Why Is There More Mass But Less Gravity At The Equator?

[common_sense_seeker]

Textbook explanations conveniently disregard this part of the calculation of the surface gravity at the equator. There is more mass between a body and the Earth's center due to the equatorial bulge and yet a lower force of gravitational attraction. This is completely counter-intuitive. Even Brian Cox mentions this anomaly in the TV programme 'What On Earth Is Wrong With Gravity?'. Does anyone agree that this is bizarre?

[OilIsMastery]

A Growing Earth Theory hypothesis:

Mass accretion aka meteorite impacts at the biggest possible target on the Earth, i.e it's widest point, the diameter/equator.

However it's not just the equator that shows gravitational anomaly. All impact sites show gravitational anomaly.

How do you find a crater under kilometers of ice? You use gravity sensing satellites, like NASA's two GRACE satellites, which are so sensitive they can measure the gravitational effect of heavy rainfall.

http://www.sciencedaily.com/releases/2006/06/060601174729.htm

The scientists used gravity fluctuations measured by NASA's GRACE satellites to peer beneath Antarctica's icy surface, and found a 200-mile-wide plug of mantle material -- a mass concentration, or "mascon" in geological parlance -- that had risen up into the Earth's crust.

Or not...:idea:

[Steve100]

Textbook explanations conveniently disregard this part of the calculation of the surface gravity at the equator. There is more mass between a body and the Earth's center due to the equatorial bulge and yet a lower force of gravitational attraction. This is completely counter-intuitive. Even Brian Cox mentions this anomaly in the TV programme 'What On Earth Is Wrong With Gravity?'. Does anyone agree that this is bizarre?

Because it is further away from the Earth's centre of mass.

[common_sense_seeker]

I'm not convinced by this statement. The assumption of a center of mass is a convenient solution for mathematics, but reality is another thing altogether. Your answer does take into account a mechanism for gravity, which is always going to be your downfall.

[Walter L. Wagner]

The earth is spinning, so the centripetal acceleration decreases the apparent gravity at the equator the most, and zero at the poles.

[rpenner]

The Earth's surface is approximated by the equipotential ellipsoid of a rotating, self-gravitating fluid. For such an ellipsoid, the equatorial bulge is at the same potential as the poles, but the force of gravity is related to the rate of change of that potential and as the bulge is further away, the rate of change is smaller and therefore so is the gravity.

[Vkothii]

...which is why NASA built a launch platform on the Florida Peninsula instead of Pennsylvania, and why Russian and Chinese launches use more fuel per ton launched.

[D H]

The earth is spinning, so the centripetal acceleration decreases the apparent gravity at the equator the most, and zero at the poles.

Partially correct. That the Earth is spinning also makes the Earth's take on the shape of an oblate spheroid.

The Earth's surface is approximated by the equipotential ellipsoid of a rotating, self-gravitating fluid. For such an ellipsoid, the equatorial bulge is at the same potential as the poles, but the force of gravity is related to the rate of change of that potential and as the bulge is further away, the rate of change is smaller and therefore so is the gravity.

To elaborate: The Earth's surface is very close to an equipotential surface of the combined gravitational and centripetal (pseudo) forces; the mean sea level is exactly an equipotential surface.

[James R]

And this has to do with, I hypothesize, pair production and positron production in the core which causes gravity

Are you claiming that pair production is the only cause of gravity? What you have said is not clear.

What is the mechanism of this supposed pair production in the core?

[OilIsMastery]

Are you claiming that pair production is the only cause of gravity? What you have said is not clear.
I'm suggesting that either positrons, or antimatter in general, or something else is causing gravity because our electrons are clearly negatively charged.

What is the mechanism of this supposed pair production in the core?
Herndon believes the core is a nuclear reactor however Tassos has said the core is not a heat engine.

Perhaps there is something more mysterious going on as suggested by Owen and Corliss and others.

"The geological and geophysical implications of such Earth expansion are so profound that most geologists and geophysicists shy away from them. In order to fit with the reconstruction that seems to be required, the volume of the Earth was only 51 per cent of its present value, and the surface area 64 per cent of that of the present day, 200 million years ago. Established theory says that the Earth's interior is stable, an inner core of nickel iron surrounded by an outer layer that behaves like a fluid. Perhaps we are completely wrong and the inner core is in some state nobody has yet imagined, a state that is undergoing a transition from a high-density state to a lower density state, and pushing out the crust, the skin of the Earth, as it expands." -- Hugh Owen, geophysicist, 1984

[common_sense_seeker]

Suggesting the core may be made of something completely new and unthought of sounds similar to my theory. It's worth considering for sure.

