Part 8 - Isostatic equilibrium

In trying to determine the possible position of the centre of mass, the author took into account the physics relating to the phenomenon referred to as Isostatic equilibrium

Essentially Isostatic equilibrium calls for the balancing of forces (associated with different weights on different areas) acting against each other through a fluid column. A motor vehicle lifting jack is a common example. In the case of Earth movement, Isostatic equilibrium is associated with the balancing of forces due to different weights of landmasses in relatively close proximity. The example (Fig.6) taken from Holmes 19 et.al shows a mountain range rising and the sea bed falling as the weight of material removed by erosion from the mountain is deposited onto the seabed. A typical example is the sinking of the land under the Hoover Dam when the dam was filled with water 16. The net uplift of the British Isles to approx. 150 feet above sea level after the disappearance of the covering ice layer at the end of the last ice age is also a case in point. Evidence of local changes in sea level &/or sinking of the landmass over the past 2000 years are etched on the Pozulli columns in Italy.

Figure 6 below. A mountain range rising and the sea bed falling as the weight of material removed by erosion from the mountain is deposited onto the seabed.

Figure 7 below. Diagramatic representation of isostatic equilibrium on a global scale. In order that balance is acheived, the heavier African column will need to be opposed by a similar weight from the shorter Pacific column. By placing the centre of the core (density = 10.7kg/m3)1 km off centre, on the African plate side the absence of 8km depth of continental crust (average density of 2.8kg/m3) on the Pacific plate is compensated for. The overall effect is that the centre of mass / centre of gravity is displaced from the major axis of rotation.

If this principle can be invoked on a global basis (Fig.7), then the ‘column’ supporting the lighter Pacific plate will need to be longer than the opposing ‘column supporting the heavier African plate with it’s large mass of continental crust. In simper terms this situation is analogous to placing the point of balance of a tapered shaft away for it’s mid or central geometrical centre to a position nearer the heavier end.  

From Fig 7 the following equation can be derived to give a simple approximation of the position of the centre of mass by considering the difference in average height between the oceanic crust of the Pacific basin and the continental crust on the African continent is taken to be 8 km. For ease of explanation the densities of the mantle and outer core is assumed to be constant.

Taking rounded values we have:

Average height difference between the Pacific basin and African continent = 8 km

R = radius of Earth = 6,400 km

µ crust = density of crust = 2.8 x 103 kg/m-3

µ core = density of the core = 10.7 x 103 kg/m-3

X-sectional area of columns = 1 km2

E = distance (km) from the core centre to the balance point

Thus the weight of the 1 km2 Pacific Column to the balance point:

= (6,400-8) x 1 x 2.8 x 103 E x 1 x 10.7 x 103 = (17897.6 + 10.7 x E) x 103

Similarly the weight of the 1 km2 African Column to the balance point:

= (6,400) x 1 x 2.8 x 103 = 17920 x 103

Solving for E at the balance point we get:

(17897.6 + 10.7 x E) x 103 = 17920 x 103

This resolves to give E = 2.09 km

For purposes of calculating the differential centrifugal forces at the Earth’s surface, the Centre of Mass was placed 1 Kilometre off-centre from the meridian on African plate side.

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