Engineering Expert Witness Blog

      Last time we learned of Johannes Kepler’s Third Law of Planetary Motion and his development of the astronomical unit (AU) and how these contributed to bringing ancient scientists a step closer to calculating Earth’s distance to the sun.   Today we’ll see why Kepler’s focus on Venus, specifically its travel through space in relation to Earth and the sun — the so-called transit of Venus — would become the crucial element to solving the puzzle.

      Astronomers had previously used the Earth itself as an optical rangefinder to calculate distance to the moon.   But unlike the moon which is relatively close to Earth, the sun is many tens of millions of miles away, too distant to be used in that manner.   When it came to finding the distance from Earth to its sun, they were stumped.

      Then in 1716 Edmund Halley had the insight to combine Kepler’s Third Law and the parallax principle with Venus’ orbital journeys to devise an ingenious solution to the problem.   The transit of Venus, first predicted by Kepler in 1627, is a rare astronomical phenomenon which only occurs every 243 years.   At this time Venus becomes clearly visible from Earth and appears as a black dot traveling a straight path across the fiery backdrop of the sun’s surface.    Figure 1 shows this phenomenon as it would look from Earth.

Figure 1

      According to Halley’s plan, two observers with telescopes would be positioned on opposite sides of the Earth.   Due to the principle of parallax their lines of sight would provide different perspectives of Venus’ path.   See Figure 2.

Figure 2

      From the perspective of Observer B, Venus’s path would appear higher on the sun’s face than the path seen from the perspective of Observer A.    As their lines of sight converge on Venus’ center, an angle forms between them, which we’ll name α.   The same angle forms as they look past Venus to the sun in its backdrop.

      Halley theorized that if the angle α could be measured, Kepler’s Third Law could be used together with trigonometry to calculate the distance between Earth and the sun, Kepler’s so-called AU.    We’ll review Halley’s methodology next time.

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