Why Gravity Varies with Latitude on a Spinning, Non-Spherical Earth: 18-Geol-B10, December 2019, Q4

Question 4: Why Gravity Varies with Latitude on a Spinning, Non-Spherical Earth (Choose 6 of 10 – equal value)

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Two independent physical causes

The International Gravity Formula corrects observed gravity to a smooth reference value that already accounts for TWO physically distinct consequences of the Earth being a spinning, oblate (non-spherical) body, so that what remains after the correction is the geologically interesting anomaly rather than this large, predictable, latitude-dependent background.

(a) At any point P off the rotation axis, the outward centrifugal acceleration a_c=ω²r partially cancels the true, centrally-directed gravitational attraction g; it is largest and most directly opposing at the equator, and vanishes at the poles (r=0). (b) Because the Earth's true shape is an oblate spheroid (exaggerated here), the polar radius is roughly 21 km shorter than the equatorial radius, so a point at the pole is genuinely closer to the planet's centre of mass and experiences a stronger 1/R² attraction than an equatorial point, independent of rotation.

How the International Gravity Formula compensates

Both mechanisms make TRUE gravity increase smoothly and monotonically from equator to pole; the International Gravity (Somigliana/GRS80) Formula, g(φ) = g_e(1+k sin²φ)/√(1−e²sin²φ), reproduces exactly this smooth theoretical trend for an idealized rotating, oblate reference ellipsoid at sea level. Subtracting g(φ) from an observed reading (the "latitude correction") therefore removes the large, purely geometric/rotational background — some 5,000+ mGal from equator to pole, dwarfing almost any geological anomaly — leaving only the smaller residual that reflects real subsurface density variation, which is the quantity of geological interest.

Topic. The rotational (centrifugal) and oblate-shape (geometric) origins of the latitude-dependent normal-gravity field compensated by the International Gravity Formula.

Key relations. a_c = ω²r (r = distance to rotation axis); g(φ) = g_e(1+k sin²φ)/√(1−e²sin²φ) (GRS80 normal gravity).

Why this works. The oblate shape is itself a long-term hydrostatic consequence of the same rotation (a spinning fluid/plastic body bulges at its equator), so both effects share one root cause, but they act on the gravity FIELD through two physically separate routes — one dynamical (an inertial pseudo-force felt only in the rotating frame) and one purely geometric (distance to the centre of mass) — which is why the formula must, and does, bundle both into a single empirically-fitted latitude curve rather than relying on either alone.

Common pitfall. Treating the latitude correction as removing only "the flattening effect" and forgetting the (larger, near the equator) centrifugal contribution, or drawing the centrifugal vector as pointing away from the Earth's CENTRE rather than away from the rotation AXIS, which only coincide at the equator.

Source. Telford, Geldart & Sheriff, Applied Geophysics, 2nd ed., §2.2 (normal gravity, International Gravity Formula, latitude correction).

Question 4 of 10: Why Gravity Varies with Latitude on a Spinning, Non-Spherical Earth

Question 4: Why Gravity Varies with Latitude on a Spinning, Non-Spherical Earth (Choose 6 of 10 – equal value)

Two independent physical causes

How the International Gravity Formula compensates