# Why invariable plane is tilted to ecliptic plane?

1. Jul 19, 2017

### HelioGeo

I googled and found this angle of earth is claimed to be 1.5787 degree. Does it change over the time? Does anyone know any history of this tilt? I wonder if it's linked to global warming.

2. Jul 19, 2017

### Bandersnatch

Hi, HelioGeo, welcome to PF!

First, do you know how the invariable plane is defined?

3. Jul 19, 2017

### HelioGeo

Not sure, isn't it related to the direction of angular momentum?

4. Jul 19, 2017

### Bandersnatch

Yes. It's the sum of all angular momenta in the solar system, with respect to its centre of mass.

So each planet (and the Sun) contributes something to it, with the greatest contribution coming from the far-off and massive gas giants (Jupiter, mainly).

Let's say we have an unlikely, imaginary solar system with two planets only, each orbiting at 90 degrees to each other's plane of rotation (like one orbiting around the Sun's equator, the other doing a polar orbit).
Each planet's ecliptic is just the plane of its orbit.
But the invariable plane will be the sum of their angular momenta, and be lying somewhere between the planes of the two orbits.
If you then took one planet and just disappear it (Death star-style), the invariable plane would change, but the orbit of the other planet would remain nearly the same, and as a result the average insolation of its surface would not change. Same if you added more planets to the mix.

In another imaginary system, one of the planets could be so massive, and contribute so much of the total angular momentum, that the invariable plane would almost always be nearly the same as its orbital plane (i.e., its ecliptic), regardless of what orbits other small planets would have.

That is to say, the invariable plane is something of a convenient (for some purposes) mathematical abstraction, and its inclination w/r to the Earth's orbit doesn't have that much meaning by itself.

Having said that, it does change, because planetary orbits change. What affects the climate of any given planet are these individual orbital changes, rather what other planets are doing and what is the resultant, particular orientation of the invariable plane.
These changes are extremely slow, though. You may want to look up Milankowitch cycles to learn more how such changes affect climate, and what are the timescales involved.

5. Jul 19, 2017

### HelioGeo

Hi Bandersnatch, thanks for the comprehension. Back to one of my questions, there's not so much information or study on this reference plane, right? To your question, if there were links between this plane and weather, It would be as dynamic as angular momentum itself, that includes both 11 years period and Milankowitch cycles. What do you think?

6. Jul 19, 2017

### Bandersnatch

Isn't there? Or more importantly, is there a need for any more than there is? It's a pretty straightforward and somewhat trivial calculation.
Which is very un-dynamic. Like with all gyroscopes, orientations of orbits tend to be very hard to change.
Also, I don't see what the 11 year solar sunspot cycle has to do with the invariable plane or angular momentum in general.

7. Jul 20, 2017

### HelioGeo

I believe you are right, I just don't know some references to support this.

8. Jul 20, 2017

### HelioGeo

I didn't forget your question. I feel there's a need. Planck Constant is a quantum of angular momentum, isn't there a need to know where was the invariable plane when Planck Constant was measured?

9. Jul 21, 2017

### Bandersnatch

No. Planck constant is not the quantum of angular momentum, even though it has the same dimensions. It's the quantum of action.

Determinations of the Planck constant don't make use of measurements of any angular momenta.
Methods of its determination are listed here:
https://en.wikipedia.org/wiki/Planck_constant#Determination

The orientation of the invariable plane has as much bearing on Planck constant as e.g. the orientation of the rotor of my desk fan, or the net angular momentum of all Ferris wheels in Uganda. Which is to say none at all.