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Johaness Kepler, using data on Mars acquired by Tycho Brahe, phenomenologically formulated three Laws of Planetary Motion that now bear his name. They are known as the First, Second and Third Laws of Planetary Motion. Isaac Newton would later derive Kepler's Laws from his more fundamental three Laws of Motion and his Law of Universal Gravitation.The First Law of Planetary Motion simply states that all planets orbit the Sun in elliptical orbits, with the Sun at one of the ellipse's foci. This law affirms the overall correctness of Copernicus' Heliocentric Model of the Solar System, but improves on it by making planetary orbits elliptical, not circular, as Copernicus suggested.The Second Law of Planetary Motion states that the line from the Sun to any planet "sweeps out equal areas in equal time" as the planet traverses its orbit. Since a planet traverses an elliptical orbit, when the planet is closer to the Sun, this law requires that it move faster. We see the Second Law of Planetary Motion in action in seasonal transitions. For example, the amount of daylight time added or subtracted per day around the Summer Solstice in the Northern Hemisphere is small compared to the amount of daylight time added around the Vernal Equinox Day, or subtracted around the Autumnal Equinox Day.The Third Law of Planetary Motion quantifies the relationship between how far away a planet is and how long it takes to orbit the Sun. This law states that the square of a planet's orbital period (its year) is proportional to the cube of its average distance to the Sun (the length of the semimajor axis of the planet's elliptical orbit).
The animation pictured on the left demonstrates Kepler's Second Law of Planetary Motion for the Earth and other Solar System objects orbiting the Sun.When you select an object and start the animation, it puts in the correct eccentricity of the planet's orbit, but you can change this. You can also change the time interval before a new sweep segment starts.Try running the animation for Earth without changing the default eccentricity and time interval. Observe that equal areas are swept out in equal times. Now change the eccentricity to a larger number (say 0.25) and press "Go" again. You will now see a dramatic speeding up of the earth as it passes near the Sun, a requirement if the Earth is to sweep out equal areas in equal times.Now try the animation for Jupiter, and pay attention to the eccentricity of Jupiter's orbit, and how long it takes for Jupiter to make one revolution around the Sun.
The next animation, pictured on the left, demonstrates Kepler's Third Law of Planetary Motion for the Earth and other Solar System objects orbiting the Sun.Run the animation for Venus, Earth, Mars and Jupiter, so that a data point is added to the graph in the lower left hand corner of the animation for each planet.Notice that the graph is linear for orbital period (p) squared plotted against average distance (a) cubed.The amazing thing about Kepler's Third Law is that it was known for a long time before it was calibrated. This law allowed astronomers to determine the average orbital radius of a particular planet in terms of the average orbital radius of Earth, the Astronomical Unit, but the value of the Astronomical Unit (AU) was not known!The first person to determine the AU was the astronomer Cassini. Later, the Astronomical Unit would be determined using the Transit of Venus.
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