[D H]

Suggesting the core may be made of something completely new and unthought of sounds similar to my theory.
You don't have theory. OIM has pyschoceramics and strawman arguments.

It's worth considering for sure.
No, it is not.

[common_sense_seeker]

Hardnose cynic.

[ElectricFetus]

Equators centripedal force makes gravity "feel" slightly less at the equator verse the poles, this also is why the earth bulges at the equator slightly, there is not increase mass in the bulge rather density of the rock has been reduced ever so slightly because it not being crushed down as hard as at the poles.

[common_sense_seeker]

ElecticFetus, this is nonsense. Centrifugal force at the equator would suggest an increase in density of the material, with the lighter matter being pushed towards the poles. The Moon dosen't spin like the Earth, but it also has flattening and a lower surface gravity at the equator. Therefore the centrifugal force argument for the Earth is unvalidated.

[ElectricFetus]

ElecticFetus, this is nonsense. Centrifugal force at the equator would suggest an increase in density of the material, with the lighter matter being pushed towards the poles. The Moon dosen't spin like the Earth, but it also has flattening and a lower surface gravity at the equator. Therefore the centrifugal force argument for the Earth is unvalidated.

No the lighter material would be pushed towards the equator, bubbles and balloons fly up not down, so lighter rock would move towards the point of least gravity by simple act of buoyancy. The Moon experiences less gravity at its earthward facing equator because its closer to the earth and thus the earth negates a little of its gravity, this is why it has ancient lava seas on the earth facing side and barely any on the other side.

[common_sense_seeker]

No the lighter material would be pushed towards the equator, bubbles and balloons fly up not down, so lighter rock would move towards the point of least gravity by simple act of buoyancy.

No, no. The centripetal force of the crust reacting against the centrifugal force of the liquid mantle is greater at the equator. The bubbles would migrate away from this high pressure zone to the poles, just like a washing machine in spin.

[ElectricFetus]

No, no. The centripetal force of the crust reacting against the centrifugal force of the liquid mantle is greater at the equator. The bubbles would migrate away from this high pressure zone to the poles, just like a washing machine in spin.

That would be if the centrifugal force was stronger than gravity, which it isn't by a long shot, instead the process is reversed with the lower density going toward the bulge and the high density going towards the poles, because gravity is "weaker" at the bulge, not stronger as would be the case if the earth were in fact a centrifuge.

[Pandaemoni]

Textbook explanations conveniently disregard this part of the calculation of the surface gravity at the equator. There is more mass between a body and the Earth's center due to the equatorial bulge and yet a lower force of gravitational attraction. This is completely counter-intuitive. Even Brian Cox mentions this anomaly in the TV programme 'What On Earth Is Wrong With Gravity?'. Does anyone agree that this is bizarre?


Because gravity increases proportionately to the mass involved, but decreases proportionately to the square of the distance involved. At the equator, there may be more mass between you and the center of the Earth, but there's also more distance, because of the bulging, and the increased distance has a bigger effect than the increased pass.

If you take a planet, and double its mass, but without changing its size, its surface gravity doubles. If you also double its radius at the same time you double the mass, surface gravity is lower than it was before. If you triple its mass and "only" double its size gravity still gets weaker at the surface.

[common_sense_seeker]

Because gravity increases proportionately to the mass involved, but decreases proportionately to the square of the distance involved. At the equator, there may be more mass between you and the center of the Earth, but there's also more distance, because of the bulging, and the increased distance has a bigger effect than the increased pass.



It still seems odd. It's like saying that if the Earth is scaled larger, then it's surface gravity is reduced. That's nonsense.

[Steve100]

It still seems odd. It's like saying that if the Earth is scaled larger, then it's surface gravity is reduced. That's nonsense.

Do you even know Newton's equation of gravitation?

[Janus58]

It still seems odd. It's like saying that if the Earth is scaled larger, then it's surface gravity is reduced. .

