Keplers Second Law Interactive (220.0K)
Johannes Kepler didn’t know why the planets behaved as they did, but he was a keen observer. In what became his 2nd law, he noted that planets move in a way that their orbits sweep out equal areas in equal time increments, even when those orbits are clearly elliptical. Use this Interactive to verify Kepler’s observation for yourself. Watch one of the planets or a comet move with the proper eccentricity in its orbit, or create a strange new orbit by moving the eccentricity slider. Make the time interval short or long. The graph will leave no doubt that the area swept out in each time interval always equals that of the one before.
Once Kepler abandoned the Copernican ideal of circular orbits, he also left behind the simplicity of uniform circular motion. Actually his mentor Tycho Brahe had already noted that one planet in particular varied greatly in its brightness and speed from oppostiion to opposition, suggesting that its orbit could not be a dependable, predictable circle.
Even naked eye observations show us that the speeds and eccentricities of the two inferior planets are strikingly different. Venus always comes to greatest elongation from the Sun at 47 degrees, but Mercury's greatest elongations vary from as little as 18 degrees to as much as 27 degrees from the Sun.
Even the speed of the Earth changes over to course of the year, as its distance from the Sun is greatest at apherlion in July, and least at perihelion in January.
Kepler's Laws and Newtonian gravity did not prove sufficient to explain the behavior of Mercury, for very accurate observations over the centuries found Mercury's orbit precessing faster than the physics of the nineteenth century could explain.