Acceleration due to gravity at latitude
The acceleration due to gravity (g) is not the same at all points on Earth. It varies due to the Earth's rotation and its shape (oblate spheroid). One key factor influencing g is latitude. Let’s understand why and derive the expression for gravity variation with latitude.
Why Does Gravity Vary with Latitude? Earth's Rotation: The Earth rotates about its axis, creating a centrifugal force that opposes gravity. This centrifugal force is maximum at the equator and zero at the poles, reducing effective gravity at the equator. Earth’s Shape (Oblate Spheroid): The Earth is slightly flattened at the poles and bulging at the equator. This means the polar radius is smaller than the equatorial radius, affecting gravity. Since gravity is inversely proportional to the square of the radius, gravity is stronger at the poles (smaller radius) and weaker at the equator (larger radius).
Consider an Object on Earth's Surface,let g be the true acceleration due to gravity at a point P on Earth as shown in diagram. Due to Earth's rotation, a centrifugal force acts outward and reduces the effective gravity. Let Earth rotate with angular velocity ω.Consider a point at latitude θ, where the object is at a radius r=Rcosθ ---(1) The horizontal component of centrifugal force is given by:
✅ g = True acceleration due to gravity (without rotation).
✅ g′ = Apparent acceleration due to gravity at latitude θ.
✅ ω = Angular velocity of Earth (7.29 x 10^-5. rad/s).
✅ R= Radius of Earth (6400 km).
✅ θ = Latitude.
This expression can be used to calculate the value of g at any latitude
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