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Kepler & Mars

Since antiquity and probably way before, people were acutely aware of the planet Mars' temperamental disposition. The angry god's mood swings were predictable to a great extent, even if the underlying reasons for them defied understanding.

People observed that Mars generally traveled eastward through the constellations of the zodiac -- except every couple of years, when the red planet unexplainably reversed course, going westward (retrograde) for a few months. When in retrograde (which this year is from July 30 till September 29), the brightness of Mars was seen to increase by leaps and bounds. In the middle of a retrograde, it always exhibited its greatest brilliance, easily outshining every star of the night sky.

In the sixteenth century, Copernicus suggested that Mars' pecularities could be explained by assuming that the planets (including Earth) revolve around the Sun -- instead of the planets and the Sun revolving around the Earth. During a retrograde, he reasoned, the faster planet Earth passes the slower-moving Mars, much like a race car driver on the inside track bypassing one on the outside. With Mars being relatively nearby at this time, this accounts for both Mars' increased brightness and its apparent backward motion.

Though Copernicus offered a partial solution to Mars' puzzling behavior, it took a Johannes Kepler to discern the riddle of planetary motion. Copernicus knew the more distant a planet, the slower it moves in its orbit. But it was Kepler who figured out the correlation between a planet's distance and its orbital period, all wrapped up in this simple equation: d3 = t2. In this equation, d = distance of the planet from the Sun, and t = the time it takes the planet to orbit the Sun.

Let's figure out the orbital period of Mars with Kepler's equation. Mars resides 1.524 times further away from the Sun than our planet Earth. This is all we need to know to compute the time for Mars to orbit the Sun:

d3 = t2
(1.524)3 = t2
(1.524 x 1.524 x 1.524) = t2
3.54 = t2
1.88 = t = Mars orbital period in Earth years
With about 365.25 days making up Earth's orbital period, we figure the number of Earth days in a martian year:
1.88 x 365.25 days = t
687 days = t = the number of Earth days in Mars orbital period

The End

by Bruce McClure

Do you like math? Click to find out how Copernicus and Kepler computed distances to Mars and the other planets.

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