Observing Venus - Calculation (by Edmund Halley)



    To find the distance between the Sun and the Earth or the Sun and Venus , astronomers used to observe the transit of planets in the Solar system. The triangular method was used for this - if observers at two different places determinate the times of the entrance and exit of Venus in or out of the Sun disc with help paralaxa they can determinate the Earth - Sun distance. The entrance of Venus to disc was at 7:19:57 p.m. and exit- at 13.22:53 p.m.(CET + 2 hours.)
    According to Halley, it is possible to measure AU in two ways: by observing the Venus transit from two places which find themselves on the same meridian (the same geographical latitude) or it can be calculated from two different places with different geographical lenghts but the result is more complicated.


Knowledges that you need to calculate the distance the Earth - Sun:

    The total of angles in a triangle must be 180 degrees.
    The Phytagoras proposition (a2 + b2 = c2)
    The definition of functin sinus
    TheThird Kepler's law ( Ta2 /Tb2 = ra3 /rb3)
    The definition of the Sun paralaxa




    In the picture we can see two obsevers who find themselves at two different places of the Earth. Both of them can see Venus on a straight line. These lines are parallel and have different angles. When they look at Venus they see its parallel.
Describing of the picture: A- the first observer's position, B- the second observer's position, A´-place where observer A sees Venus at the Sun disc, B´- place where observer B sees Venus at the Sun disc,Sz - centre of Earth, SS - centre of Sun,P - paralaxa, re - distance between the centre of Sun and the centre of the Earth, Rv - distance between the center of Venus and centre of the Sun.