Undergrad Displacement of the centre of mass of the Earth

[Hussein Tofaili]

What will happen if the center of mass of Earth was displaced for some distance away from its origin? Will that affect the Earth's rotation around itself or even around the Sun?

 

[lekh2003]

There will be dangerous consequences when playing with Earth's orbit. If the Earth got any closer to the sun, it would continue to orbit, but with the dangerous chace of colliding with Mars (though this depends on the extent of displacement). If moved any farther away, it may collide with other small asteroids which otherwise were well out of the way of Earth's orbit (again depending on the displacement).

Regardless of direction of displacement, there will be adverse effects on the environment and weather would completely change. Earth's day might change, Earth's year might change.

You can actually try this with Universe Sandbox.

 

[jbriggs444]

What will happen if the center of mass of Earth was displaced for some distance away from its origin? Will that affect the Earth's rotation around itself or even around the Sun?

Can you clarify the question? You want to move the center of mass of the Earth. Is this without moving the Earth itself and without moving any portion thereof? Or are we allowed to move the whole thing away from here and then plop it down over there?

Edit: In the thirty seconds that it took you to read this post, I moved the center of mass of the Earth about 900 kilometers [sun-relative]. Hope I didn't make you spill your coffee.

 

[osilmag]

If you are trying to ask what would happen if the center of mass is shifted, my answer would be that the Earth would start to wobble on its axis.

 

[CWatters]

Might be problems with the atmosphere and sea if the centre of gravity is more than say 10-20 miles offset? It would be like having a very high plateau on one side of the planet.

 

[jbriggs444]

Might be problems with the atmosphere and sea if the centre of gravity is more than say 10-20 miles offset? It would be like having a very high plateau on one side of the planet.

It's a bit difficult to move the center of gravity of an object that is fluid enough to form a spheroid under its self-gravitation and rotation without simply moving the entire object.

 

[willem2]

The Earth could be displaced in all kinds of ways. You can use conservation of energy and momentum to find out what will happen. both will be constant if there is no external force on the earth.
The total (potential and kineticl) energy of the Earth is.
E = - \frac {GmM}{r} + \frac {1}{2} m v^2
(Potential energy is 0, if the Earth is infinitely far away from the sun, otherwise negative)
If the total energy is smaller than 0, the Earth will keep on circling the sun, otherwise it will escape.
The angular momentum is the vector product of the momentum of the earth, and the radius vector. (vector from the sun to the earth).
http://hyperphysics.phy-astr.gsu.edu/hbase/amom.html
For elleptic orbits, these will be at right angles at the minimum and maximum distance from the earth, and the magnitude of the angular momentum is
L = m v r.
With these conservation laws (and the quadratic formula) you can work out what the minimum and maximum distance to the sun will be.