Talk:Equatorial bulge

message: I propose that the physics content of the oblate article is merged into the equatorial bulge article. --Cleonis | Talk 11:47, 17 March 2006 (UTC)
thread_title:  Proposal: merge the physics of the [[oblate]] article 

message: *The equatorial bulge of Atmosphere is much more important than the ocean and litosphere bulges. This is why the cumulonimbus top level may reach from the ground 20 km high along the ICT and much less at middle and high latitudes. That also means that the equatorial bulge in oceans is more important than in the solid continental Earth level. --Fev 01:42, 7 April 2007 (UTC)
thread_title:  Ocean and Atmosphere 

message: Cleonis: I will thank you if you stop writing in my answer and bringing up some themes they don't have anything to do with what I am trying to say here. If you have something to say, I will like to see it in a paragraph with some title like I did before. Thank you. --Fev 15:36, 14 April 2007 (UTC)
thread_title: This is not fair

message: I copy and paste from above:
 That also means that the equatorial bulge in oceans is more important than in the solid continental Earth level. --Fev 01:42, 7 April 2007 (UTC)
thread_title:  How the Geoid differs from the reference spheroid 

message: *First, I am going to finish what I was writing above, and later, if I do not have more important things to do,. I'll try to answer these new questions you are bringing up —The preceding unsigned comment was added by Fev (talk • contribs) 00:31, 15 April 2007 (UTC)
thread_title: Let me finish

message: If I want to fint the actual difference between two mountains in Norway, that being Galdhøpigen and Gaustadtoppen. I am given to understand that I put 59 point 85 on the calculator, then press the cosinus button. Minus is next, and then it is 61 point 62, then cosinus again. Then =, but what do I multiply with? Is it enough with 21360 metres, or does the ocean also bulge at the eq.-line? --82.134.28.194 (talk) 13:14, 14 January 2011 (UTC)
replies: text: What do you mean by "the actual difference"? — Yes, the ocean also bulges; the reference ellipsoid is (approximately) mean sea level. —Tamfang (talk) 20:51, 15 July 2012 (UTC)
thread_title:  a mathematical challenge....? 

message: The alternative explanation is drawn down from observations of rotating stars where the mass of the star is roughly the same but a faster rotation generates a greater spherical deviation between equatorial and polar diameters -http://www.jpl.nasa.gov/releases/2001/release_2001_150.html .The uneven rotational gradient between equatorial and polar coordinates is a trait of differential rotation and generates an uneven spherical shape ,the faster the rotation,the more uneven the rotational gradient and subsequently the greater spherical deviation.It makes no sense to reference the Earth's spherical deviation from the dead center of the Earth when the mechanism borrowed from fluid dynamics does a better job of explaining the deviation notwithstanding that this mechanism fits neatly with a crustal evolution/motion.In some ways 'equatorial bulge' is a misnomer as the mechanism is spread out across the rotating globe hence the planet's spherical deviation is a better description.This explanation was given in 2005 and long before discussions of rotation entered plate tectonics but fundamentally differential rotations kills two birds with one stone so that it brings two planetary features close together using a common mechanism Gkell1 (talk) 14:23, 3 July 2011 (UTC)
thread_title: Alternative explanation

message: To get the Earth's mean radius, we must start with a definition of 'mean radius'.  Is it the radius of a sphere of equivalent volume?  (That, at least, is easy to compute.)  Is it the average, taken over the surface area of the geoid, of distance to the core?  If the latter, which distance: the obvious straight line, or the component parallel with local gravity?  Likely there are other candidate definitions.  —Tamfang (talk) 20:54, 15 July 2012 (UTC)
thread_title:  which average 

message: I have an extra piece of information that I never learned but am pretty sure is true. Is it the case that when ever a planet is rotating, it's oblate but the oblateness changes the gravitational field of the planet and that in turn makes it even more oblate, so when ever a planet is rotating, it is more oblate than it would be if it had the gravitational field that it would have had if it was a sphere. Blackbombchu (talk) 02:51, 17 June 2013 (UTC)
thread_title:  Calculating oblateness 

