LAB 06 - KEPLER'S 3RD LAW

KEPLER'S 3RD LAW

In this activity, you will use Kepler's 3rd law of planetary motion to determine either the average distance from the sun or the orbital period for an imaginary planet.    Johannes Kepler used the decades long observations obtained by Tycho Brahe of the motion of Mars across the sky to deduce the underlying principles that governed its motions and explained when why the red planet went into retrograde roughly every two years.   Although Kepler was not aware, his three laws of planetary motions revealed important aspect regarding the effects that the force of gravity has on planets orbiting the sun (or any two objects orbiting each other in space).   

Kepler's first law of motion was simply that the planet's orbit was shaped like an ellipse with one the sun at one of the focal points.  This flew in the face of both Ptolemy's model and the heliocentric model proposed by Copernicus which had the planet's following perfectly circular orbits.   Tycho's positional data simply did not fit a circular orbit, but they did fit an elliptical one as Kepler found out after trying numerous other shapes first for months! 

His second law is a definite reflection of the force of gravity at work as a planet goes around the sun.   Imagine a string stretched perfectly straight connecting the planet and the sun.  As the planet moves through its orbit, the spring "sweeps" over a region of space like the hands moving around the face of an old clock.  It turns out that, as the planet moves around its orbit, it moves fastest when it is close to the Sun and slowest when it is further away.  Kepler's noticed this and stated his second law as the planet sweeps our equals areas in equal times as it moves in its orbit about the sun. 

Kepler's third law is based on a trend that he notice when he compared the average distance between planet and sun and the time it takes (called period) for the planet to complete one orbit.   It turned out that, if you squared the period it would roughly equal the cube of the average distance.   Kepler's third law of planetary motion in formula form is as follows:

Where is P is the period in Earth's years and a is the average distance between sun and planet in astronomical units.   

In this week's lab, you are going to put Kepler's 3rd law formula to work on some imaginary planetary data as follows:

• • If you are given the period of the planet, then calculate the average distance.
  • If you are given the average distance, the determine the planet's period.

The following video demonstrates the math you need to do in this lab using the online Desmos Scientific Calculator. 

In the following video, the math is demonstrated using a standard scientific calculator app.

These are the examples explored in the above videos.  They represent the two scenarios you will encounter on in the questions.