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
I need actually answers.
