Photonic Propulsion | Part 2 | Understanding Radiation Pressure
This is part 2 of the article series discussing the possibility of using Photonic Propulsion in order to explore deep space.
If you missed part 1 and you’d like to read it (I suggest you do), click here.
Enjoy!
Have you ever stood outside on a scorching hot summer day?
Where I’m from, you’d start sweating the second you stepped outside.
Here, peak summer temperatures reach 90°F. It’s very hot 🔥.
Heat isn’t the only thing the sun provides.
It gives out light 💡.
I mean, obviously.
What isn’t as obvious is that the light received from the sun actually has a small force. A tiny degree of pushing power.
This is called radiation pressure.
Radiation pressure is the amount of pressure transferred onto a body of mass from a source of light. Light is made up of tiny particles called photons. Even though photons are considered to be massless, they carry momentum because of their high energy.
So when photons hit a surface, it results in a transfer of momentum from the photons onto the body of mass.
In simpler terms, light has the ability to push mass.
Essentially this means, that earth is constantly being pushed by sunlight. It’s subject to the constant force exerted by sunlight.
But then why aren’t we being pushed away into outer space as a result of radiation pressure?
Well, this is because the force that is exerted on earth as a result of radiation pressure is a negligible amount.
It isn’t strong enough to push earth out of orbit.
Let’s do some quick math 🧮
This is an equation that can be used to calculate the net force received as a result of radiation pressure.
- F is the net force
- a is the reflection coefficient
- P is the incident energy received from light in watts
- c is the speed of light in a vacuum.
If we plug in values from the context of radiation pressure exerted on earth from the sun, we get
With this force, it would be possible to ever so slightly move an object with a mass of 76,940 metric tons.
If you want a deeper look into this equation check it out here
A ton-force of 76,940 might sound like a lot. From our relative point of view, it is! But when you take earth’s total mass into account along with the sun’s gravitational pull, this seemingly huge amount becomes miniscule. Light’s pushing effect is cancelled out as it’s easily overpowered by the sun’s gravity.
But, the goal isn’t to move earth.
The goal is to explore deep space.
Using the force of radiation pressure from sunlight, a way to travel and explore deep space through photonic propulsion can be developed.
To do so, it’s required to understand the forces behind radiation pressure on a deeper level. Using a simulation with primarily my own research, I was able to better understand these forces.
Before we dive deeper into the physics of solar sails, you must understand what a solar sail actually is.
A solar sail is a spacecraft that uses radiation pressure as it’s form of propulsion. Previous solar sails have been designed in the shape of a square but other designs, such as heliogyro sails and spinning disc sails, have been explored.
Learn more about solar sail designs here
Typically, solar sails are made of ultra-light yet highly reflective materials in order to optimize it’s velocity.
They’re usually very thin. IKAROS, a Japanese solar sail, had a thickness of 7.5 micrometers. Lightsail 2, the Planetary Society’s version of a solar sail, was only 4.5 micrometers thick! If you aren’t aware, this is up to 10 times thinner than a strand of human hair!
Along with the need to be very thin, it must also be very durable to withstand the extreme conditions of space during long distance spaceflight.
Now, let me show you what I actually learned 💭.
The Physics of Solar Sailing ⚛️
A very simple yet very well articulated simulation guided me into understanding radiation pressure and it’s possible application into photonic propulsion, specifically through solar sailing.
If you’re interested, I’d take a couple seconds to explore it. It’s really simple and easy to use, providing a surface level demonstration of the forces of radiation pressure on a solar sail.
In the context of the simulation, the solar sail starts off at 1 astronomical unit (AU) or about 92955807.3 miles away from the sun.
When I was messing around with the simulation, I saw some basic patterns of behavior at varying distances between the sun and the sail, different masses of the sun, and different sail lengths.
The greater the mass of the sun was, the more of a gravitational pull it had. So, the solar sail would most likely accelerate at a slower rate or get pulled in. Inversely, the lower mass the sun had, the less of a gravitational effect it had on the sail. The solar sail would most likely be able to increase its rate of acceleration and continue on it’s path into deep space.
I say “most likely” as the position, trajectory, and velocity of the sail can be affected by other factors such as the size, reflectivity, and weight of the sail.
If the solar sail was closer to the sun, it’s velocity in direction to the sun would begin to increase. This is due to a stronger gravitational force acting on the solar sail. The further the solar sail was to the sun, it’s velocity in direction to the sun would decrease. Basically, the closer the sail was to the sun, the more it would be affected by its gravity.
The bigger the solar sail was, the faster it was able to accelerate. The smaller the sail was, the slower it would accelerate. Depending on it’s position, it would actually begin to be pulled in.
