An Oblate Spheroid – Why Is The Earth Round?

image of earth

On 4 October 1957, the then Soviet Union placed an artificial satellite, Sputnik-1, into an orbit around the Earth, heralding the Space Age. Space exploration was no longer science fiction. Sputnik-1 was in fact a small satellite. Its diameter was only 58cm and it weighed about 83kg. it took 97 minutes and 17 seconds to complete one Earth orbit, which was 228 km at its nearest point to the earth and 947 km at the farthest. But being the first satellite, Sputnik-1 marked a new era in human history.

The word ‘orbit’ acquired special significance. An orbit may be described as a path or trajectory traced by a celestial body or a satellite, under the influence of gravitational or other force to go around the Earth or another body. Though natural forces basically determine the shape and size of orbits of artificial satellites, human ingenuity and imagination have described the orbits in amazingly accurate detail.

The Earth’s shape is one of the most influential factors in determining near-Earth orbits of artificial satellites. By the 1950s it was known that the North and South Poles are nearer the Earth’s center by about 21km than is the equator. The Space Age offered a new order of accuracy and a new insight. An analysis of satellite paths around the Earth in 1958 showed that the polar diameter was shorter than the equatorial diameter by 42.77 km. the flattening of the poles was confirmed but was overestimated by 170 meters. The same year, an American satellite, Vanguard-1, designed to go into a 500 km circular orbit, was found deviating from the predicted path.

An astronomer, Dr John O’Keefe, explained the difference and said that the path was narrower on top of the Earth and wider at the middle than had been believed before. It was also confirmed that the South Pole was about 40 meters nearer to the center of the Earth than was the North Pole. This led scientists to say that the Earth was slightly pre-shaped.

Desmond King-Hale of the Royal Aircraft Establishment (UK) refined the idea. He and his colleague, G.E. Cook, carried out a detailed study of the Earth’s shape, based on the path of 27 satellites. Accordingly, the South Pole was found to be 25.8 meters below the level previously accepted, while at the North Pole it was located 18.9 meters above the flattened sphere, in other words, the South Pole is nearer to the center of the Earth than the North Pole by 44.7 meters and not 40 meters. This asymmetry about the equator affects the orbits of an Earth satellite by resulting in a difference of about 10 km in the orbit, which is about 200 times the discrepancy causing it. This would mean that if the orbit is measured accurately to the nearest 200 meters, the shape of the Earth could be known to be within about 1 meter.

An important feature of the Earth is its equatorial bulge. The radius at the equator (6,378.14 km) is longer by some 21 km than at the poles (6,356.79 km). This extra radius makes the difference for certain orbits near the Earth. As a satellite goes from the southern to the northern hemisphere in a west-to-east direction, its orbital plane swings westward under the influence of the gravitational pull at the equator. If the satellite goes to the northern hemisphere in an east-to-west direction, the orbital plane swings eastward. This perturbation is known as ‘regression of the nodes’. Nodes are the points at which a satellite crosses the equatorial plane of the Earth.

Besides the shift of the nodes, the orbital plane has another apparent rotation to an observer on the Earth. This is caused by the daily rotation of the Earth around its axis. By the time a satellite in a low orbit completes one full orbit (say in one-and-a-half hours), the Earth would have turned by 22.5º to the east. An observer will see the plane of the orbit shifted westward by the same angle.

Satellites have added a mew dimension to geodesy, the science of surveying and mapping the Earth’s surface. By revealing the gravitational anomalies of the Earth, they have helped scientists to outline the real shape of the Earth. In addition, satellites have become accurate tools to determine location, distance and direction-which are all useful in several fields, such as navigation, geophysical prospecting, civil engineering and intercontinental missile deployment.
Even the pear-shaped Earth assumes that the equator is an exact circle. It is not so in reality; it is elliptical.

The shape of the Earth varies with longitude as well as latitude. An analysis of orbits of a large number of satellites has revealed a new profile of the Earth. The basic reference shape of the Earth’s surface in terms of the gravitational equipotential, called ‘geoid’ , almost coincides with the mean sea level of oceans (ignoring the effects of tides, winds, etc.) upon which mountains and valleys are superimposed. One can find the shape of sea-level surface, if the gravitational pull is known in detail. The extent of gravity can be deduced by the small changes in orbits that a satellite undergoes.

The geoid maps of the pear-shaped Earth showed new features of the Earth. One, based on 800,000 observations, revealed a depression in South India, 110 meters deep and a hump 81 meters high near New Guinea. NASA’s Seasat, launched in 1978, gathered considerable data on the shape of the Earth by monitoring the deviations in the height of sea surface. This was done by radar altimeter that measured its own height by noting the round-trip time taken by a short radar pulse sent to the surface.

The accuracy of geodetic measurements can be improved by using laser beams. This has been studied extensively. Two Italian satellites, Lageos-1 and -2 were sent into Earth orbit (1992) at an altitude of 590 km but at different inclinations. Earth satellite had 426 equally spaced cube-corner reflectors and appeared like a golf ball. Laser beams were received from transmitting ground stations. A comparison of the round-trip delays was studied by researchers in 30 countries. The data enabled geologists to monitor the earth’s crustal plate movements, measure the wobble in the Earth’s axis of rotation and better understand the ocean tides.

The importance of precise gravity measurements to an orbit was dramatically brought out by the Apollo 11 moon landing mission. It is now known that Neil Armstrong landed 6 km away from the target, because the gravity of the lunar surface was not known precisely.

A satellite, Gravity Probe-B of NASA and Stanford University, launched in April 2004 into an Earth orbit of 640 km, is designed to test the extraordinary effects of gravity on space-time as predicted by Einstein. Gravity is defined as the warping and twisting of space-time by massive objects.

The satellite makes the most precise measurements ever of the way in which massive celestial bodies like the planets distort the fabric of space and time, as predicted by Einstein. The measurements are based on the tiny changes in the orientation of four perfectly spherical, quartz gyroscopes, kept near absolute zero temperature on the satellite, and aligned to the star, IM Pegasi/ HR 8703.

The gyroscopes can change by as little as 0.041 arc seconds. Gravity anomalies provide extraordinary insights into the movement of oceans and how they influence the climate.

Uneven mass distribution within the Earth’s crust causes gravity differences. The Earth’s center of gravity changes constantly in response to mass redistribution on the surface of the globe, caused by shifting masses within the oceans and by soil moisture, snow and groundwater movement. The altimeter data collected by ERS-1 and TOPEX-POSEIDON missions showed anomalies in the marine gravity field. A device called DORIS on the latter satellite measures the satellite’s location and altitude above the reference ellipsoid (an approximation of the Earth’s surface) to with in centimeters.

The 2004 earthquake (the fourth largest in the last 100 years) slightly changed the shape of the Earth. It shifted the North Pole by a few centimeters, estimated at 2.5 cm. it decreased the oblateness (flattening at the top and bulging at the equator) by a small margin-one part 10 billion. Scientists say that this only continues the long-term trend of the Earth becoming less and less oblate. The earthquake decreased the length of the day by 2.68 microseconds.

Scientists have also found that the Earth’s core rotates faster than its surface by about 0.3º to 0.5º per annum. The diameter of the solid inner core is 2,400 km, while that of the fluid outer core is 7,000 km. it was only in 1936 that the inner core was discovered and merely 25 years ago was it proved that the inner core is solid and not liquid.

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