I asked this question many years ago on a Usenet group, and the answer was along the lines of what we're seeing is many millions of years after those orbits began, and that they all eventually flatten out due to the gravity of the other objects in orbit.

So you could have 2 objects at roughly the same orbital distance but perpendicular to one another (eg. one orbiting the star's poles and the other around it's equator), and over time the small amount of gravitational force they exert on one another will bring them roughly into the same plane.

Hopefully someone better versed in the topic can come along to explain it better than I can.

It's not. But orbits do tend to coalesce around the same plane, this is true. Planets pull on each other, and over time this results in orbits being on a similar plane. However, it's not perfectly flat - there is some variation, just look at Pluto as a good example.

The same orbital mechanics that cause star systems to look this way also translates to galaxies.

In short, stuff likes to stay together, but when said stuff is in motion, they instead form orbits of similar inclination. The rings of Jupiter and Saturn also display this. If I remember correctly, part of that mechanism is called "Sheparding"

And if you were to go what one would consider "up" from this percieved orbital plane, then you'd be going in that direction. There's nothing special, there's just less stuff there. The same orbital mechanics apply, you're just on a much more inclined orbit.

It's a common shape in the universe: large spherical mass in the center, plane of objects rotating around it.

Imagine a new object orbiting Saturn in a random direction. At some point (two, actually), it will cross the plane of the rings. Eventually it will crash into an object. The average of the impact will be closer to the plane. Eventually, it will either align with the plane or its orbit will be unstable.

The system starts out as a big cloud of debris orbiting a central point. Each particle is orbiting in its own way, there isn't any organization. Since there is no organization, most of these particles are going to bump into each other. This changes the speed and direction of the particles, some of them will clump together and most of them ending up gathered at the center of gravity of the entire system. This eventually gets large enough to become your star.

As the remaining particles become clumped together into larger items they will begin exerting gravitational pull on other objects. One plane of orbit will become dominant, and the remaining clumps will gradually settle down into their orbits, in the same general plane, in the same direction. Those that don't will have their orbital speed reduced enough that the object ends up gathered into the center.

Space itself is 3-dimensional (or 4-d if you include time....and even higher dimensional orders if you want to get into deeper theories).

The reason almost all solar systems (including our own) are relatively flat, or disk-shaped, is because of the way solar systems are formed. Solar systems start as large clouds of gas and dust which coalesce into orbiting objects. The gas, dust, and objects "flatten out" as they spin around the central star because of the physics (conservation of angular momentum).

So even though the planets, asteroids, etc, in our solar system are all mostly moving along a relatively flat plane, the surrounding space is not 2-dimensional. Our planets also vary in how flat their orbits are. For example, Mercury's orbit has a tilt of about 7 degrees from flat.

Best video you'll ever see on the topic imo (and very short)

https://youtu.be/tmNXKqeUtJM?si=1KrwzaG-b3hW-GkW

So, gravity isn't linear, but rotation is.

For reference, I'm a regular guy who looked up the answer, so maybe someone else can get more in depth, but I'll offer my basic understanding.

The planets weren't just plopped down in a straight line, they are all chunks of space debris that flew off of bigger chunks of space debris.

If you covered a ball in paint and spun it REALLY fast in a box slightly bigger than the ball, you'd end up with a line of paint on the walls that lines up with the center of the ball.

The planets are like that paint, but gravity essentially "reaches out and ties a tether" to them that keeps them from going further away. And the whole time, EVERYTHING is spinning and floating further away from the point of the Big Bang.

When things collide, they transfer their movement energy. If things collide like this >- They will continue in roughly the same direction. If they collide like this -> <- their movement will cancel out and they will fall into the sun.

Satistically, at the "beginning of time", in a random sphere around the sun, things will not be completely the same. So everything will either collide and fall. Or it will collide and continue in roughly the same direction. What we have now are the leftovers that were moving in roughly the same direction and colliding so little that they didn't fall into the sun because of that.

The same is true for the "disk": If you start with a roughly evenly distributed sphere of gases or something, there is a middle somewhere where there is a little bit more mass than anywhere else. That's where things will go.

Actually, the answer is complicated.

Gravity isn't the only relevant aspect here. Gravity makes that you have to look at the combination of "sun + planet". They behave like 1 body together. But "sun + 10 planets" is like 10 different of these combined bodies: "sun + planet 1", "sun + planet 2", "sun + planet 3"...

Imagine it was different. Imagine a system of several planets rotating around the sun with all their rotational planes at different angles.

This system would be very asymmetric all the time. Now in general when asymmetric bodies rotate, then that motion is not stable. They tend to change their motion, that is, the rotational axis changes until it reaches the maximal inertia moment.

Take a plate or a stick and throw it up high while rotating it at a random angle. Then do it again with a very asymmetric thing. Watch how it's motion changes.

It becomes stable when the inertia moment is maximal.

https://en.m.wikipedia.org/wiki/Moment_of_inertia

For the system with several planets, the stability of the whole system is maximized when all the rotational planes are the same, because then the inertia moment of the whole system is maximal.

I like this visual on how our solar system moves Like a spiral, with gravity keeping us tethered to the sun

https://youtube.com/shorts/HDSKuln-5qU?si=DUaRtrO2aU1AaHyS

Because everything is in the process of falling the same direction. It's like if you throw a bucket of water and ask why none of the droplets went sideways.

Gravity comes off the sun in 3 dimensions. The sun is a ball and gravity radiates from it in all directions. if we went up we would still be in the suns gravitational field.