Bumping the Earth out of Orbit

[mooeypoo]

The other thread got me thinking.

 

The Earth's axis of rotation (around itself) can change after an earthquake. See here as an example http://www.geekosystem.com/chile-earthquake-earth-axis/

 

I know that rotation isn't the same as orbit, but they are related, and I'm trying to think, theoretically speaking, if this can affect the actual orbit. I'm not talking about noticeable effects, I just want to know if theoretically this will have an effect.

 

What I'm thinking is simple - if the Earth's axis shifts, the mass distribution on that previous axis changes too. More than that, it won't just "shift" axes - it will bobble, so we get a pendulum effect. wouldn't that affect the orbit?

 

I'm not sure if this makes sense, but I look at Kepler's laws (http://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion) and specifically, the proportionality constant that uses M in it. Obvioiusly, the mass itself doesn't change when the earth bobbles but the constant has "4 pi" in it, which implies a sphere. What happens if it's not a perfect sphere?

 

I also tried to think about an extreme. Let's say the planet was the shape of a cucumber (avoid dirty jokes, please) so we have an elongated mass to the extreme. Would the constant still be relevant? I can't find the derivation of that constant online, and I don't have my kinematics book anymore.

 

So to summarize my questions/thoughts:

 

1. Would changing the earth's rotation axes (or "wobbling") affect the orbit considering the earth is NOT a perfect sphere?

 

2. Would any other shape (elongated, for example) affect the orbit?

 

 

I'm just wondering here.

 

~mooey

[SMF]

This isn't my area, but I think I recall that the tides on earth are slowing the moon so the earth-moon distance is increasing. Eventually the tides will stop the earth from rotating, relative to the moon, so that both would be tidally locked (not just the moon). If you change the earths rotation, this would shift the time to tidal lock and alter the ultimate moon-earth orbit. I don't know if this would ultimately effect a change in the earth-moon orbit around the sun. SM

[lemur]

If the wobbling of the Earth put its center of gravity closer to the sun at certain moments in its rotation, wouldn't that cause its gravitation attraction with the sun to increase at those moments? Still, I'm wondering even if that would happen, wouldn't the equal and opposite reaction of the wobble mean that for every moment of increased gravitation and thus acceleration, there would be a corresponding moment of decreased gravitation and deceleration?

[Cap'n Refsmmat]

I'm not sure if this makes sense, but I look at Kepler's laws (http://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion) and specifically, the proportionality constant that uses M in it. Obvioiusly, the mass itself doesn't change when the earth bobbles but the constant has "4 pi" in it, which implies a sphere. What happens if it's not a perfect sphere?

[math]4\pi^2 = (2 \pi)^2[/math]

 

If you do the Newtonian derivation of Kepler's laws, the pi comes out of the circumference of the orbit, not the spherical nature of Earth.

 

http://www-istp.gsfc.nasa.gov/stargaze/Skepl3rd.htm

 

1. Would changing the earth's rotation axes (or "wobbling") affect the orbit considering the earth is NOT a perfect sphere?

 

2. Would any other shape (elongated, for example) affect the orbit?

I would think the wobble would change the orbit if you consider the physical center of Earth as the orbital path, but not if you consider Earth's center of mass. The center of mass will orbit the same no matter how Earth wobbles around it.

 

If the wobbling of the Earth put its center of gravity closer to the sun at certain moments in its rotation, wouldn't that cause its gravitation attraction with the sun to increase at those moments?

Absent an external force (like something smashing into Earth), it will not wobble about its center of gravity. Internal forces cannot shift the center of gravity, though they can redistribute mass around it.

 

Still, I'm wondering even if that would happen, wouldn't the equal and opposite reaction of the wobble mean that for every moment of increased gravitation and thus acceleration, there would be a corresponding moment of decreased gravitation and deceleration?

No, that's not how equal and opposite reactions work. The reaction force does not act upon the same object as the initial force. For example, if I push on the bookshelf next to me, I act with a force on the shelf, and the shelf acts on me with a reaction force, pushing back on my hand. The two forces act on two different objects.

[mooeypoo]

 

I would think the wobble would change the orbit if you consider the physical center of Earth as the orbital path, but not if you consider Earth's center of mass. The center of mass will orbit the same no matter how Earth wobbles around it.

That's a good point, the center of mass, but if the earth wobbles so does the center of mass. If the earth's orbit would've been created from scratch like this, that would've made sense, but what would happen if *now*, when we already have a stable orbit, the earth starts wobbling?

 

If we wobble and fluctuate and forth on our orbit, it will result in perturbation on that orbit, more so than we have so far...

 

No?

 

I'm trying to think how to calculate these. I'll need to find my mechanics book.

 

 

[Cap'n Refsmmat]

That's a good point, the center of mass, but if the earth wobbles so does the center of mass. If the earth's orbit would've been created from scratch like this, that would've made sense, but what would happen if *now*, when we already have a stable orbit, the earth starts wobbling?

 

If we wobble and fluctuate and forth on our orbit, it will result in perturbation on that orbit, more so than we have so far...

The center of mass will not wobble in orbit absent an external force. Earth can wobble around its center of mass, but the center of mass will continue in its nice tidy orbit.

[PhDwannabe]

All things proceed outward from their core.

 

JUST TELL ME IF THE ORBIT IS FURTHER AWAY IN THE FUTURE.

[mooeypoo]

The center of mass will not wobble in orbit absent an external force. Earth can wobble around its center of mass, but the center of mass will continue in its nice tidy orbit.

Right, that makes sense. I guess I am wondering what other effects would there be, then. If we shift the center of mass while the earth is in orbit, the center of mass will proceed on the same orbital path, but the earth as an object will wobble around. I assume this will affect the atmosphere/exposure to the sun/etc.

 

So even outside of just orbital effects, what other effects would there be if we change the shape of the earth (even slightly) mid-orbit? Also, could the moon be a factor here?

 

I think I need to go over all the equations again and examine all the effects to try and be clearer in my thought/question. I'm having a bit of a hard time right now... braindead from preparing to an exam.

 

~mooey

[swansont]

Changing the orbit requires a change in angular momentum (and possibly a change in energy, but that's not required), and we know that total angular momentum is conserved in the absence of an external torque. So you either need an outside influence exerting a torque, or you have to have a way to trade spin for orbital angular momentum.