Earth Spin Gravity Quiz


Article E13


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Earth is not a sphere. It is an ellipsoid. Its radius at equator is 6378 km, at pole 6357 km. Difference is 21 km, say 20 km. Pole to equator (curved) distance is 10000 km. Bulge increases from pole to equator, at average rate of 1 km for 500 km distance. There are plans to link some water-surplus rivers in north India with some water-deficit rivers in south India.
Will water have to "ascend" by 1 km in a 500 km long link for "flow from north to south"? Will it need any special pumping? (This question applies to all countries in north hemisphere, such as India. Use words "flow from south to north" for south hemisphere.)
No. Only Earth spin and gravity are considered here, taking Earth as a smooth ball. Its revolution around Sun, its tilted axis, solar and lunar attractions, winds, ocean currents, icebergs, earthquakes, mountains and several other influencing factors are ignored.
Note 1
Hold a horizontal rod at middle, with two equal balls (or spoons) suspended with equal strings at the ends. Strings remain vertical. Rod bends slightly. Rotate the rod at its center in horizontal plane. Strings become slant. Balls move outward with centrifugal forces. Both strings transmit equal and opposite force to the rod, which slightly expands. A circular horizontal disk, with many suspended balls around it, is like a merry-go-round. It will expand under rotation, with balls moving outwards. Imagine many balls in plane of a disk. It expands on rotation. Visualize Earth as made of many circular disks parallel to equator. All disks, with varying radius and equal speed of rotation, expand unequally with largest bulge at equator.
Note 2
Now imagine some depressions on Earth, filled with water to form oceans and lakes. Also imagine air-envelope. Water and air particles are mobile but joined to the solid Earth with invisible strings of gravity. These strings slightly change angles under centrifugal forces. Same effect applies to other mobile objects like soil, animals, surveying instruments etc.
Note 3
Due to spin and gravity, the Earth (including its solid part, seas, and atmosphere) takes ellipsoidal form. Force acting on an object on stationary spherical Earth surface is due to gravity, in line with vertical (perpendicular to surface). All verticals meet at the center of Earth. For spinning ellipsoidal Earth, the object is subjected to two forces. Gravity force (to center of ellipsoid) and Centrifugal force (perpendicular to axis of rotation). These two forces combine to form an inward force perpendicular to surface of Earth and zero force tangential to surface. Thus, there is no force to move any object (such as water in north-south links) along surface. Verticals at the surface (except those at equator and poles) do not pass through the center of ellipsoid. Also note that the air at equator would not "fall" to poles, which are "20 km below" as implied in the quiz. Cool hill stations have rarefied air. Equator is not a cool zone. This too is explained by above analysis.
Note 4
Actual land surface is not smooth. Various ups and downs are measured to make contour plans. Tides influence sea levels. MSL (Mean Sea Level) is taken as zero datum level, for these contours. MSL conforms to the ellipsoidal shape, and not the spherical shape. So these contours will apply to all water transfer schemes, disregarding any bulge effect. All links (canals and pipes) would need suitable slopes or pressures, for proper flows.

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Updated on : $ January 1, 2015 $
Author : Madhukar N Gogate