How this instrument works
Radiation pressure is the mechanical push that an electromagnetic wave exerts on whatever it strikes, and it exists because light carries momentum even though a photon has zero rest mass. For a wave of energy E, the momentum is p = E ⁄ c, so a beam delivering power I over one square metre each second hands over momentum at the rate I ⁄ c — and momentum delivered per second per area is, by definition, a pressure. The units work out to newtons per square metre, the pascal, same as any other pressure.
The (1 + r) term in the formula is what separates a black panel from a mirror. A fully absorptive surface (r = 0, Reflective surface set to 0) simply keeps the momentum it receives, so P = I ⁄ c. A fully reflective surface (r = 1) sends the light back the way it came, and reversing a photon's momentum costs twice as much force as merely stopping it, so P = 2I ⁄ c. James Clerk Maxwell predicted this doubling from his electromagnetic theory in 1873, and Pyotr Lebedev, then separately Ernest Nichols and Gordon Hull, confirmed it with torsion balances in 1900 and 1901 — a genuinely difficult measurement, since the forces involved are tiny.
The formula assumes the light hits the surface square-on. At a grazing angle, the pressure drops sharply, by a factor of cos²θ from the normal — once because the same power spreads over more surface area, once again because only the component of momentum perpendicular to the surface pushes on it. That angle dependence is why a solar sail is steered by tilting, not by throttling: turning the sail face away from the Sun reduces thrust without touching the light source at all.
- Enter the light's power per area in Radiation intensity, W ⁄ m² — the irradiance measured face-on to the beam, such as a solar-panel test rating or a laser's power divided by its spot area.
- Set Reflective surface to 1 for a mirror-like, fully reflective target, or 0 for a matte, fully absorptive one.
- Read Radiation pressure in pascals. Expect a very small number — everyday light levels sit in the micropascal range.
- To compare surfaces, run the same intensity twice, once with each Reflective surface setting; the reflective result is always exactly double the absorptive one.
Worked example — noon sunlight on an absorptive panel
Take sunlight at 1000 W ⁄ m², roughly its strength at the ground near solar noon and also the standard test condition used to rate photovoltaic panels, striking a matte black surface that absorbs essentially everything it receives, so Reflective surface is 0. The formula gives P = I(1 + r) ⁄ c = 1000 × (1 + 0) ⁄ 299,792,458 = 3.33564095198 × 10⁻⁶ Pa, about 3.34 micropascals. That is roughly a hundred-millionth of ordinary atmospheric pressure — no hand could feel it, but a torsion balance in vacuum reads it directly.
Switch Reflective surface to 1 and leave the intensity unchanged: P = 1000 × 2 ⁄ 299,792,458 = 6.67128190396 × 10⁻⁶ Pa, exactly double. That doubling is why spacecraft solar sails, such as NASA's Advanced Composite Solar Sail System and its reflective aluminized film, are built shiny rather than dark — the same sunlight buys twice the thrust off a mirror finish as it does off a black one.
Questions
Why does a mirror feel more radiation pressure than a black surface?
Because reversing a photon's momentum takes more force than just stopping it. An absorptive surface keeps the incoming momentum, giving P = I ⁄ c. A reflective surface sends that momentum back the way it came, so the surface must supply the incoming push and the outgoing push, giving P = 2I ⁄ c — exactly double, which is what setting Reflective surface to 1 instead of 0 does in the formula.
Is radiation pressure the same force that pushes a comet's tail?
Not entirely. A comet's dust tail is shaped mainly by this photon radiation pressure, but its separate ion tail is shaped by the solar wind — a stream of charged particles from the Sun, not light. The two forces point in slightly different directions and scale differently with distance, which is why a comet often shows two visibly separate tails.
Why is the pressure such a tiny number for ordinary light?
Because the speed of light, 299,792,458 m ⁄ s, sits in the denominator. Dividing an everyday intensity like 1000 W ⁄ m² by a number in the hundreds of millions produces a result in the micropascal range no matter what the intensity is. Radiation pressure only becomes a dominant force over astronomical distances, long timescales, or extremely intense beams such as focused lasers.
Does radiation pressure actually matter for real satellites?
Yes. Solar radiation pressure is a standard perturbation in orbit-determination models, alongside gravity and drag. It slowly bends the orbits of geostationary and GPS satellites, and its effect scales with a spacecraft's area-to-mass ratio, so large, light structures such as deployed solar arrays or sails are affected the most. Mission planners must model it explicitly for multi-year position accuracy.
Can Reflective surface take a value between 0 and 1?
In this instrument it is a two-state switch: 1 for fully reflective, 0 for fully absorptive. Physically the underlying formula, P = I(1 + r) ⁄ c, does support fractional reflectivity for a partially mirrored surface, but this calculator is built around the two clean, verifiable limiting cases rather than an in-between estimate.
Who first measured radiation pressure, and how?
Pyotr Lebedev in 1900, followed independently by Ernest Nichols and Gordon Hull in 1901, suspended a set of mirrored and blackened vanes on a fine torsion fibre inside a vacuum chamber and shone light on them. The vanes twisted by an amount matching Maxwell's 1873 prediction, confirming that light carries momentum decades before the photon concept existed.