A video shows two spherical objects (made up of particles) collide. The title refers to them as two planets colliding. When the objects are indeed as large is planets (however large that might be), the video seems sped up. What if the objects are smaller than that, like the size of marbles? Would they still move as slowly (relatively to each other) as if they were planets?

So, to put it differently, when scaling such a situation down, would they move faster relative to each other? Could the video be showing 'real-time' progression when they would be marbles?

Updated question

If there are two situations that both have two spherical objects in them that have the exact shape etc. (so both situations only differ in proportion), and you would look at both situations at the same time, would one be progressing quicker than the other?

Disclaimer: I have limited physics knowledge. Please help me improve this question if it is unclear or hard to understand.


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    $\begingroup$ I don't understand the question. I don't see what the initial relative velocities would have to do with the size of the 'planets'. A couple of observations though: The simulation appears to be rendered with the centre of mass in the centre of the frame, hence why things (incorrectly) appear to slow down a bit. If you scaled the planets down to the size of marbles then gravity would no longer dominate and the collision would look very different. $\endgroup$ – lemon Oct 31 '16 at 14:37
  • $\begingroup$ I tried clarifying my question. Forget the video. I guess the answer is no, as you're saying the gravity 'dominates less' when the size is smaller, which makes the behaviour different the smaller we go. $\endgroup$ – bzeaman Oct 31 '16 at 14:47
  • $\begingroup$ You updated question still does not make sense. Collisions between 2 planets or between 2 marbles can be fast or slow, regardless of size. $\endgroup$ – sammy gerbil Oct 31 '16 at 17:46

Yes, there is a scale factor. The easiest way to recognize this is to look at some parameter that would influence the "speed of the event".

Obviously, in the case of a collision between spheres, their elasticity has something to do with the way the collision evolves. And this in turn relates to the speed of sound in the material that the sphere is made of: until the information about the collision makes it all the way across to the other end of the sphere, the contact point doesn't "know" how big the objects are that are colliding, and pressure keeps increasing.

For two objects made of the same material, the speed of sound is constant - but the time taken for the pressure wave to traverse the sphere is linear with size.

So a collision of a 1 cm sphere will appear to play out about 100 x faster than the collision between two 1 m spheres, and as you scale up to the size of a planet, time scales would slow down a LOT more.


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