TRANSIT OF VENUS 2012
Dr. S. S. R. Perumal
Joint Director, B. M. Birla Planetarium
Tamilnadu Science and Technology Centre
Chennai 600025
 1631,1639
1761,1769 1874,1882
 2004,2012, 2117…
 By
using the geometry of the transit, we
can deduce the solar parallax, s, as
s = Re(re/rv - 1) /d

where, Re is the radius of Earth, re is the radius of the orbit of
Earth and rv is the radius of the orbit of Venus,  is the
parallax shift to be measured on transit day and d is the
vertical distance between the two observing sites. In the
above expression, we find that the basic requirements for
finding the Astronomical Unit are 1. the radius of the Earth
(Re), 2. the ratio of the sizes of the orbits of the Earth and the
Venus (re/rv) and 3. the parallax shift  at the distance of d.
http://www.eso.org/public/outreach/eduoff/vt-2004/Education/EduSheet3.html
β s = Δβ ((r e / r v ) - 1)
where  is the parallactic shift that will have to be measured on the
Transit day. Since re/rv is known s can be calculated.
s
/s
s
If re/rv is known s can be calculated. The distance re to
the sun from the earth = d/s where d is the distance
between the observers
Parallax s of the sun is defined as the angle subtended
by the earth’s radius at the sun
s= Res/d
s = Re (re/rv - 1)  /d
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Distance between observers at places A and B
The distance AB can be deduced from the latitudes of the
two observing places. In the diagram, φ 1 and φ 2 are the
latitudes of A and B, and R is the radius of the Earth.
In the right angled triangle that divides the isosceles
triangle RAB
sin ((φ 1 + φ 2 ) / 2) = (AB / 2) / R
 Then the distance AB is
AB = 2 R sin ((φ 1 + φ 2 ) / 2)
If both cities are in the same hemisphere, the angle is
(φ 1 - φ 2 ) / 2 and also the geometrical situation changes if
the cities are on different longitudes.
s = Re(re/rv - 1) /d
Thus to determine s need the following
1. Radius of the earth
2. Ratio of the radii of the orbits of
the earth and Venus.
3. Parallax of Venus on the Transit
day
d is north south distance
 Elongation
of Venus = angle between
direction of sun and direction of Venus = angle
VES. This is the angle needed
 School
Address
 Team Member1
Member 2
 Latitude
Longitude Date
 Alt 1 Alt 2 Ave Time Az I Az 2 Ave
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2
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