I am studying the thermal radiation (Stefan–Boltzmann law) by myself
$$P = \epsilon \sigma A T^4$$
here $\epsilon$ is the emissivity, $\sigma$ is Stefan-Boltzmann constant, $A$ is the surface area of the radiating object, $T$ is the temperature of the radiating object. As my understanding, $P$ is the power radiating out of the source. But to figure out the power on the object away from the source due to the radiation, I find the calculation from the book
$$P_\text{desc} = \epsilon \sigma A (T_\text{src}^4 - T_\text{desc}^4)$$
again, $\epsilon$ and $A$ are the parameters for the radiating source. My question is why the power on the destination object only depends on the temperature^4 difference? So the parameters of the destination object (like it's surface area, heat capacity, etc.) have nothing to do with that power? I don't understand this from the physical point of view.
So if that's true, to calculate the power absorbed by the earth due to sun, should the following calculation sufficient?
$$P_\text{earth} = \sigma A_\text{sun}(5778^4 - 287^4) $$ where $5778K$ is the temperature of the sun surface, $287$ is the average temperature of the earth surface.