Flux of sunlight on Earth

Question

The luminosity of the Sun is 4∗10^33 erg s^−1, and its distance to the Earth is 1.5∗10^13 cm.

What is the flux of sunlight on the Earth, in units of erg s^−1 s^−1 cm^−2?

Answer 1

Luminosity is the total amount of energy produced by a star in a given time interval (e.g. ergs/s)

Flux is how much energy passes through a detector at a given location, or more specifically, flux is the amount of energy incident on an area in a specified amount of time.. This determines the apparent brightness of the source.

On astronomical scales, the Sun (or any star) can be taken to be a point source with a specific luminosity, or emitting a certain amount of energy over time. The energy expands out from the point in a spherical shell, so the emitted energy is spread over the surface area of a sphere of radius the distance from the star...the surface area is proportional to square of the distance from the star.

All of this reduces to the following relationship:

Flux = Luminosity / (4 * distance^2)

Flux = (4 * 10^33 ergs/s) / [(4)(1.5 * 10^13 cm)^2] = 4.4 * 10^6 ergs/s-cm^2