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Thursday, March 30, 2017
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Explaining Planetary Motion


Planets have been very much in the news lately, and not just those of our particular solar system.

NASA has announced the discovery of seven Earth-sized exoplanets, a planet that orbits a star other than the Sun, orbiting dwarf star named Trappist-1.

This discovery has created a great deal of excitement in the astronomy community because it seems to indicate that there could be a very large number of “habitable” planets in the Milky Way Galaxy.

It seems that humans have come a very long way in discovering and tracking things in the heavens, as it has only been a mere 400 years since Johannes Kepler postulated his laws of planetary motion. Kepler is also making a bit of a celebrity appearance of late as he was recently featured as the question for a Final Jeopardy answer during the same week as NASAs exoplanet announcement. So, it seems like it is time to visit or revisit, these laws of planetary motion, especially since Kepler was postulating them based upon observations in our little corner of the Universe.

Johannes Kepler was a brilliant mathematician that found himself caught up in the scientific debate of whether or not the Sun or the Earth was the center of the Universe. He supported Nicholas Copernicus’ heliocentric theory, that the planets orbited the Sun, based upon his analysis of the observations of the locations of the planets as they were tracked through the night sky. Through his mathematical analysis based upon the three postulates of motion, Kepler was able to mathematically predict the motions of the known planets at the time, and explain the odd motion of the planet Mars. With the advent of the telescope scientists like Galileo and Copernicus had been tracking and documenting the motions of the planets. But, Mars didn’t behave like Mercury or Venus. Mars at times appeared to move backward across the sky, what we now refer to as the Mars retrograde. (If you followed the motions of the planets last year, you might have observed this phenomenon. Mars appears to put a loop in its orbit as observed from the Earth. Why? Because the Earth’s orbit around the Sun is inside of the orbit of Mars, and thus due to relative motion, i.e. the Earth is moving at a different rate than Mars, there is an observed retrograde across our sky.)

The three postulates made by Kepler are very simple, 1) the orbits of the planets around the sun are elliptical with the Sun located at one focus of the ellipse (Law of Ellipses), 2) an imaginary line drawn from the center of the Sun to the center of the planet will sweep out an equal area of the ellipse in equal intervals of time (Law of Equal areas), and 3) the ratio of the square of the period of the transverse of the planet is equal to the cube or the average distance from the sun (Law of Harmonies). These three mathematical assumptions had significant ramifications throughout the scientific and mathematical worlds.

Using the observational data and these assumptions, Kepler was able to explain the motion of Mars, and subsequently the motion of later discovered planets.

Isaac Newton working with Kepler’s assumptions put forth mathematical derivations that led to the development of calculus as well as were critical in his presentations of his laws of motion, including the Universal Law of Gravitation. For history buffs, you can go online to the Cambridge Digital Library and see Newton’s calculations in the development of this “Prinicipia Mathematica,” where he provides a proof of Kepler’s Laws as a starting point for his discussions.

Kepler’s three postulates, now considered Laws, were very revolutionary. Yet, a mere 400 years later, they are being validated again and again in other star systems. The types of observations that were made which led to their development are still being conducted using more and more sophisticated telescopes and equipment. And, it seems keeps him very current.

Editor’s note: This is a series of science-related articles by author Frankie Wood-Black, Ph.D., REM, MBA, to appear in Mid-Week section of the Ponca City News. The author currently runs her own environmental consulting firm based in Ponca City, Sophic Pursuits, Inc., and also serves as a Physics Instructor and the Director for Process Technology at Northern Oklahoma College.

THE TRAPPIST-1 star, an ultra-cool dwarf, has seven Earth-size planets orbiting it. This exoplanet system is called TRAPPIST-1, named for The Transiting Planets and Planetesimals Small Telescope (TRAPPIST) in Chile.

THE TRAPPIST-1 star, an ultra-cool dwarf, has seven Earth-size planets orbiting it. This exoplanet system is called TRAPPIST-1, named for The Transiting Planets and Planetesimals Small Telescope (TRAPPIST) in Chile.

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