Distance and Mass within the Solar system and beyond - an Historical summary.


The shape of the Earth.
Pythagoras (6th c  B.C.) was perhaps the first to guess the roundness of the Earth. 
It could be deduced from the observation of ships sailing over the horizon and Anaximenes 
(585BC) understood why the shadow of the Earth on the Moon during a Lunar eclipse was circular. 
 Also the elevation of the Pole Star increased when travelling north from the equator and 
was constant if traveling East to West. The Greek astronomer Eratosthenes (ca 250 BC) 
was able to deduce an approximate circumference from the length of shadows at places separated 
in latitude. At Syene the Sun was vertically overhead while at Alexandria it was 7deg from vertical.  
He expressed the diameter as 5000 Stade (1stade = 517ft). The diameter was also deduced by Poseidonius 
(135-50 BC) and Ptolemy (87 -165 AD)

The globe rotated.
The rotation of the Earth although assumed, was not proven until 1851 when the French physicist
Foucault perfomed an experiment with a pendulum in the Pantheon at Paris.  
This rotation is also measurable using an idea of Newton, who suggested that a weight dropped 
from a great height would fall east of the line of projection because the top of the tower would 
be moving faster. An experiment based on this principal was performed in a 500 ft mine shaft.  
An average deviation of 1 inch was in line with prediction. 

The accurate size of the Earth,
This was determined by triangulation of the surface. The Dutchman W. Snell [Snellius] (1591-1626) 
was a pioneer of this method.  A line between two points in the meridian great circle was measured 
by geodetic triangulation from a baseline of known length. The length of the baseline was found by 
very careful measurement. In 1671 Picard invented a wheel with a mechanical counter similar to a 
modern odometer.  Determining the latitude of the two points by astronomical observation and knowing 
their distance apart enabled the number of miles in 1 degree to be found, and hence the circumference 
and diameter.  One of the first determinations of  a “triaxial terrestial ellipsoid” was made by a 
Russian geodesist F. Schubert in 1859 (Ref-3).   Hayford in 1909 determined the shape to be an 
oblate spheroid  1/297. 

The Mass of the Earth
The Earth’s mass is measured by a comparison of the force between two known masses and those masses 
with the Earth.  The Earth is the only planet whose mass can be measured in a laboratory using Newton’s 
formula F=GM1M2/d2 .   The earliest estimate was the “Mountain method” where the deflection of a plumb 
bob was compared in the close vicinity of a mountain.  Maskelyne used the peak of Schiehallion in 
Scotland, but the first accurate determination was made by Henry Cavenish in 1797 using a gravity 
balance.  Von Jolly used the same method in 1881 and obtained 6 x10e24 Kg.

Distance and mass of the Moon
The average distance of the moon is found from triangulation using the Earth’s diameter as a baseline.




Further reading:
1) General Astronomy - H Spencer Jones (1951)
2) Introduction to Astronomy - C.Payne-Kaposchkin (1956)
3) Fundermental Constants of Astronomy  K.A.Kulikov - 1955 (translated 1964)