Why is the solar system often shown as a 2D plane?

• Whenever I have learned about the solar system I always see the orbits displayed as a virtually flat plane.

Are all of the orbits in the solar system really like this? If so, why? It seems like a rather large coincidence for all of our planets + the asteroid belt to be on virtually the same plane.

See this video.

Because it is roughly a plane. But no scientifically accurate depiction of the Solar System will show it as a 2D plane. I mean it is obvious that the picture you show is not to scale or anything, and I don't think it is meant to be.

• This is not a coincidence at all, but a direct consequence of the way the solar system was formed.

The generally accepted model is that solar systems (including our own) form out of a Protoplanetary disc. Gravitation causes mass to collapse around a protostar, which always has some angular momentum (as does everything). Wikipedia explains it better than I can:

Protostars typically form from molecular clouds consisting primarily of molecular hydrogen. When a portion of a molecular cloud reaches a critical size, mass, or density, it begins to collapse under its own gravity. As this collapsing cloud, called a solar nebula, becomes denser, random gas motions originally present in the cloud average out in favor of the direction of the nebula's net angular momentum. Conservation of angular momentum causes the rotation to increase as the nebula radius decreases. This rotation causes the cloud to flatten out—much like forming a flat pizza out of dough—and take the form of a disk.

And then, from this protoplanetary disk, planets form. Consequently, they're all in the same plane.

As such, the inclinations of each planet's orbit are pretty close to that of Earth's:

Planet  Orbital InclinationMercury 7°Venus   3.39°Earth   0°Mars    1.85°Jupiter 1.3°Saturn  2.49°Uranus  0.77°Neptune 1.77°

Are they all positive inclinations?

It appears so, as for why, that's a different question.

That much I'd be willing to accept as chance. Its only 1/8 instead of 1/infinity.

@Dgrin91 It would be (1/2⁷) = 1/128, I think.

Aren't orbit inclinations always positive, between 0 and 90 degrees?

@Stu I was thinking that but I'm not 100% sure.

@Stu I believe what was meant are retrograde orbits with an inclination over 90° (below 90° are prograde and around 90° polar orbits), e.g. Saturn's Phoebe that's suggested might be a captured Kuiper belt object and in 173° orbital inclination to the ecliptic. Those orbits are sometimes called "negative" or even their inclination marked as negative degrees to the polar orbit. E.g. Sun-synchronous "frozen" polar orbits are often said to be at around -1° (or better said 360°/365.25 days in a year, clockwise, so negative to prograde anti-clockwise).

@gerrit I could be wrong, but I believe 1/2^7 would be the chance that the planets line up in that particular order. I dont care for the order, just that Earth is last. As for always being positive, I'm not sure of the terminology but I presume that a relative point is taken. Above that is positive, below is negative.

Inclination isn't always positive. It can be zero, after all. Inclination is always non-negative, between 0 and pi radians (0 and 180 degrees), inclusive.

The reason that inclination is always non-negative is by the way it's defined, $\arccos \frac{\vec h \cdot \hat z}{||\vec h||}$ . The range of the inverse cosine is $[0,\pi]$ (or 0 and 180 degrees if you insist on using degrees).

Just to clarify. The definition of inclination is the solid angle between Earth's orbit plane and planet's orbit plane. It does not have anything to do with orientation. So it is clear that Earth's is 0º and others must be less than 90º. Important point is that all are less than 7º. About the sign, it is a common language to mark them as positive if the planet rotates in the same direction Earth does, and negative otherwise.