THE RELATIVE DISTANCES TO THE SUN FROM EARTH AND VENUS

by Knut Jørgen Røed Ødegaard

With the transit of Venus in 1769 the astronomers for the first time managed to measure the distance to the Sun fairly accurately. But the relative distances were already well known.

Nicholas Copernicus (1473-1543) understood that the planets, including the Earth are orbiting the Sun and that the Earth is not in the center of the Universe. In 1543 he published a describtion of the Solar system. It gave a determination of the mutual distances between the Earth and the Sun and Venus and the Sun.

This is how he calculated it:

Orbits of Earth and Venus. D is the center of Venus'orbit. C is the center of Earths orbit. At point F the "evening star" Venus is visible from Earth being in point B. At point E the "morning star" Venus is visible from Earth being in point A Illustration: astronomy.no

Copernicus used these, observed maximum angular distances between the Sun and Venus (numbers are from observations made in the antique!):

Angle DBF = 47.3 degrees, angle DAE = 44.8 degrees.
From here on we need the trigonometric sine function.
It follows that BD=DF/sin 47.3 and AD=DE/sin 44.8 where DE=DR=radius in Venus' orbit.
Radius of Earths orbit AC is one half of BD+AD.
This gives that AC/DE=1/2 [ (1/sin 47.3) + (1/sin 44.8) ]
And therefore DE/AC=0.7196 which is the value calculated by Copernicus as the relationship between the radies of the orbits of Venus and the Earth.

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