Planetary Orbits and Distance from Sun

Johannes Kepler (1571-1630) is credited with one of the giant strides toward the relativity theory produced by Isaac Newton in 1687 which describes motion in terms of forces. Kepler published two books on astronomy to describe his findings based on the observational data of Tycho Brahe; the first book was Astronomia Nova (The New Astronomy) published in 1609 and the second book was Harmonices Mundi (Harmony of the Worlds) published in 1619. In these works, Kepler put forth three ideas now regarded as Kepler's Laws. These laws are

1. the planets circulate around the sun in elliptical orbits with the sun at one focus.

2. the radius vector from the sun to a planet sweeps out equal areas in equal times.

3. the square of the time of one complete revolution of a planet about its orbit (the orbital period) is proportional to the cube of the distance from the planet to the sun.

In this project you are going to statistically verify Kepler's Third Law.

In the table below, orbital periods are given in Earth days and Earth years (which consists of 365 days) and the mean orbital distance is given in Astronomical units (AU).

One AU is the distance from the Earth to the Sun or 1.5 x 10⁸ km.

Planetary Orbits and Distance from Sun

Using this data and a statistical package or a graphing calculator, make a scatterplot with the orbital period in years as the independent variable and the cube of the distance as the dependent variable. Fit a line and a quadratic to this data set and discuss which equation best fits the data set.

Using the quadratic equation, predict Venus' distance from the Sun given that its orbital period is 225 days. If the orbital period of Jupiter is 11.9 years, what would be its predicted distance from the Sun? If the distance from Uranus to the Sun is 19.18 AU, what is the predicted orbital period? Discuss the reasonableness of your answers.

Related Links:

National Geographic's Virtual Solar System

The Electronic Universe Project