Keplers Second Law Interactive
Keplers Second Law Interactive

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. Now he found that indeed, the speeds of the planet changed in their orbits, as well as the planets closer to the Sun having to move faster, as Copernicus had already noted. It was the accurate observations of his mentor that were vital to this breakthough.

 1 Upon whose accurate observations of planetary motion did Johannes Kepler rely for developing his laws of planetary motion? Need a Hint? A) Nicholas Copernicus B) Tycho Brahe C) Galileo Galilei D) Isaac Newton

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.

 2 This planet at opposition in August 2003 was brighter than Jupiter, but when it comes to oppostion in November 2005, it will be considerably fainter. Tycho realized these varaitions must mean its orbit is not circular. Which planet is this? Need a Hint? A) Mercury B) Venus C) Mars D) Saturn

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.

 3 What do these elongations tell us about the size and shape of the orbits of these inferior planets? Need a Hint? A) Venus has a circular orbit of about .4 A.U., and Mercury's more elliptical orbit has a perihelion of .23 A.U., and an aphelion of .32 A.U. B) Venus has a circular orbit of .73 A.U. from the Sun, while Mercury's more eccentric orbit varies from a perihelion of .31 A.U. to an aphelion of .45 A.U. C) Venus has a circular object of .7 A.U., but Mercury has a perhelion of .44 A.U., and an aphelion of .32 A.U. D) Venus and Mercury both have circular orbits of .7 and .4 A.U., as Copernicus described in his heliocentric model.

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.

 4 The annelemma is a graph of the changes in the time of noon, by apparent solar time, as the sun changes its noon altitude by 47 degrees from winter to summer solstice. When would the Earth's speed be greatest, and the Sun appear to be most ahead of schedule? Need a Hint? A) Winter Solstice B) Perihelion C) Summer Solstice D) Vernal Equinox

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.

 5 Why was this anomaly noted for Mercury, and not any other planet? Need a Hint? A) Mercury's orbit is the most eccentric of the planets. B) Mercury's distance from the Sun is the least of any planet. C) Mercury's speed is greater than any other planet. D) Merury is hotter than any other planet.