message: I know this is an old argument, and I suppose I am taking a politically incorrect view.
But I have a great deal of difficulty accepting that rotation causes centripetal force.  I have similar difficulty accepting that centripetal force could cause a bulge.  (well I suppose the centripetal force of my belt causes my tummy to bulge).
Seriously though, rotation tends to push objects away because of their linear momentum.  That constitutes a centrifugal force, which results in the equatorial bulge.
Gravity pulls everything in, thereby imposing a centripetal force.  
Ultimately equilibrium must be maintained within the planet, which is achieved when the mass of the bulge itself generates enough gravitational (centripetal) force to overcome the centrifugal force of rotation.
no?
Doc.Ian (talk) 21:04, 24 September 2016 (UTC)
thread_title:  Centripetal Force 

message: I removed the following "mathematical explanation" of the bulge:
:The standard formula for this [centrifugal] force is the relationship F_c =  Mv^2 / R. However, velocity at the surface is equal to the product of radius and rotational velocity, and therefore the force is directly proportional to radius. Viewing the globe as a series of rotating discs, the radius R toward the poles decreases and thus a smaller force is produced for the same rotational velocity (approaching zero at the pole). Moving towards the Equator, v^2 increases much faster than R, thus producing the greatest force at the Equator.
:In addition, because Earth's dense metallic core is included in the cross-sectional disc at the Equator, it contributes more to the mass of the disc. Similarly, there is a bulge in the water envelope of the oceans surrounding Earth; this bulge is created by the greater centrifugal force at the Equator and is independent from tides. Sea level at the Equator is 21.36 km higher than that at either pole, in terms of distance from the center of the planet.
There are many things wrong with it.  "Radius" is ambiguous; it should be "distance from the axis". One cannot analyze the disks separately, because every disk contributes gravity to every point on the surface with different force and direction, so that integration disk-by-disk is very difficult. A homogeneous sphere has the same external gravitational field as the same mass concentrated at its center, but that is not true for a disk.  Moreover, each disk has different (and non-homogeneous) density. --Jorge Stolfi (talk) 02:07, 1 April 2019 (UTC)
thread_title:  Bad explanation 

message: The summary states: "An equatorial bulge is a difference between the equatorial and polar diameters of a planet due to the centrifugal force exerted by the rotation about the body's axis."
Later it's stated that: "Generally any celestial body that is rotating (and that is sufficiently massive to draw itself into spherical or near spherical shape) will have an equatorial bulge matching its rotation rate."
I saw a number of papers that used the term "equatorial bulge" for celestial bodies such as the Sun, Titan (not believed to be an equatorial ridge), and the moon.
I propose changing the summary to say: "An equatorial bulge is a difference between the equatorial and polar diameters of a celestial body due to the centrifugal force exerted by rotation about the body's axis."
(I suck at Wiki markup, forgive me) JackW2 (talk) 12:11, 27 March 2021 (UTC)
replies: text: I am not sure if this applies to any bodies other than planets. Asteroids, comets, etc. are too small to be gravitationally rounded and equatorial bulge cannot be defined for them, while stars as far as I know do not rotate like a rigid body (for example solar rotation differs between equator and poles by as much as 50%, while many giant stars seem to have an irregular shape conditioned more by local differences in convection than rotation) so this is again not applicable. And, rounded moons are for all purposes planets, planetary scientists generally include them when talking about planets, and not referring to them as such is a pervasive popular science thing (see https://arxiv.org/abs/2110.15285 for historical background of such usage, refer also to planetary-mass moon) 93.103.223.236 (talk) 09:22, 10 April 2023 (UTC)
thread_title:  Planet versus Celestial Body? 

message: The formulas given for equatorial and polar radius inline are a_e = a\, (1 + \tfrac{f}{3}) and a_p = a\,(1 - \tfrac{2f}{3}); however multiplying those together to get the volume does not match; a_e^2 a_p \neq a^3 (the terms involving f only cancel out to linear order). I worked back from the mathematical definition of flattening f = \tfrac{a_e - a_p}{a_e} and  this way one can obtain different expressions a_p = a\,(1-f)^\frac{2}{3} and a_e = a\,(1-f)^{-\frac{1}{3}} which can indeed be linearized to the given expressions for small f. However I was unable to find any suitable literature to cite here so I'm unaware if this linear approximation is just how it's conventionally done for simplicity so I refrained from directly editing this in article. Additional input would be appreciated. 93.103.223.236 (talk) 09:11, 10 April 2023 (UTC)
thread_title:  Expression for equatorial and polar radius