Radiation Pressure Calculator
Calculate radiation pressure from stars using p = xLcos²α/(4πR²c) for external pressure or p = 4σT⁴/(3c) for stellar interiors. Free online astrophysics calculator with charts.
About This Calculator
The Radiation Pressure Calculator computes the pressure exerted by electromagnetic radiation on surfaces, a key concept in astrophysics and space exploration. Radiation pressure arises because photons (particles of light) carry momentum — when they strike a surface, they transfer that momentum, producing a force. While negligible on Earth, this pressure becomes critically important in stars and for spacecraft propulsion using solar sails.
This calculator supports two modes. External mode calculates the radiation pressure from a star at a given distance using the formula p = xLcos²α / (4πR²c), where x = 1 for absorbing surfaces or 2 for perfectly reflective surfaces, L is the star's luminosity in watts, R is the distance in meters, α is the angle of incidence, and c is the speed of light. Internal mode calculates the radiation pressure inside a stellar interior using p = 4σT⁴ / (3c), where σ is the Stefan-Boltzmann constant (5.670367 × 10⁻⁸ W·m⁻²·K⁻⁴) and T is the temperature in kelvin.
For context, the Sun emits 3.828 × 10²⁶ W of power. At Earth's average distance of 1 AU (1.496 × 10¹¹ m), sunlight produces a radiation pressure of about 4.54 μPa on an absorbing surface. A perfectly reflective solar sail at the same distance experiences about 9.08 μPa — double the thrust. Inside the Sun's core at 15 million K, radiation pressure reaches approximately 1.3 × 10¹³ Pa (130 billion atmospheres), which is essential for maintaining hydrostatic equilibrium against gravitational collapse.
Applications
Radiation pressure drives several important astrophysical phenomena and technologies. The solar wind and radiation pressure together shape cometary tails, with the dust tail pushed away by sunlight. Massive stars (O and B types) lose significant mass through radiation-driven stellar winds. In space technology, solar sails like the Planetary Society's LightSail 2 (2019) demonstrated controlled orbit changes using only sunlight pressure, paving the way for future deep-space missions that do not require propellant.
Frequently Asked Questions
What is radiation pressure?
Radiation pressure is the pressure exerted by electromagnetic radiation on any surface it strikes. Photons carry momentum and when they hit a surface they transfer that momentum producing a tiny but measurable force. For sunlight at Earth distance the radiation pressure is about 4.5 μPa on an absorbing surface and 9 μPa on a reflective surface.
How do you calculate radiation pressure?
For radiation arriving from a star use p = xLcos²α/(4πR²c) where x is 1 for absorbing or 2 for reflective surfaces L is the star luminosity R is distance from the star α is the incident angle and c is the speed of light. For stellar interiors use p = 4σT⁴/(3c) where σ is the Stefan-Boltzmann constant and T is the temperature.
What is radiation pressure inside the Sun?
Inside the Sun where temperatures reach about 15 million K the radiation pressure is enormous around 1.3 × 10¹³ Pa or about 130 billion atmospheres. This immense pressure helps counterbalance the Sun gravity preventing gravitational collapse and maintaining hydrostatic equilibrium.
Can radiation pressure be used for space propulsion?
Yes solar sails use radiation pressure from sunlight for propulsion. A large reflective sail captures the momentum of photons producing a tiny but continuous thrust. The Cosmos 1 mission tested this concept in 2005 and several successful solar sail spacecraft including LightSail 2 have demonstrated orbit changes using only sunlight pressure.
How does radiation pressure affect satellite orbits?
Solar radiation pressure creates a small perturbing force on Earth satellites gradually altering their orbits over time. For large lightweight satellites with high area-to-mass ratio this effect can be significant and must be accounted for in orbit determination and station-keeping calculations.
What units are used to measure radiation pressure?
Radiation pressure is measured in pascals (Pa) the SI unit of pressure. Typical values range from nanopascals (nPa) for starlight far from stars to gigapascals (GPa) inside stellar interiors. One pascal equals one newton per square meter. Common conversions include 1 atm = 101325 Pa.
Why does a reflective surface experience more radiation pressure?
A reflective surface experiences twice the radiation pressure of an absorbing surface because reflecting a photon reverses its momentum direction. The absorbing surface stops the photon receiving only its incident momentum (Δp = p). The reflective surface reverses the photon momentum (Δp = 2p) doubling the force and thus the pressure.
Is radiation pressure detectable on Earth?
Sunlight at Earth distance produces a radiation pressure of only about 4.5 μPa which is roughly 45 billionths of atmospheric pressure. This is far too small to feel directly but can be measured with sensitive laboratory instruments like the Nichols radiometer developed by Ernest Nichols and Gordon Hull in 1901.