Question 2 of 10: Gravity Variation with Latitude

Question 2: Gravity Variation with Latitude (Choose 6 of 10 – equal value)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Mechanism 1: rotation — the centrifugal effect

The Earth rotates about its polar axis, so every point on its surface (except the poles themselves) undergoes circular motion and experiences an outward centrifugal acceleration a_c = ω²R cosφ, directed radially away from the rotation axis (not from the Earth's centre), where ω is the Earth's angular velocity, R is Earth's radius, and φ is latitude. This outward acceleration partially cancels the true, inward gravitational attraction, so the NET gravity measured by an instrument (which cannot separate the two) is reduced by the local component of a_c resolved along the local vertical. At the equator (φ=0), a_c is at its full radial value and acts exactly opposite to gravity, giving the maximum reduction; moving toward the poles, cosφ shrinks and the vector also tilts away from the local vertical, so its gravity-reducing effect shrinks smoothly to exactly zero at the poles (φ=90°, where a point on the axis has zero radius from the axis and hence zero centrifugal acceleration).

Mechanism 2: the Earth's oblate (flattened) shape

Because the Earth is not a perfect sphere but an oblate spheroid — flattened at the poles and bulging at the equator, itself a consequence of the same rotation, but treated here as the second, independent mechanism affecting the FIELD — the solid Earth's surface at the poles sits closer to the planet's centre of mass than the surface at the equator (polar radius ≈6357 km vs. equatorial radius ≈6378 km, a difference of about 21 km). Since gravitational attraction increases as the inverse square of distance to the centre of mass, a point on the surface at the pole is measurably closer to the bulk of the Earth's mass than a point at the equator, and so experiences a stronger true gravitational pull, independent of any rotation effect.

Net effect: both mechanisms increase gravity with increasing latitude

Both mechanisms act in the same sense: the centrifugal effect subtracts LESS from true gravity as latitude increases (reduction shrinks from a maximum at the equator to zero at the poles), and the oblateness effect makes the true attraction itself LARGER at higher latitude (shorter distance to the centre of mass). Consequently, measured gravity increases monotonically from equator to pole. This combined behaviour is codified in the International Gravity (Somigliana/GRS80) Formula:

$$g(\varphi) = g_e\,\frac{1+k\sin^{2}\varphi}{\sqrt{1-e^{2}\sin^{2}\varphi}}$$

with g_e = 978,032.5 mGal the normal gravity at the equator, k = 0.0019319 and e² = 0.0066944 (GRS80 constants). Evaluating this formula gives normal gravity of 978,032.5 mGal at the equator rising to 983,218.5 mGal at the pole — an increase of about 5,186 mGal (5.2 Gal), roughly 0.53% of the equatorial value, entirely attributable to these two mechanisms.