# Understanding Solar Radiation Force: Maths & Derivation

• UniPhysics90
In summary, the conversation is discussing the understanding of the mathematical concepts behind the absorption of photons by dust. The speaker is unsure about the derivation and asks for clarification on the force of a single photon and its duration of absorption. The responder explains that the concept of force for a single photon is not very meaningful and suggests calculating the difference in momentum instead.

#### UniPhysics90

I'm having a little trouble understanding this, mainly the way the maths behind it works. I can't find any kind of derivation on the internet which is 'simple' and at a level I can understand.

My understanding is that the photons from the Sun are absorbed by dust, so transferring momentum from the photon to the 'dust'

I know that

Flux of photons = L/4*pi*r2

I THINK that

Force on a spherical particle of radius a = (pi*a2)*flux*fraction absorbed*force due to a single photon

Is this correct? If it is, what is the force due to a single photon?

Thanks!

Talking about the 'force' of a single photon is not very meaningful. After all, force is something that you continuously apply, the absorption of a photon of course has some duration, but I hve no clue what that would be. What you can calculate is the difference in momentum due to the photon absorption (which is just the momentum of the photon, the constant of Planck divided by its wavelength).

If you would speak of the force of this photon it is just this momentum divided by the duration of the absorption.

## 1. What is solar radiation force?

Solar radiation force, also known as solar radiation pressure, is the force exerted by the sun's electromagnetic radiation on an object. It is responsible for the motion and behavior of objects in space.

## 2. How is solar radiation force calculated?

Solar radiation force is calculated using the equation F = P/c, where F is the force in Newtons, P is the solar irradiance in watts per square meter, and c is the speed of light in meters per second.

## 3. What is the derivation of the solar radiation force equation?

The solar radiation force equation is derived from the principles of electromagnetic radiation and the interaction between photons and matter. It involves the use of Planck's law, the Stefan-Boltzmann law, and the momentum equation.

## 4. How does solar radiation force affect spacecraft?

Solar radiation force can affect spacecraft in various ways, including causing orbital decay, altering the trajectory, and creating torque. It is important for spacecraft designers to consider and account for solar radiation force in their designs.

## 5. What are some real-world applications of understanding solar radiation force?

Understanding solar radiation force is crucial for various industries, including space exploration, satellite communication, and solar energy. It also plays a role in climate change and atmospheric studies. Additionally, understanding solar radiation force can help predict and mitigate the effects of solar storms on Earth.