Kepler and Mars--Understanding How Planets Move

Jun. 04, 2001

by Edna DeVore - Deputy CEO

Mars -- the Red Planet, the god of war, the home of life? Of all the planets in the solar system, Mars ranks first on a short list as a home for life beyond Earth, past or present, in the minds of scientists and science fiction writers alike. Today, we are a bit closer to a definitive answer than we were when ancient people looked up at the ruddy "star" glimmering in the evening sky and called it Mars.

The study of Mars led early astronomers to understand how the solar system works, and to develop a model that displaced Earth -- and humans -- from the center of the universe. They made one small step toward our current understanding of the universe.

Mars looks red when seen in the sky, and is especially prominent in the summer skies this year. Why? Every two years Earth, with its smaller orbit, catches up and passes by Mars as we both circle the Sun. When we pass by Mars and are between it and the Sun, astronomers call this an opposition.

On June 13, 2001 Mars will be opposite the Sun in the sky. Mars will rise over the eastern horizon opposite the sunset. A few days later, June 21, we will actually be a bit closer to Mars, the closest since 1988. The result is that Mars appears larger in diameter through telescopes -- it's closer so it looks bigger -- and appears brighter to the naked eye. The reason why Mars isn't closest at opposition, when we are passing it, is because we travel around the Sun in an elliptical orbit, and so does Mars. Indeed, Mars' motion is at the heart of how a mathematician, Johannes Kepler, discovered that the orbits of the planets are not circles, but ellipses, around the Sun.

Kepler lived about four centuries ago. He worked as a teacher and mathematician, along with his duties as court astrologer and astronomer. He had both the good fortune and misfortune to work for the last great astronomical observer of the pre-telescope age, Tycho Brahe. Brahe spent years measuring the position of astronomical objects, including Mars, with great care. His goal was to understand the motions of the planets. But Brahe, who lacked the mathematical skills to analyze all the data, hired Kepler.

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The relationship between the domineering, party-going astronomer Brahe and the shy, mystical mathematician Kepler was difficult. Brahe finally challenged Kepler to figure out the orbit of Mars, a problem Kepler wrestled with for nearly a decade. Brahe gave Kepler the data for Mars, including the measurements of Mars at successive oppositions over a period of many years. Mars' motion never quite fit that of a circular orbit, nor an orbit of multiple circles upon circles favored by Brahe and other contemporary astronomers. In desperation, Kepler fit the data to an ellipse -- and it worked.

Kepler's discovery was based on observational data. Basing his work on Copernicus' then-revolutionary theory that displaced Earth from the center of the solar system (and the universe, too), Kepler's calculations added mathematical credibility to Copernicus' idea that the Sun was actually at the center (actually, at one of the two foci of the ellipse) with Earth and the other planets revolving around it.

Kepler's discovery of elliptical orbits marks the beginning of modern, scientific astronomy. He based his explanations upon observations, rather than making the observations fit an assumed model of the universe. Prior to Kepler, planets were believed to orbit Earth in circular paths. The many variations of their motions were accommodated by adding more and more complex sets of circles upon circles in order to rationalize the observations. Although this worked moderately well, the future position of planets could only be roughly predicted.

Kepler changed all of that. Altogether, he discovered three relationships, now called "Kepler's laws" that describe the orbital motion of the planets.

Law of Ellipses (1609). The orbit of each planet is an ellipse, with the Sun located at one focus. Earth is closest to the Sun in January and farthest from the Sun in July as it travels along its elliptical orbit.
Law of Equal Areas (1609). A line drawn from the planet to the Sun sweeps out equal areas in equal times. This geometric description captures the fact that a planet's orbital velocity varies in a regular way -- the farther the planet is from the Sun, the more slowly it moves along its orbit. Earth moves fastest in January, and slowest in July.
Harmonic Law (1618). The square of the sidereal period of a planet is directly proportional to the cube of the semimajor axis of its orbit. In non-technical terms, planets move more slowly, and in a predictable way, the greater their distance from the Sun. Mercury speeds once around the Sun in just 88 days, Earth takes one year, Mars almost two years and distant Pluto almost 250 years. Kepler could not tell us why planets orbit as they do, but he could tell us how they orbited. He showed us what Brahe's observations of Mars revealed, but not the reason for this behavior. Only later, when Isaac Newton discovered that gravity keeps the planets in orbit about the Sun, did we understand why Kepler's laws describe how planets orbit. So when you go out and take a look at Mars this summer, remember the shy mathematician that turned the solar system inside out.

At NASA Ames Research Center, scientists Bill Borucki and David Koch lead a team that proposes to find Earth-sized planets around distant Sun-like stars -- good places for ET to live. The mission will observe these distant "Earths" as they orbit across the face of their "suns." The decrease in the star's light reveals the presence of the planet, which is called a transit. Once observed, the science team will use Kepler's laws to predict when these distant worlds will again transit their suns and confirm the discovery. These high-precision observations need to be made from space, and Borucki and Koch have named the satellite-observatory in honor of Kepler, the first astronomer to understand how planets orbit their stars.