Final answer:
The luminosity of the Sun is calculated using the Stefan-Boltzmann Law by multiplying the Sun's surface area and the fourth power of its temperature, along with the Stefan-Boltzmann constant. The flux at Earth's orbit is then found by dividing the Sun's luminosity by the surface area of a sphere with a radius equal to the distance from the Sun to the Earth.
Step-by-step explanation:
To calculate the luminosity (L) of the Sun using the Stefan-Boltzmann Law, we first need the surface area (A) of the Sun, which can be calculated with the formula A = 4πR², where R is the Sun's radius. The Stefan-Boltzmann constant (σ) is a known physical constant. The formula for luminosity is L = AσT⁴, where T is the surface temperature of the Sun.
To calculate the flux (F) at the orbit of the Earth, we use the formula F = L / (4πd²), where L is the Sun's luminosity and d is the distance from the Sun to the Earth. This gives us the power received per unit area at the Earth's distance from the Sun.
For example, if the Sun has a radius of about 6.96 x 10⁸ meters and a surface temperature of approximately 5,778 K, and using the Stefan-Boltzmann constant σ = 5.67 x 10⁻⁸ W/m²·K⁴, the luminosity of the Sun can be calculated. Then, knowing that the average distance from the Sun to the Earth is about 1.496 x 10¹ⁱ meters, we can compute the solar flux at Earth.