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(A) The relationship between the brightness ratio of two celestial objects and their magnitudes is given by the formula: $\frac{I_1}{I_2} = 100^{(m_2

Vedclass · Accepted Answer

$10000$

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(A) The relationship between the brightness ratio of two celestial objects and their magnitudes is given by the formula: $\frac{I_1}{I_2} = 100^{(m_2 - m_1)/5}$.Here,for Venus,the magnitude $m_1 = -4$.For the dimmest visible star,the magnitude $m_2 = 6$.Substituting these values into the formula:$\frac{I_1}{I_2} = 100^{(6 - (-4))/5} = 100^{10/5} = 100^2$.Calculating the result: $100^2 = 10,000$.Therefore,Venus is $10,000$ times brighter than the dimmest visible star.

Assuming that the dimmest visible star to the naked eye has a magnitude of about $6$. The brightness of planet Venus (magnitude = $-4$) with respect to this star is ........ times brighter.

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