Disclaimer moved out of page:
Disclaimer: I calculated the equation myself for a homework assignment making some approximations but it seems to remain the same.
Charles Matthews 06:57, 30 Apr 2004 (UTC)
It's great to have someone able to write proper English :)Pfortuny 07:08, 30 Apr 2004 (UTC)
Sadly, proper need not be correct ... I've fixed it now. Charles Matthews 08:44, 7 May 2004 (UTC)
Potential energy and kinetic energy.
I wrote in the article:
- Perfect spherical shape is the shape of least gravitational potential energy, the oblate shape corresponds to a higher gravitational potential energy as compared to a perfect sphere.
To which User:Urhixidur added:
- —but only if the object is not rotating.
That brings us to the question, is rotational energy a form of potential energy or a form of kinetic energy?
In general, in linear motion, kinetic energy is not a form of potential energy. I find rotational kinetic energy rather hard to categorize. A flywheel is somewhat like a battery. A flywheel is used to store energy, and if you spend all the stored energy it is empty at some point, just like a battery.
In general, if a reservoir of stored energy can be increased by doing work then it can be seen as a form of potential energy.
In the scenario of weights contracting, it is rather a Hofstadterian self-referential system. If the system is not rotating then pulling the weights closer to the "middle" makes no difference; no work being done. If the system is rotating a force is required to achieve a contraction, and that force is doing work then: the contraction increases the amount of rotational energy.
In all I would say that the gravitational potential energy does not depend on whether there is rotation or not. There are good reasons for categorising rotational energy as a form of potential energy, but it is certainly not a form of gravitational potential energy. --Cleon Teunissen | Talk 19:21, 15 August 2005 (UTC)
- I was just trying to make clear why oblateness occurs. If the object is not rotating, an oblate shape will have some potential energy to dissipate: it is not the lowest energy shape. When rotating, a specific oblate shape becomes the lowest energy one, which is why the shape is assumed by spinning objects such as the planets. If the casual reader comes across just "the oblate shape corresponds to a higher gravitational potential energy as compared to a perfect sphere", then he'll wonder why the Earth (and Jupiter, Saturn, etc.) don't relax to the spherical shape from their current oblate shape, since there is potential energy awaiting release. The text as it currently stands could probably be clarified further.
- Urhixidur 03:51, 2005 August 16 (UTC)
Sure the casual reader will wonder why the oblate planets do not relax to the spherical shape, but that very question is answered in the next paragraphs. The current text seems to indicate that there is more to gravitational potential energy than just gravitational potential energy.
Hier is a version of the explanation that stays as close as possible to discussing forces, rather than shifting to discussing it in terms of conversions of energy.
- Gravity tends to contract celestial bodies into a perfect sphere, the shape where all the mass is as close to the center of gravity as possible. Perfect spherical shape is the shape of least gravitational potential energy, the oblate shape is a state with more gravitational potential energy than that.
- To get a feel for the type of equilibrium that is involved, imagine sitting on a swivel chair, with weights in your hands, whilst rotating. If you pull the weights toward you, your rotation rate goes up (by conservation of angular momentum). The amount of rotation rate increase is such that after the increase you need to pull harder on the weights than before. If there is an upper limit to the amount of inward force that you can bring into play, then at some point you cannot pull the weights in any closer.
- Something analogous to that happened in the formation of the Earth. Matter was first coalescing into a slow rotating disk-shaped distribution, and collisions and friction converted kinetic energy to heat, allowing the disk to self-gravitate into an oblate spheroid.
- As long as the proto-planet was still too oblate to be in equilibrium, self-gravitation could contract the distribution of matter. The contraction increased the rotation rate, making further contraction harder. There is a point where further contraction would require a stronger force than the tendency to contract to a spherical shape can provide. That point is the final equilibrium shape.
It is relatively unknown that in contraction of a rotating system the rotational energy is not conserved. It is customary to discuss the situation in terms of conservation of angular momentum. It is often not recognized that in order to contract a rotating system work must be done.
I think it is a bit odd that contraction of a rotating system is always discussed in terms of conservation of angular momentum, for in all other situations dynamics is discussed in terms of conversions of energy. For example, when a cannon is fired, the projectile will shoot out of the barrel towards the target, and the barrel will recoil, as per conservation of momentum. But no physicist will write: the projectile leaves the barrel at high velocity because the barrel recoils. There is very little explanatory power in that. What a physicist will write is that the explosion of the gun powder converts potential chemical energy to the potential energy of a highly compressed gas. As the gases expand that potential energy is converted to kinetic energy of the projectile.
To me it makes more sense to discuss contraction (and relaxation) of a rotating system in terms of conversion of energy; that brings it into line with the ususal way to discuss of dynamics, and it has much more explanatory power. --Cleon Teunissen | Talk 07:09, 16 August 2005 (UTC)
Why is oblate special?
