Kepler’s Third Law relates the period of a planet’s orbit to its distance from the sun. In its original form, the law states that the square of the period P² is proportional to the cube of its distance from the Sun R³. This simple statement of the law holds to a reasonable degree of accuracy-at least in agreement with the observations available to Kepler - because the Sun is so much more massive than the planets, and because, except for Pluto, the orbits are nearly circular.

The applet below shows you the orbits of three of the planets.   You can step the model forwards and backwards in time, or run it forward as an animation, by pressing the top row of buttons.  The bottom row of buttons controls a timer which allows you to keep track of the amount of time passing in the model.

Take a look at the movement of VENUS and EARTH around the sun. Notice the relative motions of the two planets, and think about how our view of Venus changes as the two planets orbit at different speeds around the Sun.

SUPERIOR CONJUNCTION occurs when the Earth, Venus and the Sun are arranged in a line but Venus lies on the opposite side of the Sun from the Earth.

INFERIOR CONJUNCTION occurs when the Earth, Venus and the Sun are arranged in a line, but Venus lies between the Earth and the Sun.

Remember that Venus is an INFERIOR planet, because it orbits closer to the Sun than does the Earth.

The ELONGATION is the angle formed by the line from the Earth to the planet and the line from the Earth to the Sun. QUADRATURE occurs when the elongation is 90 degrees.

In order to verify Kepler's Third Law, you will measure the distances from the SUN to the two planets and time their orbital periods.

Record your measurements on the handout sheet.

Now let's take a look at the orbits of MARS and the EARTH.

Mars is a SUPERIOR planet because its orbit lies outside that of the Earth.

CONJUNCTION occurs only once in the orbit of a superior planet, when the planet lies along the same direction as the Sun (and behind the Sun).

OPPOSITION occurs when the direction to Mars is opposite that of the Sun as viewed from the Earth.

Again, verify Kepler's third law by making the distance and timing measurements, and record your results.

Next, take a look again at the orbit of MARS and the EARTH. Think about how different the motions would appear if you were an observer on the three objects: Sun, the Earth, Mars.

The SIDEREAL period of a planet is the time it takes the planet to make a complete revolution around the Sun from a particular point on the celestial sphere back to the same point again AS SEEN FROM THE SUN.

The SYNODIC period of a planet is the time it takes the planet to go from a given elongation back to the same elongation again AS VIEWED FROM THE EARTH.  Keep in mind that it is the difference between the longitude of the planet and the sun that matters, not the longitude of the planet itself.

You have already measured the SIDEREAL period for Mars.  Now measure and record the SYNODIC period.  You can switch to the Earth centered view by pressing the CENTER button, and selecting Earth.