The sun has a raduis of 6.96*10^8m and a surface temperature of 5780K. How much power is radiating?
I would assume it to be a black body.
http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law
To calculate the power radiated by the Sun, we can use the Stefan-Boltzmann law, which states that the power radiated by a blackbody is proportional to the fourth power of its temperature.
The formula for the power radiated by the Sun is given by:
P = σ * A * T^4
Where:
P is the power (in watts)
σ is the Stefan-Boltzmann constant (5.67 x 10^-8 W/m^2K^4)
A is the surface area of the Sun
T is the temperature of the Sun in Kelvin
Now, let's calculate the power radiated by the Sun:
1. Calculate the surface area of the Sun:
Given the radius of the Sun as 6.96 x 10^8 m, we can use the formula for the surface area of a sphere:
A = 4πr^2
Substituting the value of the radius, we have:
A = 4 * π * (6.96 x 10^8 m)^2
2. Calculate the power radiated by the Sun:
Now, substitute the values of the surface area and temperature into the formula:
P = 5.67 x 10^-8 W/m^2K^4 * A * (5780K)^4
Plug in the value of A calculated in the previous step, and simplify the equation to find the final answer.
Note: The power calculated is the total power radiated by the Sun in all directions.