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?
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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