Why do the planets in our solar system revolve around the sun in roughly the same plane?


Question:
Do other solar systems move this way too?

Answer:
I think the current theory is that it comes from the origin of the solar system as a spinning mass of material. This material had a certain angular momentum, which was retained as the material coalesced into the sun and the planets and moons and other bodies. So there are only a few planets and moons whose orbital and rotational angular momentum vectors are not aligned with each other (like Neptune, and Venus, Triton and a few of the smaller, more distant moons of Jupiter and Saturn).
If you had a 9 strings tied to 9 balls and you held them in your hand, and then began to spin in a circle, would not all the balls be on the same plane as the centrifical force attempted to pull them away from you. Think as the suns gravity as the string.
They don't take the plane their lugage is too big for the overhead.
Our planets were formed from a solar extrusion caused by a massive passing star billions of years ago. The passing system also lost three of its most distant trubutaries (acquired by our sun), which had different orbits from the planets produced by the extrusion.

This accounts for the 'retrograde' motions detected by astronomers.

This happened when our sun was still pulsing similar to stars we see called Cepheid variables.

I could write a little more on this, not much more, but I will stop here because I am sleepy and there are a lot of smart people out there waiting to jump on mistakes.

However, what I have said is for SURE. Also, we still have much to learn about our own solar system, including exactly how things sorted out after the above events AND exactly how many planets we have. One got too close to Jupiter and broke up. That still leaves 14.
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