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Combination of the pictures from Germany and Namibia
v s�� � � � �
1E E
E v v
r r
s s sr r r
� � � �� �
�� � � � � � � � � �
„Shadow“ 2
„Shadow“ 1
Sun
Venus
Earth
Observer 1
Observer 2
���
v�
s�
s
rErE
rVrV
v
E
r
r
�
w
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: linear distance betweenthe observers
: relative radius of Venus‘ orbit
: angle of projection
: parallactic displacement
1
sin w sin w1 1E
s � V
rAU
r�
�� �� �
� � � � � �
�� ��
w
Observer 1
Observer 2
Venus
Here the parallactic displacement of Venus becomes visible by
combination of the above Germany and Namibia pictures
Usual explanation: Both „shadows“ have positions on the sun
with an angular difference of
The following relation can easily be shown:
��.
Because the relative distances of sun, Venus and earth are
known the following relation holds:
Internet Project
Observing, Photographing and Evaluating the
Transit of Venus, June 5/6th, 2012Coordinated by U. Backhaus, Dep. of Physics, University of Duisburg-Essen, Germany
http://www.venus2012.de
The passage looks slightly different when observed from dif-
ferent locations on earth. This so called parallax effect is due
to the distance between Venus and earth or, more precisely,
due to the different distances of the sun and Venus from the
earth. Therefore, measurements of the parallax effect allow
the derivation of the distance to the sun.
But the angular differences are smaller than the apparent
radius of Venus. They can be recognized only by exact
measurements and by combinating simultaneously taken
pictures. Therefore, as in 2004 an international cooperation
between schools, amateur astronomers and universities has
just started to prepare careful observations of the transit.
Determination of
* the geographical positions (latitude and longitude) of the
participants,
* the radius of the earth,
* the orbital radius of Venus (without using Kepler's third law!)
and
* the siderical period of Venus.
Projects for Preparation:
If the linear distance between the observers and the angle
of projection w are known, the distance r between the sun
and the earth can be calculated by the following relation:
�E
Some theory:
Daylight side of the earth when
Venus leaves the sun:
From this part of the world the
3rd and 4th contact can be
observed.
The main goals of the project are:
* to form new contacts between schools,
amateur astronomers and universities,
* to get acquainted with internet collaboration,
* to gather information due to transits of Venus
in history,
* to learn photographing the sun and determi-
ning the exact orientation of the pictures,
* to learn determining the exact position of an
object on the sun's disc,
* to learn the mathematical methods of evalu-
ating observations made from different loca-
tions and, finally,
* to get an impression and an own measure for
the distance to the sun.
Daylight side of the earth when
Venus enters the sun:
From this part of the world the
1rst and 2nd contact can be
observed.
Pictures simultaneously taken 2004 from Essen (U. Backhaus),
Germany (left), and Namibia (E. v. Grumbkow) (right)
On June 5/6th, 2012 Venus will pass the sun's disc - an
extremely rare event which happened already in 2004 but will
not rerun until 2117. Those so called Venus transits played an
important role for the determination of the distance between
the sun and the earth, the so called Astronomical Unit (AU).