Flux from the Sun on the Earth using the Stefan-Boltzmann law

What is wrong with this computation, plase? I am getting the result of 4291.65 W m^{-2} instead of 1361 W m^{-2}. Thank you very much

import numpy as np

R_S = 6.957e8  # m
au = 149597870700 # m
sigma_SB = 5.670374419e-8 # W m-2 K-4

# Sun parameters
R = 1 * R_S
d = 1 * au
T = 5777.2  # K

Earth_factor = R**2 * np.pi / d**2

E = sigma_SB * T**4 * Earth_factor
print('SB', E)

• Here's a tip: What's the ratio between the obtained and the expected result?
– pela
Nov 28, 2023 at 12:41
• Also: May I suggest using astropy.units? It's great for keeping track of units (although that's not your problem here).
– pela
Nov 28, 2023 at 12:43
• Thank you, pi. is the factor, but I do not know why. Nov 28, 2023 at 15:23
• Your Earth_factor is the ratio between the surface area of the Sun and the surface area of the sphere at which the Earth revolves (so to speak). The former is $4\pi R_\odot^2$, the latter is $4\pi(1\,\mathrm{AU})^2$, so both the 4's and the π's cancel. That is, Earth_factor = (R_S/d)**2.
– pela
Nov 28, 2023 at 20:20