How did a new satellites get in the right position?

It's actually really simple.An orbit can only remain stable if the orbiting body is moving at the right speed at the right distance. Too fast, and the body will fly away. Too close, and the body will fall into whatever it is orbiting.The simple answer is that those bodies that happened to be the correct distance away at the correct speed are the ones remaining in the solar system - that is, they are the objects that did not fly away or fall into the sun (or other nearby bodies). Those bodies attracted the smaller particles in their immediate area and grew to the planets, asteroids, and comets that remain today.The moon is essentially the same case. The current model of the origin of our moon is that it was created as the result of a large collision with Earth. The majority of the debris would have fallen back to Earth over years. Some happened to be in a relatively stable orbit (the moon is actually moving a few centimeters away from the Earth each year, as I recall) with the Earth, and this debris accreted over many years into the moon. The moon does not fall into the sun because it's basically in the same stable orbit as the Earth.Hopefully this should explain it to you. It's not as if these satellites were suddenly poofed into existence and placed specifically in their orbits. It's literally an inevitability that the matter which happens to be moving at the right speed at the right distance will be all that remains after the remaining particles are either attracted to a stable body or thrown out of the system.

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Every time a fundy breaks the laws of thermodynamics, Schroedinger probably kills his cat.

You're understanding of the Big Bang is far too close to a conventional explosion. In reality, it wasn't similar at all. The Big Bang is less about particles flying away from a single point and more about the actual space expanding. Imagine a bunch of dots on a deflated balloon. Now, inflate the balloon. The dots will spread apart, but it's not the same as all of them simply flying away from each other.Gravity casues the early matter to be held together despite the expansion of space. The result is essentially a multitude of clusters of matter, which are the precursors to modern galaxies.This is still very much an oversimplification, so please bear with me.Unfortunately, the Big bang doesn;t really have anything whatsoever to do with the formation of a solar system - it's a completely different topic (there were no heavy elements, for example, in the first eons of the universe's existence).Planetary formation is very different.Given a nebula, which is basically just a large amount of gas in a localized area, the gravitational attraction of the gas will cause it to concentrate itself and squeeze towards the center of mass. If there is a sufficient amount of gas, the force of gravity will be sufficient to induce nuclear fusion, and birth a star.The remaining material, still circling the star in what's essentially a whirlpool into the new star's gravity well, will have some clusters of debris at the appropriate distance and speed to have a stable orbit with the star. The material in between these orbits will either be flung into space, accrete to the orbiting bodies due to their gravitational attraction, or fall into the new star.Once this process is complete, a solar system will have formed. Occasionally a stray asteroid will be captured by a planet's gravity and become a new satellite rather than being drawn down into a collision (as seems to be the case with the two diminutive moons of Mars, for instance). Some moons will form from the debris left over from the planet's formation, happening to be in a stable orbit, exactly as the planets formed around the star.The important things to remember:1) The Big bang wasn't an "explosion" in the way we think of a stick of dynamite. Space expanded, matter was not being propelled away from itself.
2) Gravitational attraction causes matter to clump up, which prevents the even distribution and decreasing density that you're envisioning.

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Every time a fundy breaks the laws of thermodynamics, Schroedinger probably kills his cat.

It's really not, though. The two models are very, very different from each other. Try readong something that's not
a) more than 10 years old. Cosmology has progressed a bit in the bast decade.
b) designed for the average joe. Many popular "science" books are dumbed down for general consumption, much like the simplified documentaries you see on TV. Wrong. As already noted, the balloon model was an oversimplification I used exclusively to draw a distinction between expansion and explosion. There are many other forces at work in the real universe beyond just the expansion of space. Gravity would be a pretty big one, and it makes sure those particles don't just move in straight lines away from each other. As has already been mentioned, the speed required for red shift is entirely dependant on your frame of reference. The entirety of space is expanding, which creates a much different model than the "zomg it blew up" version you're using. It does no such thing. Also, as has been mentioned, an evenly expanding space will make it appear that two objects actually accelerate away from each other, not merely moving at a set speed. Again, you're trying to use an "explosion" model becasue that's what the Big Bang is typically described as to the general public. That's the dumbed down version, and is only a weak analogy to the Big Bang so that you don't need a degree in astrophysics to get the basic idea.

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Every time a fundy breaks the laws of thermodynamics, Schroedinger probably kills his cat.

From what I understand, those distances are too small, and gravity is holding the bodies in our solar system together anyway.The expansion is observed in the redshift of very distant stars, and the fact that the further distant the star, the more intense the redshift (so the more space is between two object, the more space is seen to expand. Like the balloon example above, two dots close together on an expanding balloon will move apart more slowly than two dots farther apart, because every square inch of the surface is expanding at the same time.

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Every time a fundy breaks the laws of thermodynamics, Schroedinger probably kills his cat.