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If you randomly assign velocities independently of distance from centre of mass, the simulation will take much longer to settle down to a near-stable configuration. The outer particles which are moving outward will have relatively high kinetic energy, so the configuration will expand further from the CoM, leading to weaker interactions and fewer collisions, ...


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A magnifying glass will produce an upright, enlarged (virtual) image when the distance to the object is smaller than the focal length, and an inversed image when the distance is larger than the focal length (in which case the size of the image decreases rapidly with increasing distance). (image by cmglee, wikimedia commons) For a black hole, the ...


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Fleshing out my answer in the comment above: The light from all the stars in the picture is lensed (i.e. it's path bent) by the black hole (or BH). The closer it passes to the BH, the larger the angle it's path is bent by. Stars far (in projection) from the BH, like A, are hardly lensed at all (in fact I significantly over-egged it in my diagram, should ...


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You can draw virtual magnets and view theirr magnetic fields using www.pic2mag.com It is a free download.


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To describe a chemical reaction first you have to define a model to describe the process, for example, in a reactive collision like A + BC -> AB + C you could use as a first approximation the transition state theory (TST) and perform the determination of the physical observables with some methodology like the quasi-classical trajectories (QCT), which solves ...


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Direct integration schemes give bad results. You can do much better by using the exact solution in the absence of gravitational interactions between the planets. You can then set up a variation of constants approach where you take the integration constants (which are the orbital parameters) as dynamical variables and write the differential equations (where ...


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The standard way to choose a time-step is to run a test simulation with multiple bodies and plot the total energy of the system versus time. The total energy should remain (roughly) constant. If your step size is too large then you will get energy drift. So simply find the largest time-step that does not produce energy drift. In the case of modelling the ...


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Find the center of mass (CM) of the two connected particles. Then, determine the distance (r) from the center of mass of the part of the spring where the third particle hit it. Then, if you could allow a collision time and force while in contact, and assume the collision to be frictionless (this is might be hard for point particles and thin spring, cause ...



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