The ratio of the Sun - Venus distance to Sun - Earth distance . . . . tov

T r a n s i t o f Venus

Discover it . . . . . . . . . . . . .
8th June 2004, 6th June 2012

B.5 The ratio of the Sin - Venus distance to Sun - Earth distance

We assume that Venus and Earth both go around the Sun in circles with the Sun at center.

Venus moves in a circle around the Sun - the inner circle.
Earth also moves in a circle around the Sun - the outer circle.
The angle VES-Venus Earth Sun (V₁E₁S in Fig1) is what we observe. It is the angle made by Venus above the horizon as the Sun sets.
Note that this angle is maximum when EV is tangent to the circular orbit of Venus. At this juncture SV, is also at right angles to E₁V₁ because the radius of a circle is perpendicular to the tangent.
Since for Venus this maximum angle is approximately 45º,VES forms a right angled isoceles triangle with base angle 45º, therefore,
V₁S / E₁S = 1/ sqrt(2) =1/1.414 (why ?)
V₁S / E₁S = V₂S / E₂S since V₁S=V₂S and E₁S=E₂S
Therefore at the transit of Venus, when Venus is at V₂, and Earth is at E₂ then
V₂S / E₂S=1/1.414
Also E₂V₂ / E₂S = 0.414 /1.414 = 1 / 3.4
In other words, at Transit, Venus is 3.4 times larger to us the the Sun. It therefore appears 3.4 times larger than its real size relative to the Sun.( Fig.2 )