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"In theory, theory and practice are the same. In practice, they are not." ..."Albert Einstein (1879~1955, Mathematical physicist, Nobel Prize 1921-Physics)"

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 Author Topic: Formation of a virtual solar system (2D particles)  (Read 13723 times) 0 Members and 1 Guest are viewing this topic. Click to toggle author information(expand message area).
Fu-Kwun Hwang
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 « Embed this message on: February 20, 2010, 02:23:48 pm »

The following applet simulate formation of a solar system.

There are N particles generated at random distributed location with random distributed velocity.
The constraint is the center of mass is located at the center and the total momentum is zero.
There are gravitation force between particles:
Because this is a 2D simulation), the force is modeled by $\vec{F}=\frac{GMm}{r}\hat{r}$.
When two particles are come too closer, i.e. (distance between center of mass $d < r1+r2$ , then perfectly inelastic collision will join two particles into one bigger particle ($M=m_1+m_2$)

Click right triangle at lower right corner to play the simulation.
Click init to set different initial condition.
You can adjust Gravitation constant G (potential energy) or Total Energy constant (E: the initial velocity $v$ for each particle is proportional to $\sqrt{E}$ or the initial number of particle N with sliders.

Click circular checkbox if you want to have a net angular momentum (counterclockwise).
The slider at the right can be used to adjust the scale for the x-y coordinate system.

Red arrow represents velocity vector for each particle, while blue arrow represents net force acting on each particles (from other particles).

If E is too large (compared to G) so that the total energy is greater than 0, it is not a closed system.
You can increase G to form a closed system.
However, the kinetic energy will be drcreased (when two particles combined into one - perfect inelastic collision).

Due to conservation of momentum, there is very rare that all particles combined into one big particle located at origin with zero velocity.
The final state consists one or two big stars with few small stars.

You can study many phenomena with this simulation. Hope you can enjoy it!

Embed a running copy of this simulation

Embed a running copy link(show simulation in a popuped window)
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• Please feel free to post your ideas about how to use the simulation for better teaching and learning.
• Post questions to be asked to help students to think, to explore.
• Upload worksheets as attached files to share with more users.
Let's work together. We can help more users understand physics conceptually and enjoy the fun of learning physics!
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macfamous
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 « Embed this message Reply #1 on: March 19, 2010, 10:54:32 am »

is it using vector or there is simple methode of this ..
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Fu-Kwun Hwang
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 « Embed this message Reply #2 on: March 19, 2010, 01:28:52 pm »

I do not understand your question.

The interaction force between any two particles are model with relation: $\vec{F}=-\frac{GMm}{r}\hat{r}$ where $r$ is the distance between any two particles. (because it is 2D model so force is proportional to 1/r).
The gravitationf force should be model with $\vec{F}=-\frac{GMm}{r^2}\hat{r}$ for 3D simulation.
And particles are generated at random position with random velocity.
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