Machines Like Us and others linked to this cool video explaining why the solar system is flat.
I’m not entirely sure the four dimensional stuff was necessary, although it was interesting. One thing to realize though, is that while the solar system is flat, it’s not flat in the same orientation as other solar systems, or to the galaxy as a whole.
The plane of the solar system (the plane of the ecliptic0, is about 23o different than the Earth’s rotational plane (the celestial equator). Which is why we have seasons.
And the plane of the solar system is inclined about 60o relative to the plane of the Milky Way galaxy. Don’t worry, other solar systems are also at varied cockeyed angles to the galaxy.
So, although spinning systems like the solar system and the galaxy are flat, they’re not flat in the same plane. Space is three dimensional. Something I often wish science fiction movie makers would learn.