# The Earth as pendulum tied not to the Sun

1. Apr 7, 2013

### Yuri B.

The thought came to my mind yesturday : does not Earth in its movement looks like pendulum tied to the Polaris ?

Only the very long one - comparable to an object swinging about 1 cm circle at a tie of about 15 000 km (if my quick calculations now are correct).

Last edited: Apr 7, 2013
2. Apr 7, 2013

### Simon Bridge

You mean as an elliptical pendulum?

An elliptical pendulum moves through tension and weight being unbalanced.

What would the the analogy to the tension and weight forces when considering the earth as an elliptical pendulum suspended from some point?

Why pick Polaris? There are good reasons not to - like that Polaris is not a fixed point.
However, any point on a line perpendicular to the plane of the Earth's orbit, that passes through the center of the orbit, would do ... is there any reason to select any particular point?

This would also mean that the other orbiting bodies in the solar system have different pendulums too ... where is the moons anchor for instance?

How would this model account for the fine details of the orbits? You'd end up having to add extra pendulums to deal with all the perturbations from a pure ellipse.

How would this model account for interactions between the earth and other bodies such as the Moon?

Sure - the orbits could be treated, in a simple model, as if they were elliptical pendulum ... in a purely superficial way ... as an analogy... but where does that get you?

3. Apr 7, 2013

### Yuri B.

Or "suspended", otherwise, from a point the south pole is oriented to - the distance to the possible suspension point is so great ! In which directions are oriented (now) the axes of other solar objects, including the Sun ? Other (elliptical) "pendulums" ?

Last edited: Apr 7, 2013
4. Apr 8, 2013

### Simon Bridge

The possible suspension points form a line as I described in post #2. Since the Earth wobbles on it's axis the axis orientation is not useful - also explained in post #2.

5. Apr 8, 2013

### Yuri B.

Yes, clear, not "pendulum"...

"What keeps our Earth's axis stable?"

6. Apr 8, 2013

### glappkaeft

Simple, it isn't (though it changes slowly).

7. Apr 8, 2013

### Simon Bridge

Nothing.
It is not 'stable'.

"stability" is a measure rather than an absolute - nothing is stable but some things have more stability than others. The Earth-Moon system owes what spin-stability it has to the law of conservation of angular momentum and it's symmetry. But you should ask these things in a different thread - your original question has been answered.

hunted for that question on answers.com and the website says it has not been asked.
can you provide a link? thanks.

There are a bunch of related questions though.

Last edited: Apr 8, 2013
8. Apr 9, 2013

### BobG

Gyroscopic stability.

Once spinning, conservation of momentum means the angular momentum vector will remain constant (both magnitude and direction). The only way to change that direction and/or magnitude is by some outside force.

Of course, those outside forces occur all the time, meaning the Earth's axis isn't really all that stable in the long term. But, the angular momentum created by a spinning planet is very large, meaning it takes a long time for those outside forces to make a noticeable difference in the axis.

In other words, the magnitude of the Earth's angular momentum is large enough to give it a lot of gyroscopic stability, even if those outside forces keep the axis from being truly stable and unchanging.

9. Apr 10, 2013

### Yuri B.

"Gyroscopic stability" - due to "conservation of momentum", or vice versa, clear. (I would have difficulty finding these precisely descriptive terms however, I thought, there may be some more to it).

Last edited: Apr 10, 2013
10. Apr 10, 2013

### Simon Bridge

There's lots more but all variations on the theme - the axis is stable for the same reasons a gyroscope is hard to knock over.

To make them precisely descriptive, you have to do the math implied by the terms.
Look up "rotational stability" for details.
http://www.astro.uvic.ca/~tatum/classmechs/class4.pdf