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Instructions
Cooperate with another observer to view the transit of Venus from two different latitudes on Earth.
Time the transit by measuring the position of Venus during the four phases, which are when the outline of Venus touches, then leaves the inner and outer edges of the Sun's outline. Both observers need to make the measurements using theodolites. Cover the theodolite lens with a sun shade to protect it from direct sunlight. The path will be different for each observer due to parallax.
Calculate the observed angle between the two paths at which the observers see Venus. Call this angle "E." This creates a triangle with two points on the Sun and one point at the midpoint between the two observers on Earth.
Divide the observed angle "E" by 0.72 to calculate angle "V." This represents the angle from Venus toward the two paths. The number 0.72 is from a calculation of Kepler's third law of planetary motion that gives the distance from the Sun to Venus being 0.72 times the distance from the Sun to Earth.
Calculate the distance between the two observers on Earth. The distance is measured through the Earth and not along its surface. Call this distance "D1."
Calculate the distance from Earth to Venus with the equation: D2 = D1 / tan(V).
Calculate the distance from Earth to the Sun with the equation: D3 = D2 / 0.28
"D2" is the distance from Earth to Venus. "D1" is the distance between the observers on Earth. "V" is the angle from Venus toward the two paths.
The number 0.28 is due to a calculation from Kepler's third law that gives the distance from Earth to Venus as 0.28 times the distance from Earth to the Sun. If you measured the angles and distances accurately the answer should be approximately 93,000,000 miles.