B Variation of Apparent Luminosity with Distance

AI Thread Summary
Apparent luminosity is measurable and varies with distance, which can be determined using parallax methods. The relationship between true luminosity and distance is expressed as ##A_X = \frac{T_X}{D_X^2}##, indicating that apparent luminosity decreases with the square of the distance from the observer. This means true luminosity can be calculated using the formula ##T_X = A_X \times D_X^2##. Additionally, if two objects have the same apparent luminosity, their distances can be compared using the ratio of their true luminosities. Understanding these relationships is crucial for accurately assessing the luminosity and distance of celestial objects.
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True luminosity of object X = ##T_X##
Apparent luminosity object X = ##A_X##
Distance of object X from observer = ##D_X##
True luminosity of object Y = ##T_Y##
Apparent luminosity of object Y = ##A_Y##
Distance of object Y from observer = ##D_Y##

Apparent luminosity is something measurable I suppose. Distance is measured by means that don't depend on luminosity (parallax?)

Assuming ##A_X = \frac{T_X}{D_X}## and ##A_Y = \frac{T_Y}{D_Y}##

So we can find ...
1. True luminosity: ##T_X = A_X \times D_X## and ##T_Y = A_Y \times D_Y##
2. The relative distance of luminous objects: Assuming ##A_X = A_Y##, we have ##\frac{D_X}{D_Y} = \frac{T_X}{T_Y}##
 
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Agent Smith said:
Distance is measured by means that don't depend on luminosity (parallax?)
https://en.wikipedia.org/wiki/Cosmic_distance_ladder
Agent Smith said:
Assuming ##A_X = \frac{T_X}{D_X}## and ##A_Y = \frac{T_Y}{D_Y}##
No, the measured luminosity drops with the square of distance. The light emitted in a short time period forms an expanding sphere around the source. The total energy of the light is constant, but spread over the area of the sphere which grows with the square of distance.
 
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So ##A_X = \frac{T_X}{D_X {^2}}##. So I'd be underestimating the true luminosity.
 
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