As the sail moved further away from the sun, the rate at which the sail was accelerating decreased. I did some research and found that the sail would eventually cease to accelerate. It would travel through the interstellar medium at fast speeds but ever so slightly slowing down as space isn’t 100% vacuum.
Space is filled with various gases such as hydrogen. Also a ton of dust. And interstellar wind. Don’t forget the virtual particles as well… definitely not 100% vacuum.
Now, you might be thinking, “isn’t this information pretty obvious?”
Well, yes it is.
What I’m more interested in, are the mathematical equations behind solar sailing. It’s these equations that can aid in building the optimal solar sail for space travel.
A Little bit Deeper 🔬
After seeing the basic effects of the suns gravity on the solar sail, I figured I’d need to learn the physics, specifically the mathematical equations highlighting the forces behind these basic effects.
Through Newton’s law of universal gravitation, you can use this basic equation to calculate the total force of gravity on the solar sail.
- F is the total force of gravity measured in newtons
- m₁ is the mass of object 1
- m₂ is the mass of object 2
- G is the gravitational constant
- r is the distance between the two objects
If I plug in values from the context of the sun and the earth, I get 16,233,115,769,787,225,890,882 Newtons!
This ☝️ is the total force that the suns gravity exerts on earth measured in Newtons. With this huge force, it is possible to move an object with a mass of 1,655,317,133,759,926,000 metric tons!
The equation will very useful when attempting to figure out optimal sail designs. Knowing how much gravity is exerted on a solar sail will yield the data necessary to figure out what sail material should be used to optimize for proper trajectory, position, and velocity.
For example, lets say that we have a solar sail that aims to orbit the sun at a close distance. Obviously, we wouldn’t want the solar sail to fall into the sun and meet it’s doom. We’d have to know what the total force of gravity from the sun is at specific points in space. This is where this equation can come into play. We would use this equation to find the force of gravity at specific points and then find materials that have the proper values of reflectivity, emissivity, and absorptivity in order to avoid having our sail meet it’s fiery doom.
I saw that the sail accelerated when it was bigger and decelerated when it was smaller, I figured that this was due to the total incident light on the sail. If the solar sail was bigger, there would be increased incident light meaning an increase radiation pressure. If the solar sail was smaller, there would be decreased incident light meaning a decrease in radiation pressure.
I was interested in finding the mathematical reasoning behind this phenomena. “Why does this happen?”
Just so you know, I question things a lot
I found these equations:
- P is equal to the total solar radiation pressure
- I is equal to the solar irradiance
- c is equal to the speed of light in a vacuum
The first equation can be used to determine the total amount of radiation pressure on a perfectly reflective surface.
The second equation can be used to determine the total radiation pressure on a surface with perfect absorption.
But what if we have a surface that isn’t perfectly reflective or perfectly absorbing?
Well, we’d have to use a different equation to determine the total amount of radiation pressure.
- P is equal to the total solar radiation pressure
- I is equal to the solar irradiance
- c is equal to the speed of light in a vacuum
- a is the coefficient of reflection of the surface
We have the addition of (1+a) to represent the total reflectivity or absorptivity of the surface.
This equation will yield an important value when determining the design specifications for a solar sail. The total amount of radiation pressure is crucial when attempting to find a good material for the solar sail. It’ll give us a value to use when attempting to find a good reflectivity value for the material of a solar sail.
Then, from this equation, we can derive the total force experienced as a result of radiation pressure in newtons.
quick fact, the unit for force “newton” was named after Isaac Newton 🍎 who is considered to be one of the fathers of modern day physics
The following equation(s) is what’ll yield us the good stuff.
- F is force experienced as a result of radiation pressure
- A is the area of the surface receiving the incident light
- I is the solar irradiance, which is the power per unit area received from the sun
- c is the speed of light in a vacuum
Since we already have the equation that gives us P, the total solar radiation pressure, we can replace the variables A and I
- F is force experienced as a result of radiation pressure
- P is the total solar radiation pressure
- c is the speed of light in a vacuum
From this equation, we can get the total force experienced as a result of radiation pressure in newtons
This value will give us the ability to determine the ideal sail design.
Will our sail need to be more reflective?
Will our sail need to be lighter?
Will our sail need to be bigger?
Determining the force of radiation pressure will allow us to effectively answer these questions.
So! We have some cool equations!
So what?
These basic equations yield the basic information needed to design a solar sail.
Of course, there’s definitely more complicated physics behind solar sailing. But the rudimentary understanding of these equations will also open the doors to many more possibilities.
When we consider other concepts such as the luminosity of a star, the conservation of momentum, orbital mechanics, the inverse square law, solar wind, and much more, these equations will provide the base understanding needed to dive deeper.
If you’re interested in some of the math I did, you can check it out here
