Determining the Earth-Sun Distance Using Mars

Mercury, July/August 2003 Table of Contents

by William Sheehan

For more than a century, astronomers tried to measure the average Earth-Sun distance, known as the astronomical unit (AU), by observing rare transits of Venus. Unfortunately, the limbs of Venus and the Sun are not sharply defined. Because of atmospheric turbulence, the darkening of the Sun toward its limb, and optical constraints on resolution, the disks of Venus and the Sun blur together, which makes accurate transit timings impossible. Without this accuracy, astronomers cannot measure the AU to extremely high precision.

After being disappointed by results at the 1874 transit of Venus, David Gill turned to observations of Mars near opposition as a way of obtaining precise measurements of the AU. When observing Mars from opposite ends of Earth (one can do this effectively simply by observing Mars at sunrise and sunset), Mars’s position relative to the distant stars appears to shift. By measuring this displacement (parallax) and knowing the length of the baseline between the two observing sites, one can determine Mars’s distance. A value of the AU follows because Mars’s distance is related to Earth’s distance from the Sun by Kepler’s third law of planetary motion, which relates the planet’s distance from the Sun to its period of revolution.

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