The universe is an unlimited space where scattered objects are constantly moving. There are no still points in the universe, and this is the reason that Archimedes’ quote, "Give me the place to stand, and I shall move the earth," although true, cannot be used to move planets.

The laws of physics that can be applied to everything, from an apple falling from a tree to the motion of the planets, govern this entire, never-ending movement. Some of history's greatest minds, like Johannes Kepler and Isaac Newton, worked on these subjects and laid the fundamental laws (Kepler — laws of planetary motion, Newton — theory of universal gravitation).

In 1679, Newton resumed his work on celestial mechanics—the effect of gravitation on the orbits of planets. In his work "Philosophiæ Naturalis Principia Mathematica" (The Mathematical Principles of Natural Philosophy), Newton laid the foundation for our current understanding of physics and the universe by stating the three universal laws of motion and the law of universal gravitation.

The Concept

The idea was to create a 2D system with moving bodies that, under Newton’s laws, would leave traces on the canvas as they moved. After a while, these traces will form a visual image, unique and inseparably linked to the initial conditions. Like the movement of Pollock’s hand holding the brush and dripping paint on the canvas, the moving bodies leave colored traces as they move on the 2D plane.

n-body Gravitational System

n-body gravitational system, is a system with n number of objects that interact with one another with the gravitational force. The objects are abstractly viewed as point particles. There are several methods to calculate the trajectories of each object. When dealing with more than two bodies, the problem has no exact solution in closed form. Numerical methods can be applied to obtain useful, albeit approximate, results for the n-body problem, and this is what I did in "Celestial Orbits."

The positions and velocities of the bodies are stored in variables. In every irritation, using Newton's laws of universal gravitation and motion, I calculate the new velocities and positions of the bodies. This process is looped over time to approximately calculate the bodies' trajectories.

Into the Code

Having all the above in mind, we can create a system with bodies scattered in space. In the system I designed, you have to select the following properties for each body you add:

• initial position
• initial velocity
• mass
• color
• moving or fixed

As you can see, you can have bodies that freely move and others that are fixed in a position. If you want to simulate a system similar to a solar system, you have to create a fixed body with a much higher mass than the moving bodies. This is the case in the "Celestial Orbits" artwork, where there are five moving bodies and two fixed bodies with ten times more mass.

For each body, you select the position, apply the rules, and watch the system evolve. The bodies will start to move, creating trajectories. In the beginning, the trajectories are symmetrical, but as each body affects other bodies, the motion starts to become more chaotic. You can control the level of "randomness" in your system by changing the position, velocity, and mass of each body.

The background of the canvas is a pattern with dots that represent the gravitational field of the two fixed bodies. There is also a bar at the bottom that indicates the progress of the calculations. After the render is completed, you can press [s] to save a 4000x4000px PNG file.

Editions

Each edition is different from the others in the following aspects:

• The distance between the two fixed bodies
• The color of the traces of the five moving bodies

The positions and masses of the five moving bodies and the masses of the fixed bodies are always the same.

There are two versions of the Celestial Orbits: the dark and the white.

About me (planckC)

As some of you might have guessed from my nickname, I love physics. Actually, I studied physics long before becoming an artist. And thus, I draw inspiration from the world of physics, mathematics, and other scientific fields. Apart from creating digital generative artworks, I also make installations and sculptures, working mainly with light, sound, and motion.