Centrifugal force? Why does the Earth bulge at the equator?

[paisiello2]

I think it's not whatever works for me but rather whatever works for the physics.

Clearly your table analogy doesn't go far enough.

 

[dauto]

I think it's not whatever works for me but rather whatever works for the physics.

Clearly your table analogy doesn't go far enough.

This thread is much ado about nothing, in my opinion. If you don't like the tables, remove them and use the floor instead...

 

[paisiello2]

This thread is much ado about nothing, in my opinion. If you don't like the tables, remove them and use the floor instead...

Whatever works for you...

 

[BruceW]

Even if you pick the "fixed" stars as your inertial frame, you will still measure a bulge in the earth. So where did the force to cause this deformation come from? It can't be a fictitious force because they supposedly do not exist in an inertial frame.

then call it a lack of a force. think of each bit of matter as it spins around the Earth's axis. If there were more force on the matter at the equator, there would be less bulge. If the forces were suddenly zero, the bulge would be infinite, because the matter would just all fly outwards at it's current velocity.

 

[paisiello2]

then call it a lack of a force. think of each bit of matter as it spins around the Earth's axis. If there were more force on the matter at the equator, there would be less bulge. If the forces were suddenly zero, the bulge would be infinite, because the matter would just all fly outwards at it's current velocity.

But is this enough by itself to cause the deformation?

Based on the postings made by others I think now that the bulge is caused by the portion of the Earth outside the equatorial region pushing or squeezing against the portion of the Earth in the equatorial region. This squeeze is caused by the Earth's gravity trying to accelerate the moving portions towards the center of the earth.

 

[D H]

From the perspective of a frame that rotates with the Earth, the surface of the Earth is very well approximated as a surface of constant potential energy, where the potential from both the gravitation and centrifugal forces contribute to the total.

From the perspective of an inertial (non-rotating) frame, the surface of the Earth is very well approximated as a surface of constant total energy, where both the gravitation force and kinetic energy contribute to the total.

These two perspectives yield the same result.

That was wrong.

It's the difference between kinetic and potential energy that is minimized, not the sum. Nothing's moving from the perspective of an Earth-fixed frame, so there is no kinetic energy in this frame. There is however a potential due to the fictitious centrifugal force in this frame, $-\frac 1 2 \omega^2 r^2 \sin^2\theta$. There is no centrifugal force in an inertial frame, but things are moving in this frame. The specific kinetic energy $\frac 1 2 v^2$ can be rewritten as $\frac 1 2 \omega^2 r^2 \sin^2\theta$. Note well: The kinetic energy in the inertial frame and the centrifugal potential in the rotating frame are additive inverses.

What this means is that the Lagrangian L=T-V is the same whether one looks at things from the perspective of an Earth-fixed (rotating) frame or an inertial frame. The principal of least action mandates the presence of an equatorial bulge.