# Radiation Pressure Calculator

Created by Dominik Czernia, PhD candidate
Reviewed by Bogna Szyk
Last updated: Feb 22, 2019

This radiation pressure calculator will help you estimate what is the radiation pressure inside and outside of stars. This type of pressure can be described in two ways:

• as a force exerted on the surface by light particles - photons,
• as a pressure in the medium in which the electromagnetic radiation propagates.

In the text below, we have explained what is solar pressure and how you can estimate it using the radiation pressure equation. The radiation pressure that reaches the Earth is almost negligible compared to other types of pressure. However, it gains in importance at high temperatures, for example in the interior of stars. If you are interested in more mundane matters, you can also check our other pressure calculators:

Have you ever heard about Cosmos 1 project to test a solar sail (lightsail) in space? In this mission, the spacecraft named Cosmos 1 was supposed to increase its velocity using radiation pressure. Read on if you want to know how solar sails work and what is the physics behind them.

## What is the radiation pressure?

Because electromagnetic waves carry energy, we can expect them to carry momentum as well. This electromagnetic radiation can be viewed in terms of particles which are known as photons (check our De Broglie wavelength calculator). When photons hit a surface, they exert a force onto that surface. The momentum of photons will be absorbed by the surface (if the material is opaque) or reflected (partially reflected).

Is radiation pressure a significant phenomenon? Let's consider the hot interior of a star. All matter with a temperature higher than absolute zero emits electromagnetic radiation described by the Planck's Law. On the other hand, you probably know that stars consist of particles which are held together by the gravitational force. Now, if there wouldn't be any radiation pressure, the star could collapse! Currently, we know that stars can exist for billions of years so we should take into consideration radiation pressure too.

## Radiation pressure equation

Our radiation pressure calculator can handle two situations. The first is to calculate the solar pressure outside the star. We have used the below radiation pressure equation:

p = x * L * cos²(α) / (4 * π * R² * c)

where

• p is the radiation pressure,
• x determines the type of surface: x = 1 - opaque surface, x = 2 - reflective surface,
• L is the luminosity of star,
• α is the angle between the light beam and the surface of absorbing / reflecting surface,
• R is the distance from the star,
• c is the speed of light c ≈ 2.99792458 * 10^8 m/s.

In practice, materials are neither completely reflecting or absorbing, so the x will be between 1 and 2. In simple mode of our radiation pressure calculator, we assumed that the light falls perpendicular to the surface (α = 0°). If you want to change it, just go to the advanced mode.

With the second solar radiation equation, you can estimate pressure radiation inside a star:

p = 4 * σ * T⁴ / (3 * c)

where

• p is the radiation pressure,
• T is the temperature,
• σ is the Stefan - Boltzmann constant σ = 5.670367 * 10^(-8) W / (m² * K⁴),
• c is the speed of light c ≈ 2.99792458 * 10^8 m/s.

By comparison, the pressure of ordinary molecules in gases increases linearly with temperature ~T (see ideal gas law calculator). Let's use our radiation pressure calculator to compare what is the solar pressure on Earth and inside the Sun. If an absorbing surface is opaque, R = 1 au (one astronomical unit 1 au is an average distance between Earth and Sun) and L = 1 L☉ (one solar luminosity equals 1 L☉ = 3.828 * 10^26 W) we obtain p = 4.54 μPa. On the other hand, if we want to compute what is solar pressure inside the corona of the Sun (T = 5 000 000 K ), we will get p = 157.6 GPa which is about 10^17 times bigger than that on Earth!

You might want to express these pressures, for example, in atmospheres (atm). Check our pressure converter to learn how to do this.

## How do solar sails work?

Solar sail (also called lightsail or photonsail) is a theoretical method of traveling in space using radiation pressure exerted by sunlight on large mirrors. It is just like the sailing boat when the wind is blowing a sail. People wanted to test the solar sail concept, and in 2005, they launched for the first time an orbital spacecraft named Cosmos 1 which had eight sail blades (15 m long with the total surface area of 600 square meters). Unfortunately, in the 83rd second of the flight, the engine broke down, and the whole vehicle fell back into the sea. However, since then several other satellites with the lightsail equipment were successfully launched into the orbit of the Earth.

Dominik Czernia, PhD candidate
Pressure outside the Sun
Type of surface
Opaque
Luminosity
L☉
Distance
au
Pressure
bar
Pressure inside the Sun
Temperature
K
Pressure
GPa
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