High School Variation of Apparent Luminosity with Distance

[Agent Smith]

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 $\frac{D_X}{D_Y} = \frac{T_X}{T_Y}$

 

[Ibix]

Distance is measured by means that don't depend on luminosity (parallax?)

https://en.wikipedia.org/wiki/Cosmic_distance_ladder

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.

 

[Agent Smith]

So $A_X = \frac{T_X}{D_X {^2}}$. So I'd be underestimating the true luminosity.