L_v = 123 mm (chord length in the photos)
D_s = 165 mm (diameter of the sun picture in the photos)
d_s=1,424_*10⁹m (sun diameter, determined from the Mercury transit in 2003)

The task corresponds to the determination of Venus diameter in the last chapter.
The covering distance of Venus in front of the sun appears to large and it must be transformed likewise (see fig. 25).

Further simplifications are done:
First I assume that the orbit of Venus coincides with the orbit of Earth. In addition the orbits are to be accepted as straight distances, which is permitted in the context of astronomical magnitudes (see error analysis ).

Fig. 25: Computation of the Venus orbit

The diagram considers that Earth and Venus both move. Since the Venus is closer to the sun, it must have a larger speed than the earth according to Kepler’s law.
During the transit time Δt = t₃ – t₁ = 20 618 seconds it moves the distance S_v, you have to determine. The earth moves during the same time the distance S_e only. Including the covering distance S_s you get a trapezoid. The quantity x is calculated from the length S_s – S_e using the theorem on intersecting lines (7):

or (8):


When you write Kepler’s law (5) by using covering distances Sv and S_e instead of speeds V_v and V_e, you get (9):

when you combine it with equation (8), then you find out (10):


with the unknown S_v as variable.

I examined this cube function using
curve sketching: You receive three solutions for S_v; a suggestive value is: S_v3 = 7,9337_*10⁸ m. If you divide S_v3 by the transit time Δt = t₁ – t₃, you receive the orbit speed of Venus: V_v = 38.48 km/seconds.
Assuming Earth orbit and Kepler’s second law (5), you can calculate Venus orbit:
R_v = 89.7 _* 10⁶ km.
Since the orbit of Venus is a good circle, you can determine the time of circulation to t_v = 2piR_v/V_v = 14,647,000 seconds or 169.5 days. With equation (4) you compute the diameter of Venus to D_v = 17,270 km.
In the following table my observed data are compared to literature values.

upper row: Observation
lower row: Literature values

In further conclusions you receive from equation (c2) (force equilibrium) the solar mass and with the well-known radius of Sun its volume and medium density. The following table shows data comparison:


upper row: Observation
lower row: Literature values

A view into the tables shows that the values represent good approximations.
I was surprised that I could determine so many astronomical parameters from these simple observations. In particular you can conclude from Suns density, that consists essentially of hydrogen and can contain small quantities of heavier elements only.
On the basis of an error analysis it shows up that astronomical data become fast inaccurate by small measuring errors and can only used as estimated values.
To determine exact astronomical values, is still a matter of art. Often you have to examine the data procedures for plausibility by a combination of different measurements. The "perfect" pictures published in the relevant literature, are attainable by using precise and extremely expensive equipment only. In contrast to this, it is the amazing that I succeeded to achieve that insight specified here.
Even with modest equipment you can find out a lot about our solar system.

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