Why do oblate spheroids get their own article, but prolate ones are simply redirected to spheroid (which discusses both forms...)? Is a merge in order here? Or are oblate spheroids more interesting that prolate ones? Jamie 08:17, 15 November 2005 (UTC)
- Probably because planets (including Earth) are oblate. ~Kaimbridge~ 10:08, 15 November 2005 (UTC)
- True. But tidal forces cause our oceans to be prolate... Jamie 19:52, 15 November 2005 (UTC)
Editorial style: third person or second person
There is currently a section in the article that looks rather awkward to me. It is written in the third person, but I think it flows better when it is written in the second person.
This is what I have in mind:
To get a feel for the type of equilibrium that is involved, you can can take place in a swivel chair, with weights in your hands, and someone brings the chair into rotation. If you pull the weights closer to yourself, their your rotation rate goes up (by conservation of angular momentum), which means that additional contraction requires a stronger force than before.
Proposal: move the physics to the 'equatorial bulge' article
The article says, 'An oblate spheroid is an ellipsoid having two equal polar semi-minor axes, shorter than the equatorial semi-major axis.' Shouldn't there be 2 equal equatorial semi-major axes, both longer than the single polar semi-minor axis? Also, it feels like there should be an explicit mention of and reference to prolate. --Heywood 00:03, 10 July 2006 (UTC)
- Look at the oblate spheroid and ellipse images:
- There are two equal polar axes——one for the north and south hemispheres——but actually an infinite number of equal length equatorial axes——making the equator a great circle——since the definition of a spheroid is related to that of the sphere:
- There are not two polar axes. There are two polar radii. Just as each axis has a positive and a negative direction, the single polar axis (the Z-axis by standard convention) has a northern (positive Z) and a southern (negative Z) direction. Likewise, there are not infinite equatorial axes, but infinite equatorial radii. Heywood was correct in stating that there are 2 equal equatorial semi-major axes. By standard convention, the X axis is positive in the direction from the center to 0 deg Latitude, 0 deg Longitude. The Y axis is positive in the direction from the center to 0 deg Lat, 90 deg East Long. Since our own Wikipedia article on Earth-Centered Earth-Fixed (ECEF) is barely a stub, see this image from this Geodetic Datum page at the University of Colorado. I've found this page very helpful in modeling the Earth for my work. --Yoda of Borg 22:57, 4 September 2007 (UTC)
- Yup, I've since figured it out (the equator is treated like an circle/ellipse, where the x-axis equals the major axis and the y-axis is the minor)! P=)
- My misconception was thinking that what was meant was this: where east-west (the "equator") was equal, while north-south (the "poles") were different. ~Kaimbridge~00:55, 5 September 2007 (UTC)
- A sphere can also be defined as the surface formed by rotating a circle about its diameter (in this case, the polar diameter). If the circle is replaced by an ellipse, the shape becomes a spheroid.
- So, for both the oblate and prolate spheroid, the polar axes are equal (otherwise it wouldn't be a spheroid). Just look at Earth, itself an oblate spheroid (yeah, there is a belief that the equator has a slight bulge on one side, but again, using that definition, it wouldn't technically be an oblate spheroid, just an irregular ellipsoid of rotation!): The equator = a = 6378.135 and the poles = b = 6356.75.
- Or am I misunderstanding something? ~Kaimbridge~14:27, 10 July 2006 (UTC)
- I think you're right. I'm yanking the Disputed tag, but I'd still like to see this reworded. Saying that there are 2 equal-length semi-minor axes led me to assume that the two axes were non-collinear. I'm not sure that this is ever non-redundant, even outside the context of spheroids. Could we reword this to say that the object has a polar, minor axis bisected by equatorial major axes? Just saying outright that the surface is an ellipse rotated about its minor axis seems the clearest to me. Also, the sphere article should probably specify that an ellipse has to be rotated around a principle axis to be a spheroid. --Heywood 16:00, 10 July 2006 (UTC)
- I think the plurality is still backwards——shouldn't it be the "polar, minor axes bisected by the equatorial axis" (i.e., the two polar, semi-minor axes——north and south——and the equatorial, semi-major axis)? ~Kaimbridge~13:57, 29 August 2006 (UTC)
Move to "Oblate spheroid"?
- I agree with you. But before one of us moves the article, lets wait for other users to put notes in this discussion. Kamope 15:51, 4 January 2007 (UTC)
- I happened to notice the above posting, as this article is on my watchlist. Currently the 'oblate spheroid' article is a redirect to the 'oblate' article. I agree that it would be better to move the content to 'oblate spheroid', which is what the content is about, and either to change the 'oblate' article into a redirect to 'oblate spheroid' or to put up a request for deletion of the 'oblate' article. --Cleonis | Talk 18:27, 4 January 2007 (UTC)
In the US, Smarties are a kind of candy which are not oblate spheroids, but closer to short cylinders, so that might be confusing for American readers. — Preceding unsigned comment added by 18.104.22.168 (talk) 15:37, 10 August 2012 (UTC)
As confirmed just above, in the U.S. Smarties are a hard candy that have the distinct shape of a short cylinder with concave ends. I suggest Smarties be replaced with something universally correct, such as Mentos. Thinktank33 (talk) 17:16, 11 January 2013 (UTC)