Question

# Radiant energy from the Sun arrives at Earth with an intensity of $1.5 kW/m^2.$ Making the rough approxima- Sion that all photons are absorbed, find (a) the radiation pressure and (b) the total force experienced by Earth due to this “solar wind.”

Solution

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a) The total energy is by definition is the energy of a single photon times the number of photons emitted ($n$), equivalently, you can define it as the power ($W$) emitted in a given period of time. Starting with this definition and considering the variation in momentum $\Delta p$ in a certain time interval $\Delta t$, we could derive an expression for the pressure ($P$) that relate it to the problem given quantities.

$\begin{gather*} \therefore W \Delta t = nhf = \frac{nhc}{\Delta \lambda}\\ \because W = IA \:\:,\:\: \Delta \lambda = \frac{h}{\Delta p}\\ \therefore IA\Delta t = n\Delta pc \\ \because F_{\text{tot}} = n \frac{\Delta p }{\Delta t} \:\:,\:\: P = \frac{F_{\text{tot}}}{A} = \frac{n\Delta p }{A\Delta t} \\ \therefore P = \frac{I}{c} = \frac{1.5 \times 10^3\:\:\mathrm{W/m^2}}{3\times 10^8\:\:\mathrm{m/s}} \\ \boxed{\therefore P = \mathbf{5\times 10^{-6} \:\:Pa} } \end{gather*}$

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