Oblate Ellipsoid: Can Earth Be Modified?

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In summary, the Earth is an oblate spheroid, meaning it is flattened at the poles and stable due to the polar radius being smaller than the equatorial radius. If the polar radius was greater, the Earth would be shaped like a spindle and could potentially tumble or flip. Tidal forces can also deform bodies into prolate ellipsoids, which may result in disintegration if self-cohesion forces are exceeded. The tennis racket theorem relates to tumbling of rigid bodies with differing moments of inertia. Neutron stars can only rotate up to a certain speed before becoming asymmetrical and radiating gravitational waves. Haumea, although not a planet, is in hydrostatic equilibrium with three different axes due to its fast rotation.
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How far can a planet's equation be changed from that of a standard sphere, or x^2 + y^2 + z^2 = r^2? What are the possible consequences?
I'm told Earth is an oblate spheroid. Is it possible for a planet to be an oblate ellipsoid (equation modified from (x/a)^2 + (y/b)^2 + (z/c)^2 = 1)? What would be the possible consequences, to include "tumbling"?
 
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The Earth is an ellipsoid, which is flattened at the poles. It is therefore described as being "oblate".

The Earth is stable and does not tumble because the polar radius is less than the equatorial radius, it is oblate.

If the polar radius was greater than the equatorial radius, then the Earth would be shaped more like a spindle. It would then be unstable, and could regularly tumble or flip.
 
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And I don't think it's possible to have a planet with three different values for ##a##, ##b## and ##c##. An asteroid or small moon, sure, but anything larger will collapse under its own weight into pretty near a sphere. That may be made oblate due to spin, but the spin implies rotational symmetry about the spin axis.
 
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Oblate spheroid and oblate ellipsoid are the same thing, no? One axis shorter than the remaining (and equal) two.

Anyhow. Other than spin doing the oblate thing, tidal forces try to deform bodies into prolate ellipsoids. The possible consequences of this process are similar to those of excessive spin, and may include disintegration when self-cohesion forces are exceeded (cf. 'Roche limit'). Use tidal forces responsibly. Keep away from children dwarf planets.
 
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There is a limit to how oblate a heavenly body can be. Neutron stars can rotate at 60,000 rpm. If they try to go faster than that they become asymmetrical and radiate gravitational waves. The spheroid is "trying" to become ring shaped, but this is unstable as the mass "wants" to aggregate in part of the ring.

It is believed that tumbling may occur in the cute little Trappist-1 solar system.
 
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Bandersnatch said:
Oblate spheroid and oblate ellipsoid are the same thing, no? One axis shorter than the remaining (and equal) two.

Anyhow. Other than spin doing the oblate thing, tidal forces try to deform bodies into prolate ellipsoids. The possible consequences of this process are similar to those of excessive spin, and may include disintegration when self-cohesion forces are exceeded (cf. 'Roche limit'). Use tidal forces responsibly. Keep away from children dwarf planets.
Brilliant responses. My post should have been r^2/a^2 + z^2/b^2 = 1. Will study the references, and thanks!
 
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Ibix said:
And I don't think it's possible to have a planet with three different values for ##a##, ##b## and ##c##. An asteroid or small moon, sure, but anything larger will collapse under its own weight into pretty near a sphere. That may be made oblate due to spin, but the spin implies rotational symmetry about the spin axis.
It's not a planet, but Haumea is in hydrostatic equilibrium or very close to it with three different axes. The fast rotation makes this a stable configuration.
 

FAQ: Oblate Ellipsoid: Can Earth Be Modified?

What is an oblate ellipsoid and how does it relate to Earth?

An oblate ellipsoid is a sphere that is slightly flattened at the poles and bulging at the equator. Earth is an oblate ellipsoid because its rotation causes it to have this shape rather than being a perfect sphere.

Can the shape of Earth be modified intentionally?

Modifying the shape of Earth intentionally on a large scale is currently beyond our technological capabilities. Such an endeavor would require enormous energy and resources, and it could have unpredictable and potentially catastrophic environmental consequences.

What would be the consequences of modifying Earth's shape?

Altering Earth's shape could have significant impacts on its climate, weather patterns, tectonic activity, and even the distribution of oceans and landmasses. These changes could lead to unpredictable and possibly severe effects on ecosystems and human societies.

Are there any natural processes that could change Earth's shape?

Natural processes such as tectonic activity, volcanic eruptions, and glacial movements can cause minor changes in Earth's shape. However, these changes are typically very slow and occur over geological timescales.

Why is Earth not a perfect sphere?

Earth is not a perfect sphere primarily due to its rotation. The centrifugal force caused by rotation causes the equator to bulge outwards, making Earth an oblate ellipsoid. Additionally, gravitational anomalies and the distribution of mass within Earth contribute to its irregular shape.

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