This is a visual representation of an N-body simulation. This project will demonstrate how celestial bodies interact with each other when under the influence of gravity. This project incorporates realistic physics in order to make the simulation as accurate as possible.
The project can be installed via the link on my website:
In order to run the project, it must be extracted from its rar format. This can be done with WinRar Software.
M - Show Mesh
SPACE - Pause
Left Mouse Click - Generate Particle
Right Mouse Click + drag - Generate Particle with an initial velocity
SCROLL - Change the initial size of the generated particle.
Newton's Law of Universal Gravitation states that every particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers" - Wikipedia
//The First Line makes sure that the force is not calculated between a particle and itself
double force = (particles.get(i) != particles.get(j)) ?
//The Second Line represents the top half of the equation (m1 * m2)
GRAV_CONSTANT * (particles.get(i).getMass() * particles.get(j).getMass() /
//The Third Line represents the bottom half of the equation
Math.pow(particles.get(j).getLocation().distance(particles.get(i).getLocation()), 2)
//The Fourth Line adds the dampening factor in. This ensures that a division by zero is not performed
+ DAMPENING) : -1;//Overall, the compact source code itself looks like this:
double force = (particles.get(i) != particles.get(j)) ?
GRAV_CONSTANT * (particles.get(i).getMass() * particles.get(j).getMass() /
Math.pow(particles.get(j).getLocation().distance(particles.get(i).getLocation()), 2) + DAMPENING) : -1;
Newton's Second Law: In an inertial frame of reference, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object: F = ma. (It is assumed here that the mass m is constant). - Wikipedia
//The First 2 Lines are used to determine the difference between the locations fo the two particles
double xDifference = particles.get(i).getLocation().getX() - particles.get(j).getLocation().getX();
double yDifference = particles.get(i).getLocation().getY() - particles.get(j).getLocation().getY();
/* The Third Line ensures that the particle is only accelerate if the force is larger than zero.
Thus, impossible "negative forces" are ruled out */
if (force > 0) {
particles.get(j).accelerate( //Acceleration Function
new Point2D(Math.signum(xDifference) * force / particles.get(j).getMass(), //X axis acceleration
Math.signum(yDifference) * force / particles.get(j).getMass()) //Y axis acceleration
);
/* Math.signum() is a function that returns the absolute value of a number while factoring in the coefficient.
eg: signum(35) = 1, signum(-78) = -1, signum(-174) = -1
The signum() value is used in the program to set the direction for the particle to travel in
Since F = ma, a = F/m, so the acceleration of the particle is it's (force / mass) */
}//Overall, the compact source code looks like this:
double xDifference = particles.get(i).getLocation().getX() - particles.get(j).getLocation().getX();
double yDifference = particles.get(i).getLocation().getY() - particles.get(j).getLocation().getY();
if (force > 0) {
particles.get(j).accelerate(new Point2D(Math.signum(xDifference) * force / particles.get(j).getMass(),
Math.signum(yDifference) * force / particles.get(j).getMass()));
}
A Perfectly Inelastic Collision occurs when the maximum amount of kinetic energy of a system is lost. In a perfectly inelastic collision, i.e., a zero coefficient of restitution, the colliding particles stick together. In such a collision, kinetic energy is lost by bonding the two bodies together. - Wikipedia
Where V is the final velocity, which is given by the formula above.
particles.get(j).setVelocity(
new Point2D(
//This represents the X velocity of the particle
(particles.get(j).getMass() * particles.get(j).getVelocity().getX() +
particles.get(i).getMass() * particles.get(i).getVelocity().getX()) /
(particles.get(j).getMass() + particles.get(i).getMass()),
//This represents the Y velocity of the particle
(particles.get(j).getMass() * particles.get(j).getVelocity().getY() +
particles.get(i).getMass() * particles.get(i).getVelocity().getY()) /
(particles.get(j).getMass() + particles.get(i).getMass())
)
);
/* particles.get(j) represents the larger particle, and particles.get(i) represents the smaller particle
When the two particles collide, the larger particle will absorb the smaller particle.
Therefore, the velocity of the particle produced will change along with its mass
The code above represents the new velocity of this particle. *///Overall, the compact source code looks like this
particles.get(j).setVelocity(
new Point2D(
(particles.get(j).getMass() * particles.get(j).getVelocity().getX() +
particles.get(i).getMass() * particles.get(i).getVelocity().getX()) /
(particles.get(j).getMass() + particles.get(i).getMass()),
(particles.get(j).getMass() * particles.get(j).getVelocity().getY() +
particles.get(i).getMass() * particles.get(i).getVelocity().getY()) /
(particles.get(j).getMass() + particles.get(i).getMass())
)
);
//Larger particle absorbs smaller particle
particles.get(i).addMass(particles.get(j).getMass());
particles.remove(particles.get(j));
The Image above shows a small particle in a stable orbit around a larger particle
