus at its peak ($-4.92$) and the brightest star, Sirius ($-1.46$), is $3.46$ magnitudes. Since the astronomical magnitude scale is logarithmic, where a difference of one magnitude corresponds to a factor of about 2.5 times in brightness, this difference translates into a significant factor. Specifically, the calculation based on the scale demonstrates that the brightest Venus appears roughly $2.5^{3.46}$ times brighter than Sirius, which equates to approximately 40 times brighter in terms of total received light intensity.
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