Why Are Orbits Two Dimensional and Not Three?

# Why Are Orbits Two Dimensional and Not Three?

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orbits are actually one dimensional if you look at their intrinsic geometry

You could say the same thing with an object that has a 3D path too (like a corkscrew). I am not sure you are helping.

Because there are only two vectors involved: the vector of the orbiting body's motion and the vector pointing from the orbiting body to the orbited body. The orbit takes place on the plane defined by these two vectors. If you were to use a force to deflect the orbiting body outside of that plane, the orbit would be realigned to the new plane as defined by the new vector of motion.

Because of conservation of angular momentum. But yeah that description is true

Orbits are 3d depending on how you set up your coordinate system or from where you look at them.

Thanks. Assuming this works out. I supose that is why it is a law.

This restates the OP in linear algebra.

I think Maxwell came up with an explaination and predicted it was full of debris but I can't remember what that was.

Spherically symmetric potential

=> Conservation of angular momentum (magnitude and direction)

=> Only planar motion conserves direction

That just assumes the moons were the same orbit eccentricity.

The rest if the moons are not so why were the ones that made the rings?

Collisions are going to, on average, knock rocks either into the atmosphere or out of orbit? Repeat over a billion years and you end up with a dominant plane/ring with the rest either out of orbit or crashed into the planet. IDK. I would be surprised if it didn't deal with probability distributions.

We don't get two dimensional orbits up here in the Oort Cloud. As soon as the chunk of rock a mere 100'000 miles from you has the same gravitational attraction as that massive ball of plasma 1 ly away - the shit is as 3D as it gets.

You hoity-toity inner system folks, on the other hand...

Better-off folks get their fusion reactor running off electrolyzed ice. Us down-to-comet people have to toil the rocks hoping to find a nicer chunk of thorium. Those are rare, but a family of 4 can live off of a couple of pounds for 1/100 of an orbital period.

Luckiest bastards plan a gravitational maneuver to get their perihelion into the inner system, charge superconductor batteries off of solar panels and get back here - maybe spend a couple periods on the round trip, but they come back filthy rich. But that's a gamble - you might as well end up in a twist like those poor shits on ʻOumuamua.

But they are 3 dimensional, user. Let's take our Moon for example, it spins not exactly in a 2D circle (well, ok, ellipse to be more precisely) but rather in a spiral