Answer:
see the explanation part
Step-by-step explanation:
8.We can use the inverse square law to calculate the intensity of radiation reaching Earth from Antares. The inverse square law states that the intensity of radiation from a point source decreases as the square of the distance from the source increases.
The formula for the intensity of radiation is:
I = L / (4πd²)
where I is the intensity, L is the luminosity, and d is the distance from the source.
Substituting the values given in the problem, we get:
I = (3.1 x 10^26 W) / (4π x (5.246 x 10^16 m)^2)
I = 3.1 x 10^26 / (4π x 2.754 x 10^33)
I = 7.1 x 10^-8 W/m²
Therefore, the intensity of radiation reaching Earth from Antares is 7.1 x 10^-8 W/m².
9.We can use the same formula as in the previous question to calculate the intensity of radiation reaching Earth from Proxima Centauri:
I = L / (4πd²)
where I is the intensity, L is the luminosity, and d is the distance from the source.
Substituting the values given in the problem, we get:
I = (6.5 x 10^24 W) / (4π x (4.014 x 10^16 m)^2)
I = 6.5 x 10^24 / (4π x 6.431 x 10^32)
I = 4.0 x 10^-15 W/m²
Therefore, the intensity of radiation reaching Earth from Proxima Centauri is 4.0 x 10^-15 W/m².
10.We can use the Stefan-Boltzmann law to calculate the surface temperature of Vega:
L = 4πR²σT⁴
where L is the luminosity, R is the radius of the star, σ is the Stefan-Boltzmann constant, and T is the surface temperature.
We can rearrange this equation to solve for T:
T = (L / (4πR²σ))^(1/4)
We can also use Wien's displacement law to calculate the Amax value:
Amax = b / T
where Amax is the maximum spectral wavelength intensity, b is Wien's displacement constant, and T is the surface temperature.
Substituting the values given in the problem, we get:
T = [(1.5 x 10^28 W) / (4π x (4.18 x 10^11 m)² x 5.67 x 10^-8 W/(m²K⁴))]^(1/4)
T = 9,667 K
Amax = (2.898 x 10^-3 m·K) / 9,667 K
Amax = 3.0 x 10^-7 m
Therefore, the surface temperature of Vega is approximately 9,667 K, and its Amax value is approximately 3.0 x 10^-7 m.
11.We can use the same formulas as in the previous question to calculate the surface temperature and Amax value of Sirius:
Surface temperature:
L = 4πR²σT⁴
T = (L / (4πR²σ))^(1/4)
where L is the luminosity, R is the radius of the star, σ is the Stefan-Boltzmann constant, and T is the surface temperature.
Substituting the values given in the problem, we get:
T = [(9.7 x 10^26 W) / (4π x (1.8 x 10^11 m)² x 5.67 x 10^-8 W/(m²K⁴))]^(1/4)
T = 9,940 K
Amax value:
Amax = b / T
where Amax is the maximum spectral wavelength intensity, b is Wien's displacement constant, and T is the surface temperature.
Substituting the value of T we calculated above, we get:
Amax = (2.898 x 10^-3 m·K) / 9,940 K
Amax = 2.91 x 10^-7 m
Therefore, the surface temperature of Sirius is approximately 9,940 K, and its Amax value is approximately 2.91 x 10^-7 m.