Kepler's Third Law Interactive
Kepler's Third Law Interactive

Keplers Third Law Interactive (200.0K)

Johannes Kepler loved math, and was delighted to find that there was a "harmony of the spheres" between the period of revolution of a planet around the Sun in years, and its average distance from the Sun in astronomical units. He found the period of the planet's revolution around the Sun in years would be equal to the cube of its average distance from the Sun in astronomical units.

 1 Let us suppose we find an asteroid with a perihelion distance of 3 AU, and aphelion distance of 5 AU. Calculate its semimajor axis (average distance from the Sun) and use Kepler's Third Law to find its orbital period in years. Need a Hint? A) 4 years. B) 8 years. C) 16 years. D) 64 years.

Since Kepler's time, we have found many new bodies orbitting the Sun, most with more eccentric orbits than any studied by Kepler, but still the third law is invaluable. In January 2004, astronomers were surprised by the discovery of the first large body beyond the Kuiper Belt, perhaps an inner member of the Oort Cloud. It was named Sedna, after the Inuit goddess of the frozen arctic seas.

 2 Preliminary estimates place Sedna's perihelion distance as 75 AU, while its aphelion is an incredible 925 AU, or about 20X more distant than Pluto! About what is Sedna's orbital period in years? Need a Hint? A) 1,100 years B) 11,000 years C) 110,000 years D) 1,100,000 years

Newton would expand this far beyond the solar system; lets look at problems with practical applications of this Third Law, where the mass of the star is not equal to our Sun's. In fact, the ratio of distance cubed/period squared is equal to the mass of the star; as long as it has one solar mass, and the distance is in AU, and the period is in years.

 3 If the star was 4 times more massive than our own, what would be the period of a planet orbiting it at 1 A.U? Need a Hint? A) 1/2 year B) 1/4 year. C) 2 years. D) 4 years.

Johannes Kepler loved math, and was delighted to find that there was a "harmony of the spheres" between the period of revolution of a planet around the Sun in years, and its average distance from the Sun in astronomical units. Let's apply it to the planet closest to our Sun.

 4 Mercury's orbit carries it to a perihelion of .31 A.U., and an apphelion of .47 A.U. Use Kepler's third law to calculate how any DAYS it takes Mercury to whirl around the Sun. Need a Hint? A) 59 days B) 88 days C) 225 days D) 243 days

Johannes Kepler loved math, and was delighted to find that there was a "harmony of the spheres" between the period of revolution of a planet around the Sun in years, and its average distance from the Sun in astronomical units. In his time, Saturn was the most distant "test case" he had to work with.

 5 Saturn's period is 29.5 years; use that to find Saturn's average distance from the Sun in A.U. Need a Hint? A) 5 A.U. B) 7.8 A.U C) 9.5 A.U. D) 20 A.U.