Gravity in Equator versus Pole of Earth

GRAVITY IN EQUATOR V/S POLE OF EARTH

Gravity on the surface of Earth varies due to its rotation. Earth rotates at a speed of 1040 mph or at an angular velocity of 7.27*10^-5 rad/s. Since Earth rotates, all points on its surface perform circular motion except the North and South Pole. The points at equator perform circular motion of maximum radii as compared to other points. Hence the angular velocity of Earth is max at its equator, decreases as we move away from equator and eventually zero at the poles.

  

Consider two points, equator and North Pole on Earth’s surface. We’ll compare acceleration due to gravity (g) between these two points.

ASSUMPTIONS:

1. The equator and pole locations are at sea level

2. Density of earth is constant throughout

CALCULATION:

 

The International Gravity Formula [IGF] for Earth is,

g (φ) = 9.780327[1+0.0053024sin²φ-0.0000058sin²2φ]

 North Pole: latitude [φ] = 90⁰

g (φ) = 9.780327[1+0.0053024sin²90-0.0000058sin²180]

g (φ) = 9.780327[1+0.0053024-0]

g (φ) = 9.780327[1.0053024]

g (φ) = 9.83218 m/s²

Equator: latitude [φ] = 0⁰

g’ (φ) = 9.780327[1+0.0053024sin²φ-0.0000058sin²2φ]

g’ (φ) = 9.780327[1+0.0053024sin²0-0.0000058sin²0]

g’ (φ) = 9.780327[1+0-0]

g’ (φ) = 9.780327 m/s²

  

CONCLUSION:

On comparing g (φ) and g’ (φ) we observe that gravity at pole is greater than that at the equator. The difference is g (φ) - g’ (φ) = 9.83218-9.789327 = 0.051853 m/s²

For a body of mass 50Kg,

Weight at pole = 50* g (φ) = 50*9.83218 = 491.609N

Weight at equator = 50* g’ (φ) = 50*9.789327 = 489.466N