Engineering
Poynting Vector Electromagnetic Intensity & Solar Sail Radiation Pressure
Calculate electromagnetic wave irradiance I = E_0^2 / (2 * c * mu_0) from peak electric field E_0 and compute absorbed (I / c) vs perfectly reflected (2 * I / c) radiation thrust.
Ideal plane-wave intensity and normal-incidence force
For a sinusoidal plane wave in vacuum, peak electric-field amplitude E0 gives time-averaged irradiance E0^2/(2*c*mu0). RMS field instead gives E_rms^2/(c*mu0); confusing peak with RMS changes the answer by a factor of two. The formula computes a scalar average magnitude, not a full Poynting vector.
A surface perpendicular to the incident beam experiences pressure I/c for perfect absorption or 2I/c for perfect specular reflection. Multiply by illuminated area for force. Oblique incidence, partial reflection, thermal emission and shadowing require additional modeling.
The chosen field is an illustrative sinusoidal equivalent, not a measured solar spectrum or fixed solar constant. Real sunlight is broadband. The 92.12 mN result assumes the specified intensity illuminates the full area normally and is perfectly reflected; it is not a prediction of continuous real-orbit thrust. The permeability input is rounded.
| Electromagnetic Wave Metric | Formula | Illustrative E0=1020 V/m, area=10000 m^2 | Zero Field (Eclipse E_0 = 0) |
|---|---|---|---|
| Free-Space Impedance Z_0 | c * mu_0 | 376.73 ohms | 376.73 ohms |
| Wave Irradiance I (W/m^2) | (E_0 ^ 2) / (2 * c * mu_0) | 1380.83 W/m^2 in this example | 0.00 W/m^2 |
| Reflected Sail Thrust (mN) | ((2 * I / c) * Area) * 1000 | 92.12 mN ideal normal force | 0.00 mN |
Time-Averaged Poynting Irradiance I = E_0^2 / (2 * c * mu_0) (W/m^2)
Enter nonnegative peak amplitude in V/m and positive vacuum constants in SI units. Squaring is performed before display rounding.
=IF(COUNT(B2:B4)<>3,"Invalid inputs",IF(OR(B2<0,B3<=0,B4<=0),"Invalid inputs",ROUND((B2 ^ 2) / (2 * B3 * B4), 2)))Perfectly Reflecting Solar Sail Thrust in Millinewtons (mN)
Uses unrounded irradiance and nonnegative illuminated area in m^2. Force is converted from N to mN. A zero area produces zero force but does not change irradiance.
=IF(COUNT(B2:B5)<>4,"Invalid inputs",IF(OR(B2<0,B3<=0,B4<=0,B5<0),"Invalid inputs",ROUND(((2 * ((B2 ^ 2) / (2 * B3 * B4)) / B3) * B5) * 1000, 2)))Perfectly absorbing surface force (mN)
For the same normal incidence and area, absorption transfers half the momentum of ideal backward reflection.
=IF(COUNT(B2:B5)<>4,"Invalid inputs",IF(OR(B2<0,B3<=0,B4<=0,B5<0),"Invalid inputs",ROUND(((((B2 ^ 2) / (2 * B3 * B4)) / B3) * B5) * 1000, 2)))Try the example
Use the original values or change them to test your understanding.