If the distance between us and a star is doubled, with everything else remaining the same, the luminosity If the distance between us and a s

Question

If the distance between us and a star is doubled, with everything else remaining the same, the luminosity If the distance between us and a star is doubled, with everything else remaining the same, the luminosity remains the same, but the apparent brightness is decreased by a factor of two. is decreased by a factor of four, but the apparent brightness remains the same. is decreased by a factor of two, and the apparent brightness is decreased by a factor of two. remains the same, but the apparent brightness is decreased by a factor of four. is decreased by a factor of four, and the apparent brightness is decreased by a factor of four.

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Thu Giang 4 years 2021-08-19T23:53:22+00:00 1 Answers 6 views 0

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  1. thanhha
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    2021-08-19T23:54:26+00:00
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    Answer:

    The luminosity remains the same, but the apparent brightness is decreased by a factor of four.

    Explanation:

    The apparent brightness, F = L/4πr² where L = luminosity and r = distance between us and the star.

    Since L is independent of the distance between us and the star, it is constant, then

    F ∝ 1/r²

    So, F₁/F₂ = r₂²/r₁² where F₁ = apparent brightness at r₁ and F₂ = apparent brightness at r₂

    If the distance is doubled, that is r₂ = 2r₁, then

    F₁/F₂ = r₂²/r₁²

    F₁/F₂ = (2r₁)²/r₁²

    F₁/F₂ = 4r₁²/r₁²

    F₁/F₂ = 4

    F₂ = F₁/4

    So, since the luminosity is constant, the luminosity remains the same, but the apparent brightness is decreased by a factor of four.

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