Question

How can you calculate solar luminosity of the Sun using Earth's solar constant?

Answer 1

383 YW

Explanation:

Let
I = solar Irradiance aka solar constant `= 1361 W/m`
`r =`sun-earth distance or A.U. `= 1.496 xx10^11m`
`A = 4pir^2` spherical area at a distance 1 A.U. from the sun
`L=` Luminosity

Imagine the sun is surrounded by an imaginary spherical surface that is 1 AU away. The earth is thus a tiny part of the surface. From earth we measure that at this distance from the sun the solar constant is 1361 W/m; therefore the imaginary surface must collect the solar flux in its totality:

`L = AI = 4pir^2*I =4pi*(1.496xx10^11m)^2*1361 W/m`
`L= 3.83xx10^26 W = 383 YW`

Bear in mind that 383 Yotta Watts is calculated from the average sun-earth distance. The earth sometimes moves closer to the sun and sometimes further away. So the solar luminosity do vary depending on the position of the sun.

Another way is to use Stefan-Boltzman's Law which is independent of the sun-earth distance.

`L = sigmaAT^4`

`sigma, A and T` are Stefan-Boltzman constant, the sun's surface area and temperature respective.

Both methods yield similar results.