Figure

1
Figure Gravity of the Earth
J.W. Goethe University. Frankfurt

• Dr. Guillaume RICHARD
• Instituet fuer Geowissenchaften 1.232
• richard_at_geophysik.uni-frankfurt.de
• www.geophysik.uni-frankfurt.de\richard

2
Overview

• 12 x 1h30 Lectures\ 12 x 45min exercises
  (optional)
• Introduction (Historical Background Literature)
• Gravity Potential
• Laplace Poisson Equations
• Solving the Laplace equation
• Solving the Dirichlet Problem
• Gravitational Potential of heterogeneous body
• Gravity of a rotating body
• Geodesy
• Sattelites Geoid
• Model for the Geoid of the Earth
• Interpretation of Geoid anomalies
• Geoid Geodynamics

3
Definition
Science of the measurement and mapping of the
Earths Surface (Helmert, 1880) Includes the
determination of the Earths external gravity
field and its temporal variations. Includes also
the determination of ocean floor and other
celestial body gravity fields.
4
Reference Systems
Introduced by users to distinguish between
curvilinear surface coordinates for horizontal
positioning and heights above some zero-height
surface for vertical positioning.
5
Figure of the EarthFrom

• 800 B.C. Homers Iliad
• 600 B.C. Thales of Milet

A disc
to

• Pythagoras ( 580-500 B.C.)
• Aristotle ( 384-322 B.C.)

A sphere
6
Foundation of Geodesy

• Erathostenes of Cyrene
• 276 BC 194 BC
• 3rd Librarian of the Library at Alexandria
• First Earths circumference measurement (250,000
  stadia 40,000 km)
• Assumptions ?

7
XVII-XVIII centuries

• First triangulation Snellius (1580-1626)
• J.D. Cassini observed the flattening of Jupiters
  poles (1666)
• Picard measures Earths radius with 0,01
  accuracy (1669)
• Using pendulum Richter discovers the gravity
  difference between pole (Paris) and equator
  (Cayenne) (1672)

8
Figure of the Earth an oblate spheroid

• Newton (1643-1727) developed a physical model a
  Rotational ellipsoid (Flattening fa-b/a1/230)
• Intense dispute between the Cassinis (elongated
  Earth) and Newton resolved by Maupertuis geodetic
  measurements and Clairault synthesis (1743)
• Clairault Theorem compute flattening from gravity
  measurements at different latitudes

9
About an ellipse

• Latitude arc and Flattening measurements

10
XIXth Gravity Geoid

• Laplace (1802) notes that the ellipsoidal-earth
  assumption is not valid at high level of accuracy
• Gauss (1828) and Bessel (1837) clearly
  distinguish between the physical surface, the
  geoid and the ellipsoid of reference.
• Helmert (1880) establishes geodesy as a proper
  science.