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We know from newton laws of gravity how planets, moons etc rotate in orbit around other bodies but how does this really get setup when we know everything starting with a big bang?

As with big bang or an exploding star, it scatters the matter away in space. Assume that exploding star was the only thing in universe for simplicity (and to retrace the big bang), how would these remnants set themselves up in orbits?

zadane
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Suppose first that all debris have the same radial velocity in the inertial frame of the star (initial frame, before the explosion). If we are in the frame of one of that bodies, we see the others moving away also radially.

But it is a coincidence, because the only conclusion from the explosion is that momentum is conserved. If the fragments have different masses, they can have different velocities and the moment be conserved anyway.

An extreme example is an explosion totally off centre, that throws away small parts of the star. Most of them will have tangential and radial velocities and end up orbiting the remaning big part of the star.