page 45
Students will use interactive web simulations to explore Kepler’s three laws of planetary motion.
Johannes Kepler was a German mathematician and astronomer who worked with the famous observed Tycho Brahe. Using observations of planetary motion, particularly the motion of Mars, Kepler developed three simple laws which describe motion of planets not only in our solar system but in planetary systems all over the universe!
Define each of the related vocabulary words.
Recognize the appropriate symbols used.
State the concepts introduced.
Distinguish between different concepts within a topic.
Interpret tables or graphs.
Evaluate the relevancy of data.
Set up and solve problems using geometry, algebra, and trigonometry as required.
Apply concepts to new situations.
Demonstrate the ability to select and apply contemporary forms of technology to solve problems or compile information.
Computer with internet access and flash capability
Two pushpins
Thread or string
There is no formal pre-lab for this lab but your instructor may have special instructions for you.
Kepler’s Laws Lab 13 pages

page 46
Before Kepler, many astronomers were working with the Copernican model of the solar system. Please explain the Copernican model by answering the following questions:
1. What did the Copernican solar system look like (you may draw a simple sketch along with your written answer)?
2. In the Copernican solar system, what were the shapes of the planets’ orbits?
3. In the Copernican solar system, what caused the observed retrograde motion of
Mars and the other planets?
Kepler’s Laws Lab 13 pages

page 47
4. Why did astronomers suspect the Copernican model was either incorrect or incomplete?
At the time that Kepler lived and worked, there was no distinction between astronomy and astrology and society often accepted supernatural explanations for phenomena without searching for natural laws to explain observations. For example, many scientists at the time (called natural philosophers then) believed that the planets moved around the sun because of angels pushing them. Kepler’s three simple laws were revolutionary not only because they accurately described the motion of planets in our solar system but also because they gave a simple mathematical description to the motion. Please state each of Kepler’s three laws in your own words:
Kepler’s 1 st
Law:
Kepler’s 2 nd
Law:
Kepler’s 3 rd
Law:
Kepler’s Laws Lab 13 pages

page 48
Kepler’s first law describes the shape of a planet’s orbit. Let’s start by making sure you know what an ellipse is! This section of the lab will be using the Planetary Orbit
Simulator at: http:// astro.unl.edu/naap/pos/animations/kepler.html
1. For the ellipse below, please label the approximate location of the: foci, semi-major axis and semi-minor axis.
Kepler’s Laws Lab 13 pages

page 49
2. Using the graphs below, pushpins and string or thread, make an ellipse on each chart with a semimajor axis of 10 graph units. Use the black dots on the charts as foci.
Kepler’s Laws Lab 13 pages

page 50
Kepler’s Laws Lab 13 pages

page 51
Kepler’s Laws Lab 13 pages

page 52
3. Use the Planetary Orbit Simulator to find the semimajor axis and eccentricity for all eight of the planets in our solar system and Pluto. Click on the “Kepler’s 1 st Law” tab at the lower left of the screen and check the “show center” box to see how the position of the sun is offset from the center of an ellipse. (You may click on or off any of the other features – feel free to explore and experiment!)
Planet Name Semimajor Axis (in AU) Eccentricity
4. Which planet in our solar system has the most eccentric orbit?
5. Which planets in our solar system have the least and second least eccentric orbits?
6. Now experiment with the eccentricity slider bar to find what eccentricity puts the sun exactly at the center of the planet’s orbit. What is the eccentricity and what is the name of the shape of this special ellipse?
Kepler’s Laws Lab 13 pages

page 53
7. There are a couple of special points along a planet’s orbit that you need to know about.
Look up the definitions of these two special locations and write your own version
(paraphrased) here:
Perihelion:
Aphelion:
8. The equation for the distance from the sun at perihelion is:
Perihelion a ( 1 ) .
The equations for the distance from the sun at aphelion is:
Aphelion a ( 1 ).
a average distance from the eccentrici ty of the orbit sun (the semi major axis)
Use these equations to calculate how much further the Earth is from the sun at aphelion compared to perihelion.
9. What percentage of the Earth’s average distance from the sun is the difference from perihelion to aphelion?
Kepler’s Laws Lab 13 pages

page 54
ND
Kepler’s 2 nd
law is about how the speed of a planet changes as its distance from the sun changes.
1. Calculate Earth’s average orbital speed in kilometers per hour and in miles per hour. To make this calculation a bit easier, simplify Earth’s orbit to a perfect circle with a radius of one AU.
Now you’re ready to observe a simulation showing Kepler’s 2 nd
Law:
First, click on the “Kepler’s 2 nd Law” tab at the lower left of the Planetary Orbit simulator.
Then, check the “sweep continuously” option
2. Select Mercury from the Orbit Settings pulldown menu and then click “start sweeping”.
Watch the simulation and explain what it is doing.
Kepler’s Laws Lab 13 pages

page 55
3. Now select “Neptune” from the pull-down menu and describe how and why the sweeps appear different from Mercury’s.
RD
Kepler’s 3 rd law is often confused with Kepler’s 2 nd
law. The 2 nd
Law describes the orbit of just one plant while the 3 rd
law compares the orbits of different planets and gives a simple and useful mathematical relationship between orbital period and orbital distance for our solar system.
1. Math is not just for calculating numbers, math is also a way of communicating how properties and quantities are related. See for yourself by answering these questions:
According to Kepler’s 3 rd Law, how would a planet’s orbital period change if the planet’s… a. eccentricity doubled? b. mass halved? c. distance from the sun quadrupled?
Kepler’s Laws Lab 13 pages

page 56
2. Use Ke pler’s 3 rd
Law to find out the orbital period of Vesta, an asteroid orbiting our sun with a semimajor axis of 2.36 AU.
1. How did Kepler’s three laws of planetary motion change human understanding of the solar system? (Be specific and thorough.)
Kepler’s Laws Lab 13 pages

page 57
2. Which of Kepler’s laws explains why more distant planets orbit more slowly than plants closer to the sun?
3. Which of Kepler’s laws explains that planets move faster when they are at perihelion than when they are at aphelion?
4. Which of Kepler’s laws describes the shape of orbits?
Kepler’s Laws Lab 13 pages