# What happens with the sea level due to the centrifugal acceleration?

What happens with the sea level due to the centrifugal acceleration?

#### D H

Staff Emeritus
This sounds like a homework question. What do you think happens?

#### granpa

Thanks for the help. I was just doubtful how it will vary in the rotating frame of reference. I know about the change in effective gravity. I could put them in formulae from books and derive the expression. But I wasn't just sure about the physics behind it.

Is the effective gravity at equator less because the centrifugal force acts in a direction opposite to it? How does that effect sea level? That is what I want to know.

I think I got it. A sphere of freely flowing material in free-fall, such as a planet in formation, forms a shape reflecting the balance between internal gravity and centrifugal force from its rotation. (Reference: http://en.wikipedia.org/wiki/Centrifugal_force_(rotating_reference_frame)). So since the effective gravity is low at poles, the sea level is high and vice versa at equator. Am I right?

#### D H

Staff Emeritus
I think I got it. A sphere of freely flowing material in free-fall, such as a planet in formation, forms a shape reflecting the balance between internal gravity and centrifugal force from its rotation.
Since the gravitational force is much greater than centrifugal force even at the equator, this is not the case.

So since the effective gravity is low at poles, the sea level is high and vice versa at equator. Am I right?
That is exactly backwards. Gravitation is greatest at the poles because (a) the poles are closer to the center of the Earth than is a point on the surface of the Earth at the equator and (b) there is no centrifugal force at the poles.

Thank you DH. That was good explanation.

#### D H

Staff Emeritus
One way to look at sea level is that it is a constant potential energy surface, where the potential is that due to gravitation plus that due to centrifugal force.

One way to look at sea level is that it is a constant potential energy surface, where the potential is that due to gravitation plus that due to centrifugal force.
Does that mean the potential energy is constant everywhere on the surface of the sea? or does that mean the earth's surface is in hydrostatic equilibrium?

#### Cleonis

Gold Member
Does that mean the potential energy is constant everywhere on the surface of the sea? or does that mean the earth's surface is in hydrostatic equilibrium?
Whether potential energy is constant everywhere depends on how you choose between two options for defining potential energy for this case.

You can opt to define as follows (this is the usual choice): there is a constant potential energy if there is no tendency to drift away in a particular direction. Here on Earth there is no tendency to drift northward or drift southward. It follows that the effective potential is the same everywhere on Earth.

The other option is to compute the Newtonian gravity from first principles (which means you need to compute the newtonian gravity exerted by the reference ellipsoid). That gravitational potential is highest at the equator, and lowest at the poles.

At MIT, in the Atmosphere, Ocean and Climate Dynamics, students can http://www-paoc.mit.edu/labweb/lab4/gfd_iv.htm" [Broken]. The kind of equilibrium state that is used in the process of manufacturing a parabolic dish is the same as the equilibrium state of the bulging Earth.

Another example is the parabolic shape of a mercury mirror for astronomic observations. Example: the http://www.astro.ubc.ca/LMT/lzt/index.html" [Broken]

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