Stefan-Boltzman law (using Python)

 

스테판-볼츠만 법칙을 이용해 태양상수를 추정해보자.

 

 

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Stefan-Boltzman law

스테판-볼츠만 법칙은 단위면적당 방출되는 에너지의 총량과 흑체의 절대온도 사이의 관계식이다. 방출되는 복사 에너지는 절대온도의 네제곱에 비례한다. 이를 이용해 태양상수를 추정할 수 있다.

 

 

 

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Computing the solar constant at the Earth 

Computing the total energy emitting from the Sun and the Earth during 1 second. Assuming that the radius of the Sun and the Earth are about 675,000km and 6,400 km, respectively. Assuming that the distance between the Sun and the Earth is about 149,600,000km.

# Stefan-Bolzmann constant (Wm^-2K^-4)
s= 5.669e-8

# the total radiant energy per 1m^2 during 1 second
M_total_unit_sun = s*T_sun**4 
M_total_unit_earth = s*T_earth**4

# surface area of the Sun and the Earth
# radius of the Sun and the Earth
r_sun = 675000*1000 #(m)
r_earth = 6400*1000 #(m)

def surface_area_of_sphere(radius):
  return 4*pi*radius**2

surface_area_sun = surface_area_of_sphere(r_sun)
surface_area_earth = surface_area_of_sphere(r_earth)

# the total energy emitting
M_total_sun = M_total_unit_sun * surface_area_sun
M_total_earth = M_total_unit_earth * surface_area_earth

print(M_total_sun)
print(M_total_earth)

# the solar constant at the Earth
r_sun_to_earth = 149600000*1000 #(m)
solar_const = M_total_sun / surface_area_of_sphere(r_sun_to_earth)

print(solar_const)

 

Computed solar constant: 1398.4883799440274