No, it isn't. If you scale the Earth larger you also increase its total mass, so you would expect surface gravity to go up. But the deformation of the Earth into an oblate spheroid does not increase ts total mass, it only changes its shape. Since the force of gravity you feel is due to the sum of all parts of the Earth pulling on you (not just that part between you and the center, and sitting at the equator puts you further from the main bulk of the Earth that provides that pull, you feel a reduction in gravity.

[rpenner]

The Earth's surface is approximated by the equipotential ellipsoid of a rotating, self-gravitating fluid. For such an ellipsoid, the equatorial bulge is at the same potential as the poles, but the force of gravity is related to the rate of change of that potential and as the bulge is further away, the rate of change is smaller and therefore so is the gravity.
This has been a trollable question since at least 2005.

http://www.physicsforums.com/showthread.php?t=59484
http://www.physicsforums.com/showthread.php?t=131329

1) The Earth is not homogeneous, as anyone who owns a gold mine will tell you.
2) The Earth is not spherically symmetric. It's lumpy. Not as lumpy as the moon.
3) Therefore the exact treatment of the gravitational force of the Earth as that of a point mass is not expected to hold. Therefore, for satellite applications the Earth's gravity is approximated by spherical harmonics and for local applications where exactness is required, locally measured values are used. A one-pound weight may not weigh one pound due to local conditions but is sure to weigh the same as another one-pound weight at the same location, because it is actually a mass standard in disguise. (The SI has no such problem since formally we would say our weight is a 0.4536 kg mass and measure a weight of 4.45 newtons in one place and 4.44 newtons in another. But when you use only balance scales the distinction between mass and weight is harder to see.)

4) The surface of the Earth rotates in almost rigid fashion (albeit slower than it did billions of years ago).
5) Therefore any measurement of acceleration or weight done to a reference to the surface of the Earth. is going to conflate gravity and centrifugal acceleration. This is Newton's version of the equivalence principle.

6) The surface of the Earth is largely the surface of a fluid (oceans) and where it is solid, that solid (continents) floats on top of fluid. Indeed, plumb bobs lean away from mountain ranges since continental rock is lighter than the fluid which it displaces.
7) Therefore the surface of the Earth will closely approximate an equipotential surface (sea level) which is perpendicular to the direction of acceleration (which is gravity + centrifugal acceleration).

8) Because the Earth rotates below a speed needed to tear it apart the Earth is approximately spherical.
9) Because the Earth rotates only about 100 times slower than this top speed, the dominant shape of the Earth is an oblate spheroid. This has the poles nearer the center than the equator.
10) Since the force of gravity is proportional to the gradient of the potential, and the potential is constant in the center no matter which way you approach it, and the equator is further from the center, then the potential must be changing slower near the equator than at the poles, and therefore the measured acceleration (weight) must therefore be lower at the equator, which is what is measured.

[Avatar]

That would be if the centrifugal force ..

Sorry for nitpicking, but I was under the impression that there is no such thing as a centrifugal "force" - it's just an effect of acceleration.

[D H]

Sorry for nitpicking, but I was under the impression that there is no such thing as a centrifugal "force" - it's just an effect of acceleration.
In that sense, there is no such thing as a gravitational "force", either. Gravitation, like centrifugal acceleration, is just an artifact of a non-inertial observer. In general relativity, an inertial frame is a reference frame that is in free-fall. Centrifugal force and gravitational force, along with the Coriolis force and the frame acceleration (aka third-body effects) are all pseudo forces.

There is no device that can be constructed that can directly measure any pseudo force. In particular, just as no device can be constructed to directly measure centrifugal acceleration, no device can be constructed to directly measure gravitational acceleration.

[common_sense_seeker]

You're all full of sh*t. The only way there could be less gravity at the equator is if there was less density. But there is no real reason why this should be so. The centrifugal force argument is an obvious red herring for anyone with a modicum of intelligence. I give up on this site. You're all thick as sh*t.

(I've had a fw ciders, and I'm off on holiday tomorrow, so I don't care)

[Steve100]

Density does not play part in gravitation.

I give up on this site. You're all thick as sh*t.

(I've had a fw ciders, and I'm off on holiday tomorrow, so I don't care)

Don't leave, you haven't showed us all your maths yet.

[ElectricFetus]

-1 * -1= +1 is WRONG, it is academic stupidity and is evil. The educated stupid should acknowledge the natural antipodes of +1 * +1 = +1 and -1 * -1 = -1 exist as plus and minus values of opposite creation

Oooook get going.

