Why do planets orbit at the same level as each other?

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By that, I mean, why do planets always orbit… horizontally(?) around the sun. Why not vertically? Space is a 3D space, I’d course. So why would the planets not end up going up as well as sideways?

Edit: Space science is a lot more complicated than I thought, and I am here for this rabbit hole. Ty everyone for your answers so far!

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Planets tend to orbit in the same orbital plane (“horizontally”, as you put it) because they form out of the same spinning disk of dust and gas (called a “protoplanetary disk”).

Here’s an [artistic computer rendering](https://commons.wikimedia.org/wiki/File:Artist%E2%80%99s_Impression_of_a_Baby_Star_Still_Surrounded_by_a_Protoplanetary_Disc.jpg) of this disk around a young a star, and here’s an [actual (radio) telescope image of a real one](https://commons.wikimedia.org/wiki/File:HL_Tau_protoplanetary_disk.jpg) (around the star HL Tauri).

Since this disk is flat and already spinning (why that’s so in a minute), planets that form around the star will tend to 1) have orbits that are close to the plane of this disk, 2) orbit the star in the same direction as the disk spins, and even 3) spin on their own axes in the same “direction” (that is, clockwise or counter-clockwise as seen from “above”).

Of course, perturbations (such as collisions or gravitational influence of other planets) during or after planet formation can sometimes change these things, making them orbit out of this plane, and even spin backward or not at all (like Venus and Uranus — here’s [a nice video](https://www.youtube.com/watch?v=2H5NfcYS3YE) showing planet spin directions and speeds).

This spin-aligning effect is also weaker at greater distances from the star (because gravity is weaker at greater distance), which explains why objects beyond Neptune (including comets, and also Pluto) can have orbits [much more out of the plane](https://assets.coursehero.com/study-guides/lumen/images/towson-astronomy-2/overview-of-our-planetary-system/OSC_Astro_07_01_Orbits2.jpg) of the solar system. It’s also much easier to alter the orbit of a small object, like an asteroid or comet, than that of a planet, which is much more massive.

As to why the initial dust and gas forms into a disk in the first place. Solar systems form out of huge clouds of gas and dust, which are initially roughly spherical. As the cloud start to contract under its own gravity (here’s a [computer simulation](https://www.youtube.com/watch?v=YbdwTwB8jtc)), whatever tiny spin it initially had will get greatly amplified (due to something called “conservation of angular momentum”), making it spin faster and faster. And then the centrifugal force will shape the contracting gas and dust into a disk — a bit like why pizza dough becomes [more flat when you spin it](https://www.youtube.com/watch?v=HWL__9yDu8I).

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