Problem — Reflective solar sail

Problem

A perfectly reflecting sail of area $A=100$ m² receives $I=1{,}4\cdot 10^3$ W/m² at $1$ AU. Estimate the radiation force using $P_\text{rad}=2I/c$.

Solution

Radiation pressure (reflecting surface). For total reflection the pressure is double that for absorption:

$P_\text{rad}=\frac{2I}{c}=\frac{2\cdot 1{,}4\cdot 10^3}{3{,}00\cdot 10^8}\approx 9{,}3\cdot 10^{-6}\ \text{Pa}$

Force on the sail. The force is pressure times area:

$F=P_\text{rad}\,A=9{,}3\cdot 10^{-6}\cdot 100\approx 9{,}3\cdot 10^{-4}\ \text{N}$

$\ev{F\approx 9{,}3\cdot 10^{-4}\ \text{N}}$

Less than a millinewton: tiny, but acting continuously in space it accumulates speed over time.

Collegamenti

Argomenti: Onde elettromagnetiche Concetti: Pressione di radiazione