Sorry for nitpicking, but I was under the impression that there is no such thing as a centrifugal "force" - it's just an effect of acceleration.

yeah that nitpicking for no reasons: we all know it not really a force.

[Billy T]

...Therefore, for satellite applications the Earth's gravity is approximated by spherical harmonics and for local applications where exactness is required, locally measured values are used. ...Nothing wrong here (or anywhere in your post) but I just wanted to point out why APL/JHU was paid By US Navy to determine the coefficients of the spherical harmonics (also called the Tesserial harmonics, I think, except for spelling errors) far out to very minor time variable terms, I think. At least twice as many as are public (not secrete, but even exactly how many are known is secrete or was.)

During the MAD era US's most secure nuclear deterrent was the Polaris sub. It needed to know exactly where it was, which way is gravitational up there and during powered flight, where the target of its ICBM is, and the details of the bumpy gravitational field it would fly thru ballistically getting there. A friend I car pooled with ran this more than decade long program. (He died just a few months ago), but he could not tell me anything detailed about it. APL solved all of these problems for the US Navy.

Ironically, the Sputnik was a big help with the sub's "Where am I exactly?" problem: Two APLers recorded its transmitted tone, which is Doppler shifted. Fitting that shift exactly allowed them to determine the orbit, which was not disclosed initially, more accurately than any other measurement method at the time. They realized that the math could be inverted. I.e. if you already knew the orbit precisely you could find where you were. So we make first the TRIAD satellites and then the DISCOS satellites.

Triad got told by uplink the exact parameters of its orbit every few days (They changed by various forces including the then unknown lumpiness of Earth's gravity, solar winds, earth's magnetic field acting on satellite currents, variable atmospheric drag, and some more I think but have forgotten)

In the insane logic of the era this need for an up link every few days was not good enough. -If the bad guys struck first and everyone was dead in the US the sub might not get to firing position, while the satellite still knew its orbit well and not be able to kill all the bad guys too, weeks later. DISCOS solved that problem as it knew where it was for (not sure I can say how long, but long enough) without any up links.

DISCOS had a free floating sphere about 1cm in diameter that was at the mass center of the satellite, called the "proof mass" (hereafter PM). The PM was an alloy of gold and platinum (I think) that was neither dia- nor para- magnetic. The PM was the true satellite the main body shield it from all the disturbances other than gravity and fired tiny thruster to follow the PM's orbit exactly.

DISCOS was expensive to make, as every resistor etc was weighed and precisely located so the CoM could be accurately set to the exact center of the PM's tiny chamber. If the CoM were ahead of the PM, the gravitational attraction of the satellite would constantly be accelerating the PM not only ONLY the Earth's gravity field. (BTW the higher order term of the harmonics "wiggle" via mass movements such as high atmospheric pressure air masses, the tides, winter snows, etc.) Eventually DISCO was retired and now we have GPS to tell the sub where it is. I suspect that DISCOS was more accurate, but as the bombs got bigger, it did not matter so much what the size of the error circle was.

I played a very minor role in all this, mainly designing a less expense version of the DISCOS system. The PM became a hollow cylinder with AC current along rigid wire on the axis. I.e. eddy currents in the PM interacted to support the PM against radial gravitational forces of the satellite It really only need to be "free floating" along the orbit to do its job adequately. You and Janus58 probably know better than me why those "in orbit trajectory direction" accelerations had to be due to only the Earth's gravity and small transverse acceleration could have other forces acting.

I did the physical modeling and set up the equations / calculations to show that the eddy current damping would be large enough to make sure the radial oscillation never could become large enough for the cylinder PM to actually hit the wire, and made an experimental test ON EARTH in tall vacuum chamber with PM as the "bob" of fine, long-wire pendulum to confirm my analysis. When the AC was on, the pendulum oscillations were damped more, just as I had predicted. - I did need some help with some of the integrals. It was the toughest applied math I had ever seen.

[D H]

Nothing wrong here (or anywhere in your post) but I just wanted to point out why APL/JHU was paid By US Navy to determine the coefficients of the spherical harmonics (also called the Tesserial harmonics, I think, except for spelling errors) far out to very minor time variable terms, I think.
The primary driver for developing high-fidelity gravity models is that there is no way to measure the acceleration due to gravity. All inertial navigation systems must instead estimate the acceleration due to gravity. Since the vast majority of the flight of a ballistic missile is ballistic (hence the name), any errors in the estimation of the gravitational acceleration will lead to errors in the projected impact point.

