Variation in Acceleration due to Gravity near the Earth's Surface

Apparent weight, measured by a spring scale, differs from true weight because Earth rotates. An object's apparent weight equals its true weight minus the centripetal force keeping it in circular motion with Earth's surface. This difference is proportional to Earth's angular speed squared, creating a maximum effect of about 0.34% at the equator and zero at the poles.

Gravitational acceleration varies with latitude because each object rotates along a circle determined by its latitude. At the equator, centripetal acceleration is maximum, reducing apparent weight most significantly. Moving toward the poles, the centripetal force component directed toward Earth's center decreases, so apparent weight increases. At the poles, there is no rotation, so apparent weight equals true weight.

Earth is an oblate sphere with an equatorial radius approximately 30 kilometers greater than its polar radius. This bulging results from Earth's rotation and partially liquid interior. Objects at the equator are farther from Earth's center, experiencing weaker gravitational pull. This geometric effect contributes to apparent weight variation comparably to the effect from Earth's rotation.

At the equator, centripetal force acts horizontally toward Earth's axis, reducing apparent weight directly. At other latitudes, centripetal force points toward the rotation axis, not Earth's center. Only the cosine component of this force acts toward Earth's center, reducing apparent weight less than at the equator. This geometric relationship explains why gravitational acceleration decreases away from the poles.

Apparent weight equals true weight minus the centripetal force component directed toward Earth's center. Dividing by mass gives the net acceleration g', which is less than gravitational acceleration g by a factor equal to centripetal acceleration. The difference depends on latitude and Earth's angular velocity, with maximum reduction at the equator where centripetal acceleration is greatest.

Earth's angular speed is relatively small, and the weight difference is proportional to the square of this angular speed. This quadratic relationship means the net effect of Earth's rotation is only about 0.34% of an object's weight. Although small, this effect smoothly varies from maximum at the equator to zero at the poles, demonstrating how rotation influences gravitational measurements.

Two factors reduce apparent weight below true weight: Earth's rotation creates centripetal acceleration, and Earth's equatorial bulge places equatorial objects farther from Earth's center. Both effects are comparable in magnitude and work together to produce the total variation in gravitational acceleration. The combined effect is greatest at the equator and decreases toward the poles.