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.

Answer 1

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.