The current best model of the Earth's gravity field is EGM2008. A link: http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm2008/index.html. As an aside, WTF is the "National Geospatial-Intelligence Agency"?

During the MAD era US's most secure nuclear deterrent was the Polaris sub. It needed to know exactly where it was, which way is gravitational up there and during powered flight, where the target of its ICBM is, and the details of the bumpy gravitational field it would fly thru ballistically getting there.
Nuclear subs have an incredibly bad idea of where they are, at least when viewed from the perspective of launching an SLBM and making it accurately hit a target thousands of miles away. The Polaris and Poseidon missiles were accurate enough to kill Russian women and children. In other words, such a missile targeted at the center of Moscow would probably have missed by tens of miles. The addition of star trackers made the Trident I missile able to kill Russian train stations and manufacturing plants: "A miss is as good as a mile" takes on a different meaning when a near miss is enhanced by a nuclear explosion.

This lack of accuracy was the primary driver in the development of the NAVSTAR system. NAVSTAR is now know as GPS. With GPS, Trident II missiles are capable of killing Russian silos. Taking out a hardened silos requires accuracy on the order of a hundred yards or better. Not bad when the initial error is on the order of a mile or so.

[Billy T]

...Nuclear subs have an incredibly bad idea of where they are,
...This lack of accuracy was the primary driver in the development of the NAVSTAR system. NAVSTAR is now know as GPS. ...Yes they were almost "lost" with weeks of inertial guidance. To be secure they needed to stay submerged and just trail a near surface antenna radars could not see. I may be biased, but think the DISCOS system was much more accurate than GPS if no up dates are available from the ground to tell the satellite where it is (so it can tell the ground user)

GPS is really a "time of flight" system. From three known points in space where three satelites are "now" - The user is at the point where three spheres centered on those known point intersect. If there is error accumulating in the satellite's "idea" as to its location (or it clock) then that error transfers, larger I think, to the ground observer's computed idea of his position.

DISCOS was just not cost effective when mid-course corrections of the IBM via stellar observations became possible but it was very accurate and only required one satellite to survive a war in space, not three. (It still used APL invented Dopper curve fit to the over fly data, not the intesection of three spheres.)
-----------------------
DH: "WTF is the "National Geospatial-Intelligence Agency"?"
BT" Have no idea, but your link seems to be providing a "geogrid of gravity" not the coefficients of the expansion; however one clever with math should be able to back the many terms of the spherical harmonic expansion out of that data. I doubt if the results would be as accurate as they are know, but still secrete. I did not skim deep enough to know where their data came from, but it may be of interest to oil companies etc. Probably not of much use if you want to know details of the "wiggles" in a ballistic missile’s flight, I would guess.

[D H]

your link seems to be providing a "geogrid of gravity" not the coefficients of the expansion;
From the site:
Introduction The official Earth Gravitational Model EGM2008 has been publicly released by the U.S. National Geospatial-Intelligence Agency (NGA) EGM Development Team. This gravitational model is complete to spherical harmonic degree and order 2159, and contains additional coefficients extending to degree 2190 and order 2159.
The 2190x2159 tide-free spherical harmonics coefficients are the primary elements product of the EGM2008 model. The link to those coefficients is right there, on the cited Web site; no secrets. They do not provide a "geogrid of gravity" per se; they do, however, provide tools to compute such a thing.

[Billy T]

From the site:
Introduction The official Earth Gravitational Model EGM2008 has been publicly released by the U.S. National Geospatial-Intelligence Agency (NGA) EGM Development Team. This gravitational model is complete to spherical harmonic degree and order 2159, and contains additional coefficients extending to degree 2190 and order 2159.
The 2190x2159 tide-free spherical harmonics coefficients are the primary elements product of the EGM2008 model. The link to those coefficients is right there, on the cited Web site; no secrets. They do not provide a "geogrid of gravity" per se; they do, however, provide tools to compute such a thing.Thanks for the correction. My footnote was wrong. I skimmed to quickly and went to some sub-links to see if APL got any credit for its contribution - could not find any.