Boris Pestoni, Vytenis ŠumskasUniversity of Zürich

AST 202 The Universe: Contents, Origin, Evolution and FutureMarch 8, 2016

� Historical approach� Methods � The actual shape of planet Earth

Contents

The earliest written mention of a spherical Earth

Pythagoras (~ 580 – 500 B.C.)

Aristotle agreed

Arguments:� Shadow is round during lunar eclipses;� Compression and convergence;� Travellers.

Aristotle (384 – 322 B.C.)

The first success!

Eratosthenes (276 – 195 B.C.)A prezi about his experiment:

https://prezi.com/d3kf13_gvvri/untitled-prezi/

Al Biruni (973 – 1048)� Biruni’s method: mountain of heigth H

Triangulation method

� If we know B1B2 and all the angles, wecan calculate A1A2.

Willebrord Snell(1580 – 1626)� Chain of 33 triangles

between two cities in the Netherlands

� Radius R = 6368,7 km

Giovanni Cassini (1625 – 1712)

� Two measurements, in north and southof France, using triangulation method: two different resultsÎ Earth is an ellipsoidand not a sphere

In which direction is the Earth flattened?� Cassini: from the

previously mentionedmeasurements, the ellipsoid is elongated in the polar regions

� Newton: as a results of the superposition of the gravitational and centrifugal forces, the ellipsoid is flattened in the polar regions.

Prolate or oblate ellipsoid?� Two expeditions, one in Peru and the

other in Lapland.� Purpose: measure the length of a

meridional degree. If the 1° meridionalarc in Lapland were shorter than that in Peru, Cassini would be right.

� Result: the meridional degree ofLapland was longer Î Newtonwas right.

Measurements of the new parameters� To measure: 1. equatorial radius a;2. polar radius b;3. flattening f = (a-b)/a or inverse

flattening I = 1/fTwo examples:

Reference ellipsoid name

a (m) b (m) I

Maupertuis (1738) 6397300 6363806,283 191IERS (2003) 6378136,6 6356751,9 298,25642

Carl Gauss (1777 – 1855)� The surface of the Earth does not have

a regular shape� Î Geoid

Limits of measurements, satellites� Molodenskii (1945): it is impossible to

determine the geoid only from measurementscarried from the surface of the Earth.

� Nowadays: satellites, GPS

Summary

Spherical Earth

Pythagoras and Aristotle: the shape of the Earth is a sphere

Eratosthenes: R = 5936 kmAl Biruni: R = 6356,7 km

Snell: R = 6368,7 km

Ellipsoidal Earth

Cassini: the shape of the Earth is an ellipsoidNewton: the ellipsoid is flattened in the polar regions

Maupertuis: a = 6397300 m, b = 6363806, 283 mIERS: a = 6378136,6 m, b = 6356751,9 m

Geodesic Earth Gauss: the shape of the Earth is a geoid that differsin different ways from the mathematical shape

Main reference: Oldrich Novotný, Motion, gravity field and figure of the Earth, Universidade federal da Bahia, Salvador de Bahia, 1998

Thank you for watching.

Questions?Have a nice day!