How to determine the Luminosity on Earth from Achernar?

Hi oem7110, you want to know how luminous earth is if you were looking at it from the sun/Achernar?

From Earth's point of view, when I look at Achernar at night, and would like to know how to determine the luminous of Achernar is based on following given data.  Furthermore, I am confusing on how luminous level are defined, does luminous already consider the size of Achernar? and how to determine the energy (W) is received on Earth?

Do you have any suggestions?
Thank you very much for any suggestions :>

Luminosity 3,150 L☉, (each L☉ corresponds to a power of exactly 3.828×1026 W)
Distance between Achernar and Earth    139 ± 3 ly = 8790360 ± 189720 AU

Distance between Sun and Earth : 1 AU
Luminosity 1 L☉

According to Wikipedia, there is a formula to determine luminosity

https://en.wikipedia.org/wiki/Luminosity#Luminosity_formula

See if this helps...

Based on following formula, the F of Achernar from earth is

F = 3,150 L☉ / (4 x pi x 139^2 ly) =  0.013 L☉ per ly, would it be correct?

Do you have any suggestions?
Thank you very much for any suggestions :>


Luminosity 3,150 L☉
Distance between Achernar and Earth    139 ± 3 ly = 8790360 ± 189720 AU
    A is the area of the illuminated surface.
    F is the flux density of the illuminated surface.

The surface area of a sphere with radius r is A = 4\pi r^2, so for stars and other point sources of light:
    F = L / (4 x pi x r^2)
where r is the distance from the observer to the light source.
Luminosity of Achernar

I'm not too sure about the mathematics involved. If someone can chime in and check these numbers, that'd be great