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Abstract: The overarching goal is to create a virtual solar system, capable of interacting with hypothetical celestial body(s), which the user may introduce into the system, evolve it at a substantially accelerated time-scale, and then hopefully provide insight and understanding into how future asteroids and comets might interact with our solar system in general; with our planet in particular. Such events are slow to evolve, rare on human timescales and typically life-annihilating when actually encountered, making them a difficult process to study in-situ.

Objectification:

What properties do celestial bodies share?

What are the fundamentals?

For the purposes of this project, I will henceforth declare the most fundamental constituent of the universe to be the “Particle,” I use the term loosely to describe any array of matter which is physically entangled and whose independent properties can no longer be distinguished from the whole… at least with respect to whatever physical property I am describing. By particle I mean a celestial entity that behaves as a coherent unit.

Every particle has a mass, a volume and occupies space.

Every particle exists at a specific place in space and time.

Spacial coordinates in 3 dimensions can be represented as x,y and z || x1,x2,x3

Time coordinates can be represented as milliseconds (an arbitrary choice) and
some number of milliseconds will represent some measure of real-time and will
be represented as some scale factor. I pick t for time and tsf = time scale

A particle in motion tends to stay in motion, a particle at rest, tends to stay at rest, unless acted upon by a force.

Particles move at some measure of distance, over some quantity of time and do so in a given direction. We will assign V for velocity, a vector quantity with components (speed and direction)

Particles are accelerated via gravity, electromagnetism or interactions with other
particles.

The mass of a particle determines its resistance to accelerations such that
more massive particles require greater forces to accelerate (or decelerate) them.
we will assign the to P, momentum a vector quantity with mass factored in

Everything that exists interacts gravitationally and thus all my particles feel
the gravitational force.

Many particles can interact via the electromagnetic force. On the scale of the
solar system, with regard to the motions of macroscopic entities… the effect
is negligible at any reasonable distance. It may or may not factor into the
way macroscopic bodies behave during collisions… i have to ponder that.

Many particles can interact via the strong and weak nuclear force. Again, does not
apply to macroscopic bodies.

No two particles (Baryons technically, as opposed to Fermions) can occupy the same volume of space at the same point in time. If two particles meet, they will interact. We will call this interaction a collision and from this event, there are consequences.

Certainly the motions of two colliding bodies are altered during collisions.
The integrity of macroscopic body may be altered during collisions, such that
one body can disintegrate into two or more unconnected entities, each no longer best
described as a single unit but better understood in their own terms.

Two or more bodies can integrate, such that they become physically
entangled in such a way that they behave as a single, coherent, comoving entity.

A macroscopic body is an aggregate entity, comprised of constituent parts, that
are physically entangled in such a way that, whatever physical property one is
examining is/are better understood/described in terms of a single entity, rather than
being understood as some product or sum of constituent contributions. Where
exactly one draws the line is certainly worth debating.

The ability of a body to stay together given an infusion of energy and/or an asymmetrical application of force might be described as its coherence or structural integrity… maybe? Mass is a huge factor here, but becomes the dominant factor past a certain threshold. The other cohesive forces such as magnetism, molecular bonding, cold-welding, differentiation (was it part of a large body which allowed it’s metals to sink to the center), etc. Before a certain threshold, these factors can be more important that mass alone… however, somewhere near the point at which a body is pulled into sphere is the point at which mass becomes the only factor worth considering.

Mass and motion can be thought of and described in terms of kinetic energy. The closing velocities, angle of impact and contributing masses determine how much of the kinetic energy remains with the departing constituents (to be carried away) and how much is converted to heat and other potentially destructive forms of energy. Things like shape, angular momentum, structural integrity and the slip/stick quality of the points of impact are all important factors in determining how much destructive energy is produced, how it is distributed and the resultant state of whatever remains. While mass and velocity precisely dictate just how much energy is available, how that energy is converted, imparted or carried away is determined by a sizeable (though finite) set of variables, some of which are difficult to ascertain far in advance of the event.

Considering the difficulties, precision doesn’t seem likely. We will have to talk in terms of likelihoods and probabilities. If two high velocity, massive objects are hurtling towards each other, the potential for cataclysmic results are obvious. Maybe after a careful consideration of the forces I can be almost certain they will collide. However, refining the exact point of collision especially if the thing is spinning is fast; knowing the structural integrity, composition and mass distribution is difficult too. Maybe the thing is a big fluffy snowball or a conglomerated collection of pebbles or sand. I have no idea what happens when a pile of pebbles or sand collides with an iron-rich asteroid… who wins? Does the sand just swallow the asteroid like a sandbag does a bullet? or does the iron-rich asteroid cause the rubble pile to explode out of its way, like shooting a container full of water… splash! What happens if two rubble piles collide or two fluffy snowballs? A guess would be no better than even odds for me… maybe the worlds greatest expert could improve his guesswork to slightly above even but still… there is so little data.

Untitled drawing

I can’t figure out what I am doing wrong. The math looks right. My masses, Distances and constants all seem right. It is just not working the way I want and I can’t figure out why. It has to be a stupid error. Here is the gravity loop:

for (var o in this.bodies) {
	var pobj 	= this.bodies[o],
		p0		= pobj.position.copy(),
		v0		= pobj.velocity.copy(),
		m0		= pobj.mass;

	for (var p in this.bodies) {
		var	tobj            = this.bodies[p],
			p1		= tobj.position.copy(),
			m1 		= tobj.mass,
			p01		= p0.vectorTo(p1),
			a01 	        = p01.getAngleDegrees(),
     d01 = p01.getMagnitude() * this.scale2m,
     fv = p01.multiply( this.G * m0 * m1 / (d01 * d01) ),
			av		= fv.divide(m0);

		v0.add(av);
	}
	pobj.velocity = v0.copy();
	pobj.position.add(pobj.velocity.copy());
}

Position VECTOR (X,Y)
Velocity VECTOR (MAG,ANGLE) (m/s)
Acceleration VECTOR (MAG,ANGLE) (m/s/s)
Mass SCALER (kg)
Radius SCALER (px)

BIG G 6.67E-011 (m^3/kg/s)
SOLAR MASS 1.9891E+030 (kg)
Earth Mass 5.97219E+024 (kg)
Earth Distance 1.496E+011 (m) = 1 AU
Jupiter Distance 778547200000 (m) = 5.204267 AU

FORCE = MASS x ACCELERATION
FORCE(gravity) = mass(sun) x mass(object) x G / (dist ^2)
ACCELERATION = FORCE/MASS(object)
VELOCITY(final) = V(init) + SUM ( ACCELERATION(x) )
POSITION = P(init) + V(final)

2013-08-25 01_11_02-32 Nearby Stars - StumbleUpon

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