Geodesy & Satellites

The 'Theatrum Orbis Terrarum' mapbook consisting of seventy maps on fi fty-three sheets with accompanying text is considered as the first 'modern atlas'. More than thirty editions were published between 1570 and 1612. © DR

The oldest description of the world that has come down to us is that of Homer in the Odyssey: a flat disc surrounded by an Ocean River. Later on, it was also from Greece that came the first theories stating that the Earth is round: theories that were philosophical for Aristotle, but scientific for Eratosthenes, who compared the length of shadows cast by the Sun at Alexandria and at Syene (Aswan). During the Middle Ages, the Earth was thought to be fl at again. So called 'TO' maps (short for Terrarum Orbis) showed all the land in the shape of a T, surrounded by an ocean, O.

First with Copernicus, then with Kepler and Galileo, the Earth became round again and lost its place in the centre of the Universe. In 1670, the Abbé Picard used triangulation to carry out the first really precise measurement of a degree of meridian, from which he worked out the Earth's radius. He immediately passed on the result to Newton, who used it to give a defi nitive statement of the Law of Universal Gravitation. However, Newton's brilliant mind was none too happy with this overly perfect spherical Earth. What if the Earth's interior was ductile, he wondered: in that case, its diurnal rotation would lead to a flattening of the sphere at the poles. No, it wouldn't, it would make it longer at the poles, retorted the French astronomer Cassini, putting forward the same reasons. So was the Earth shaped like a tangerine or a lemon? Two French expeditions, one as close as possible to the North Pole, the other to the equator, settled the question: the English scientist was victorious.

From that time on, which saw Clairaut found modern geodesy*, the Earth was considered to be an ellipsoid of revolution*, flattened at the poles. In addition to such geodesic methods, d’Alembert and then Laplace employed field measurements to calculate the fl attening of the Earth using astronomy. As part of his theory of perturbations, Lagrange invented the concept of potential, and was no longer content to defi ne the terrestrial ellipsoid by its fl attening. The notion ' shape of the Earth ' was replaced by that of 'geoid', which represented the equipotential surface* that coincided with the mean sea level.

First map of a global model of the terrestrial geoid interpolated from measurements of terrestrial and marine gravity. © Physical Geodesy, Weikko Heiskanen 1967, published by W.H. Freeman and Co.

The arrival of satellites was to radically change the field. With Sputnik 2, geodesy entered the space age. This is because while Lagrange's theory of perturbations explains how the shape of the Earth deviates the trajectory of an orbiting body, conversely, measuring such deviations makes it possible to fi nd out the coefficients Jn which are part of the mathematical formula that defi nes this geoid. J2 can be obtained through terrestrial measurements. In 1958, D. King-Hele determined J2 with Sputnik 2 (and confirmed the value, which was already known). The American Vanguard 1 satellite launched shortly afterwards was used to evaluate for the first time the differences between the ellipsoid and the geoid. The coefficients J3 and J4 were obtained in 1959 by Kozai. The Earth is pear-shaped: the geoid is 10 metres above the ellipsoid at the North pole, and 30 metres below it at the South pole. The US then launched satellites dedicated to geodesy (ANNA 1B and LAGEOS). W. Kaula developed models that opened the way for today's very complete models, such as GRIM in Europe, and EGM in the US. Compared to the reference ellipsoid, the geoid shows, in addition to the deviations along the axis mentioned above, anomalies of several tens of metres, extreme examples of which are a high in New Guinea (+83m) and a depression off the south of India (- 103m).

The first geodesic satellites orbited the earth at high altitude (5 900 km for LAGEOS) in order to escape completely from atmospheric friction, with the risk of not being very reactive to small undulations in the geoid. Things changed radically from the year 2000, with the development of ultra-sensitive accelerometers to measure very precisely the 'gravitational anomalies'* allowing for the forces of atmospheric friction acting on the satellite. This means that CHAMP (400km) and the two GRACE (470 km) satellites can fl y at very low altitudes. In order to improve the accuracy of these measurements, the future European GOCE mission will be placed into an even lower orbit (250 km). scientific reasoning and measurements made it possible for the 'shape of the Earth' to change from a sphere to the ellipsoid of revolution.

However, it was thanks to satellites that we discovered the slightly 'lumpy' shape of the ellipsoid. And knowing the shape of the geoid ever more accurately will make it possible to develop increasingly precise missions. Space geodesy is a 'dialectic' science: knowledge of potential models is improved by observing the trajectories of satellites, while the position of satellites is better determined by improved potential models.