# Radiation Pressure Calculator, Formula, Calculation With Example

It is one of the best tools used to calculate the radiation pressure inside and outside stars. This radiation pressure can be of two types one is the pressure on the medium through which the electromagnetic radiation propagates and the other is the force exerted on the surface by the photons. Radiation pressure is the pressure exerted on a surface due to the transfer of momentum between an object and an electromagnetic field.

Solar radiation pressure is due to solar radiation at close range. Because electromagnetic waves carry energy, they can also carry momentum. This electromagnetic radiation is photons. The speed of photons is either absorbed or reflected.

This radiation pressure calculator gives the pressure outside and inside the star. This radiation pressure calculator will help you estimate what the radiation pressure is inside and outside the stars.

This type of stress can be described in two ways. As a force exerted on the surface by light particles – photons, Following are the steps to find solar radiation pressure easily.

• Note down the given details from the question.
• Multiply the surface value with the luminance and Gauss square of the angle.
• Find the product of the square of the distance from the star, the speed of light, and 4π.
• Separate the product from step 2 through step 3 to get the radiation pressure out.
• Multiply 4 times the constant with temperature to the power of 4.
• Divide that by 3 times the speed of light to get the heck out of stellar pressure.
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Radiation pressure formula P(pa) in pascal is equal to the type of surface x and multiply the luminosity of star L(w) in watts and multiply the square of the the light beam and the surface of absorbing / reflecting surface cos2 (α) and divided by the four 4* π and multiply the square of distance from star R2(m) in meter and multiply the speed of light c(m/s) in meter per second .Hence the radiation pressure formula can be written as

P(pa) = x * L(w) cos2 (α) / (4* π *R2(m)*c(m/s))

### Derivation:

Radiation pressure outside the star p = x * L cos2 (α) / (4* π *R2*c)

Radiation pressure inside the star is p=4 *σ *T4 / (3 *c)

Where

C =is the speed of light

T = is the temperature

R = is the distance from star

Σ =is the stefan Boltzmann constant and σ =5.670367 *10-8 w / (m2 – k4)

L=is the luminosity of star

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X = is the type of surface

α = is the angle between the light beam and the surface of absorbing / reflecting surface

### Example:1

If the star surface is opaque, luminosity is 2 solar, distance is  2 au and inside temperature 5000000k.Find the radiation pressure?

Given that

Type of surface is opaque so x =2

Luminosity =2 solar luminosity

Distance R =2 au

Temperature t =5000000 k

Outside sun radiation pressure p = x * L cos2 (α) / (4* π *R2*c)

P=1*1*cos2(0) /(4*3.14*22*299792458)

P=9.41μPa.

Inside radiation pressure p =4 *σ *T4 / (3 *c)

P=4*5.670367 *10-8 * (5000000)4 /(3* 299792458)

P=157 Gpa

Therefore, the pressure inside the star is 157 Gpa, outside the star is 9.41μPa.

### Example:2

Calculate the luminosity L=400w and  distance =200m.Find the pressure value?