The Shape of the Earth
Transcription
The Shape of the Earth
The Shape of the Earth From Erastotenes to the Space Age Why do I care about the shape of the Earth? Need a framework within which all mapping and spatial information can be positioned and this is most effectively done using the Earth’s surface as a reference. But the shape of the earth also tells us something about the planet’s interior and about the processes that have shaped the earth. As measurement accuracy has improved we can measure the changes in shape and hence infer the forces acting within the planet. • First measurements of the radius of the Earth are attributed to Erastotenes, working in Alexandria. • Caravans cover the distance Alexandria-Syene in 50 days at 100 stadia/day. • α ~ 1/50 the of a circle •Circumference = 250,000 stadia. R = 39773 stadia •1 stadium = 185 m (or 157 m if an itinerant stade- Pliny) •R ~ 7400 km. (or 6280 km) Telescopes replaced the gnomon, and measurement tapes replaced the camels, but this method formed the basis for all subsequent measurements of the dimensions of the Earth until the advent of satellites. • Second major development was about 2000 years later with the debate between Paris and London on the departures of the shape from sphericity Giovanni Cassini “At Paris you imagine that the earth is shaped like a lemon, or of an oblique figure; at London it has an oblate one.” Voltaire This led to the famous 18th Century arc surveys in Lapland and Ecuador and to the conclusion, quoting Voltaire, ‘He (Newton) flattened the Cassinis as well as the Earth’ Newton César-François Cassini de Thury • Shape of the earth is scientifically defined in terms of a surface of constant gravitational potential. • The direction of gravity is everywhere normal to this surface so that one can move along this surface without doing any work against gravity. • If gravity can be measured everywhere outside of the earth then it is possible to compute the shape of the equipotential surfaces. • In the absence of winds and ocean currents the ocean surface would be an equipotential surface. This defines the ‘geoid’. Jeffreys 1957 Orbit perturbations 20 10 0 -10 -20 North pole 10 0 -20 Equator -20 0 10 Metres South pole -30 -20 -10 0 10 King Hele ~1958 Gaposchkin and Lambeck 1969 Equipotential surface (normal to gravity) Direction of gravity Gravity anomalies Convection, mantle-style lithosphere mantle core The shape of the earth: (i) Constrains the density distribution within the crust and mantle, (ii) Constrains the stress distribution within the planet (iii) Provides constraints on the forces acting within the planet GRACE Mission Gravity Recovery And Climate Experiment April-May 2002 Aug 2002 Sept 2002 Oct 2002 Oct 2003 Nov 2003 Dec 2003 Jan 2004 Positioning (Geodetic) Satellite Tracking Accuracy 10 cm 1960 1970 1980 1980 Epoch Days GSFC SL 5 1970 Doppler Navsat SAO SE 1969 SAO SE 1966 1960 Camera GPS operational ~ 1 year 1m ~ 1 year 10 m ~ 5 years 100 m 1990 1990 2000 Laser Doppler GPS VLBI 1 cm 1 mm 2000 Long-baseline radio interferometry Laser ranging to satellites Global Positioning System - GPS _ Navigation Mode – handheld GPS instantaneous position with an accuracy of 1-5 m _ Geodetic Mode – 1 to 10 mm coordinate accuracy from several hours of observations. – < 1 to 2 mm/yr accuracy from several years of observations Satellite Altimetry Focussing on the Sumatra December 26 2004 earthquake and tsunami Summatra earthquake: December 26, 2004 GPS results Summatra earthquake: December 26, 2004 Satellite altimetry Summatra earthquake: December 26, 2004 GRACE results Cumulative gravity changes (in micro Gal) Gravity anomalies that remain constant throughout the interval Gravity change induced by the Sumatra earthquake Hydrological signal associated with ground and surface water changes in the Mekong River Where is it all going? • Accuracy will continue to improve • The time required to obtain the high accuracy will be reduced • Can anticipate that the observations of the shape of the earth will form an important part in monitoring the health of the planet • Key challenge No. 1: to develop understanding of the processes underlying the change observed • Key challenge No, 2: to develop the collaborative mechanisms to ensure that the results of this monitoring can be distributed globally, recognised as harbingers of change and used for forecasting purposes. 100 m 1960 Camera 1970 1980 1990 2000 Laser Doppler GPS 10 m VLBI 1m 10 cm 1 cm 1 mm 1960 1970 1980 Epoch 1990 2000