I am trying to determine which on Earth's surface has the lowest gravity. Googling is not finding anything concrete. My natural inclination would be to think of Mount Chimborazo in Ecuador, being on the equator (centripetal force) and also being the furthest point from the Earth's center. However, the GRACE gravity map has the area listed in red for high gravity, presumably due to local mineral anomalies or mantle structure.
Newtonian Gravity – Where is the Lowest Gravity on Earth’s Surface?
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The same thing that makes the surface rotate: the fact that it always rotated. Because angular momentum is (almost) conserved our planet has no other option than to always rotate. (Of course in reality this picture is complicated by interactions with rest of the universe, but those are just small corrections). You can ask then why did it rotate in the first place and this has to do with the origin of the Solar system.
So, the main question is not what makes Earth rotate but what layers of Earth rotate at what speed. If Earth were a solid body then it would rotate with same angular speed everywhere. But the interior of the Earth is liquid, so the picture is quite complicated. Only thing that is obvious is that every part of Earth must rotate (at some speed or other) because of friction: if one layer (say crust) were rotating and other (say mantle) weren't then after a little while it would start to rotate anyway because the atoms of the moving layer would drag the atoms of the static layer with them.
To say anything more than this one would have to consider precise materials and fluid equations in the interior of Earth. Hopefully someone else will come along and complete the picture.
Lots of places state that the Earth's gravity is stronger at the poles than the equator for two reasons:
- The centrifugal force cancels out the gravity minimally, more so at the equator than at the poles.
- The poles are closer to the center due to the equatorial bulge, and thus have a stronger gravitational field.
TL;DR version: There are three reasons. In order of magnitude,
The poles are closer to the center of the Earth due to the equatorial bulge. This strengthens gravitation at the poles and weakens it at the equator.
The equatorial bulge modifies how the Earth the gravitates. This weakens gravitation at the poles and strengthens it at the equator.
The Earth is rotating, so an Earth-bound observer sees a centrifugal force. This has no effect at the poles and weakens gravitation at the equator.
Let's see how the two explanations in the question compare to observation. The following table compares what a spherical gravity model less centrifugal acceleration predicts for gravitational acceleration at sea level at the equator ($g_{\text{eq}}$) and the north pole ($g_{\text{p}}$) versus the values computed using the well-established Somigliana gravity formula $g = g_{\text{eq}}(1+\kappa \sin^2\lambda)/\sqrt{1-e^2\sin^2 \lambda}$.
$\begin{matrix} \text{Quantity} & GM/r^2 & r\omega^2 & \text{Total} & \text{Somigliana} & \text{Error} \\ g_\text{eq} & 9.79828 & -0.03392 & 9.76436 & 9.78033 & -0.01596 \\ g_\text{p} & 9.86431 & 0 & 9.86431 & 9.83219 & \phantom{-}0.03213 \\ g_\text{p} - g_\text{eq} & 0.06604 & \phantom{-}0.03392 & 0.09995 & 0.05186 & \phantom{-}0.04809 \end{matrix}$
This simple model works in a qualitative sense. It shows that gravitation at the north pole is higher than at the equator. Quantitatively, this simple model is not very good. It considerably overstates the difference between gravitation at the north pole versus the equator, almost by a factor of two.
The problem is that this simple model does not account for the gravitational influence of the equatorial bulge. A simple way to think of that bulge is that it adds positive mass at the equator but adds negative mass at the poles, for a zero net change in mass. The negative mass at the pole will reduce gravitation in the vicinity of the pole, while the positive mass at the equator will increase equatorial gravitation. That's exactly what the doctor ordered.
Mathematically, what that moving around of masses does is to create a quadrupole moment in the Earth's gravity field. Without going into the details of spherical harmonics, this adds a term equal to $3 J_2 \frac {GMa^2}{r^4}\left(\frac 3 2 \cos^2 \lambda - 1\right)$ to the gravitational force, where $\lambda$ is the geocentric latitude and $J_2$ is the Earth's second dynamic form. Adding this quadrupole term to the above table yields the following:
$\begin{matrix} \text{Quantity} & GM/r^2 & r\omega^2 & J_2\,\text{term} & \text{Total} & \text{Somigliana} & \text{Error} \\ g_\text{eq} & 9.79828 & -0.03392 & \phantom{-}0.01591 & 9.78027 & 9.78033 & -0.00005 \\ g_\text{p} & 9.86431 & 0 & -0.03225 & 9.83206 & 9.83219 & -0.00013 \\ g_\text{p} - g_\text{eq} & 0.06604 & \phantom{-}0.03392 & -0.04817 & 0.05179 & 0.05186 & -0.00007 \end{matrix}$
This simple addition of the quadrupole now makes for a very nice match.
The numbers I used in the above:
$\mu_E = 398600.0982\,\text{km}^3/\text{s}^2$, the Earth's gravitational parameter less the atmospheric contribution.
$R_\text{eq} = 6378.13672\,\text{km}$, the Earth's equatorial radius (mean tide value).
$1/f = 298.25231$, the Earth's flattening (mean tide value).
$\omega = 7.292115855 \times 10^{-5}\,\text{rad}/\text{s}$, the Earth's rotation rate.
$J_2 = 0.0010826359$, the Earth's second dynamic form factor.
$g_{\text{eq}} = 9.7803267714\,\text{m}/\text{s}^2$, gravitation at sea level at the equator.
$\kappa = 0.00193185138639$, which reflects the observed difference between gravitation at the equator versus the poles.
$e^2 = 0.00669437999013$, the square of the eccentricity of the figure of the Earth.
These values are mostly from Groten, "Fundamental parameters and current (2004) best estimates of the parameters of common relevance to astronomy, geodesy, and geodynamics." Journal of Geodesy, 77:10-11 724-797 (2004), with the standard gravitational parameter modified to exclude the mass of the atmosphere. The Earth's atmosphere has a gravitational effect on the Moon and on satellites, but not so much on people standing on the surface of the Earth.
Best Answer
Lowest gravity on earth surface is near Sri Lanka based on the articles below.
http://www.expertcore.org/viewtopic.php?f=13&t=3537&start=0&sid=4f7757b9c5105a7ba859ddc46c616102
http://www.timeseye.com/2011/12/sri-lanka-best-place-for-space-port.html