Variation Of G Due To Shape Of Earth

The Earth is not exactly spherical and is ellipsoidal. As a result, it is flatter at the poles and bulges at the equator. The Earth’s polar radius is 6.357 x 106 metres, and its equatorial radius is 6.378 x 106 metres. Because gravity’s acceleration is inversely proportional to the Earth’s radius, g near the pole is greater than g at the equator.

Variation in g as a result of the Earth’s Shape

The shape of the Earth is an oblate spheroid, not a fully spherical sphere. The Earth’s polar radius (radius at the poles) is 21 kilometres lesser than the equatorial radius (near the equator).

According to the formula, the acceleration due to gravity is inversely equal to the square of the Earth’s radius. At the equator, the Earth’s radius is greater; at the equator, g is smaller. In the case of poles, the opposite is true. Assume the Earth’s form is somewhat elliptical. As a result, the distance from the pole and the equator to the centre will differ.

As a result, the distance from the centre to the pole (RP) and the equator (RE) is as follows:

RE versus RP

We can deduce the relationship between RE and RP as follows:

GM/R2 = g

Then, if G and M are taken as constants in the acceleration formula,

gP = GM/RP2 

gE = GM/RE2 

As a result, the gravitational accelerations at the equator and pole are calculated as follows:

gP is more than gE.

The relationship of gravitational acceleration is gP / gE = RE2 / RP2 and is derived from the distances between the poles and the equator.

As a result, the gravitational acceleration at the equator is smaller than that at the pole.

Earth’s Rotation Causes g to Change

The change in g is caused by the centrifugal force acting on the Earth’s rotation. When the Earth rotates, all objects are subjected to a centrifugal force that acts in the opposite direction of gravity.

Consider a sample mass (m) located on a latitude that intersects the equator at an angle 𝜃. When a body spins, every particle within it moves in a circular motion around the axis of rotation, as we have seen. The Earth spins at a constant angular velocity , while the test mass travels in a circular path of radius ‘r’ at an angular velocity.

A centrifugal force is exerted on the sample mass since this is a non-inertial frame of reference (mr2). The test mass is attracted to the planet’s core by gravity (mg). These forces are called co-initial forces because they act from the same point, and they are called coplanar forces because they fall on the same plane.

If the two coplanar vectors make two sides of the parallelogram, the resultant will always be along the parallelogram’s diagonal. It is based on the parallelogram law of vectors. Based on this, the magnitude of the apparent value of gravitational force can be calculated at the latitude through parallelogram law of vectors.

The radius of the circular path followed is r = R cos 𝜃, where r is the radius of the circular path followed.

As a result, the preceding expression becomes,

g’ = g – 2R cos2 𝜃

where g′ is the apparent amount of gravity acceleration at the latitude due to earth rotation, and g is the real magnitude of gravity at the latitude without considering earth rotation.

Numerous Factors Influence g

The following four elements have a significant impact on g:

• The Earth’s spherical shape.

• The Earth’s rotational motion.

• Height above the surface of the Earth.

• Depth below the surface of the Earth.

Factors are Influenced by g

G is the universal gravitational constant, M is the planet’s mass, and

R is the distance between the point in question and the Earth’s centre.

As a result, the acceleration due to gravity (g) is determined by the mass of the Earth, the gravitational constant (G), and the distance between the planet’s centre and the object.

Variation in the Value of g

Variation of g due to the shape of Earth

The earth’s radius at the equator is greater than its radius near the poles because it is an oblate spheroid. Because the acceleration due to gravity for a source mass is inversely proportional to the square of the earth’s radius, it varies with latitude due to the earth’s shape.

g decreases when the earth rotates

Since a body placed on the earth’s surface moves along a circular route as it rotates, it experiences a centrifugal force, which causes the body’s apparent weight to drop.

Explain the Earth’s form

The shape of the Earth is an ellipsoid with an irregular shape. The Earth looks to be spherical, although it is more ellipsoid in shape when viewed from space. However, even an ellipsoid is insufficient to describe the Earth’s distinctive and ever-changing shape.

Conclusion

The Earth’s form is roughly spherical. The rotation of the Earth causes a modest flattening in the poles and a bulging around the equator. As a result, an oblate spheroid with an equatorial diameter 43 kilometres (27 miles) bigger than the pole-to-pole diameter is a better approximation of Earth’s shape.  Because gravity’s acceleration is inversely proportional to the Earth’s radius, g near the pole is greater than g at the equator.