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Given information: Aeryn: Parallax: 0.0101″ Flux: 6.20e-8 W/m²…

Given information:
Aeryn:
Parallax: 0.0101″
Flux: 6.20e-8 W/m²

Crichton:
Parallax: 0.0068″
Flux: 8.10e-9 W/m²

Dargo:
Parallax: 0.0276″
Flux: 2.90e-10 W/m²

To calculate the distance and luminosity of Dargo:

Distance:
Distance (in light years) = 1 / Parallax (in arcseconds)
Distance (Dargo) = 1 / 0.0276 ≈ 36.23 light years

Distance (in meters):
1 light year = 9.461 × 10^15 meters
Distance (Dargo) = 36.23 light years * (9.461 × 10^15 meters/light year)
                 ≈ 3.43 × 10^17 meters

Luminosity:
Luminosity (in watts) = Flux (in watts per square meter) * 4 * π * (Distance in meters)^2
Luminosity (Dargo) = 2.90e-10 W/m² * 4 * π * (3.43 × 10^17 meters)^2
                 ≈ 4.78 × 10^27 watts

Now let’s calculate the luminosities of the other stars:

Aeryn:
Luminosity (Aeryn) = 6.20e-8 W/m² * 4 * π * (Distance of Aeryn in meters)^2
                   = 6.20e-8 W/m² * 4 * π * (1 / 0.0101)^2 * (3.43 × 10^17 meters)^2
                   ≈ 1.34 × 10^26 watts

Crichton:
Luminosity (Crichton) = 8.10e-9 W/m² * 4 * π * (Distance of Crichton in meters)^2
                     = 8.10e-9 W/m² * 4 * π * (1 / 0.0068)^2 * (3.43 × 10^17 meters)^2
                     ≈ 3.36 × 10^25 watts

To convert the luminosities into Ls (solar luminosities), we can use the conversion factor:

1 Ls (solar luminosity) = 3.828 × 10^26 watts

Converting the luminosities:

Luminosity (Dargo) in Ls = 4.78 × 10^27 watts / (3.828 × 10^26 watts/Ls)
                       ≈ 12.50 Ls

Luminosity (Aeryn) in Ls = 1.34 × 10^26 watts / (3.828 × 10^26 watts/Ls)
                       ≈ 0.35 Ls

Luminosity (Crichton) in Ls = 3.36 × 10^25 watts / (3.828 × 10^26 watts/Ls)
                          ≈ 0.09 Ls

Corrected answers:

Distance of Dargo: 36.23 light years or approximately 3.43 × 10^17 meters
Luminosity of Dargo: Approximately 4.78 × 10^27 watts or 12.50 Ls

Luminosity of Aeryn: Approximately 1.34 × 10^26 watts or

0.35 Ls

Luminosity of Crichton: Approximately 3.36 × 10^25 watts or 0.09 Ls

 

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