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KEPLER’S LAWS*
OBJECTIVE:
Students will use interactive web simulations to explore Kepler’s three laws of planetary
motion.
BACKGROUND
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!
SKILLS/COMPETENCIES:
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.
MATERIALS:
Computer with internet access and flash capability
Two pushpins
Thread or string
PRE-LAB
There is no formal pre-lab for this lab but your instructor may have special instructions
for you.
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LAB
TASK 1: BACKGROUND
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?
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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 1st Law:
Kepler’s 2nd Law:
Kepler’s 3rd Law:
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TASK 2: KEPLER’S FIRST LAW
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.
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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.
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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 1st 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?
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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 sun (the semi - major axis)
eccentricity of the orbit
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?
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TASK 3: KEPLER’S 2 ND LAW
Kepler’s 2nd 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 2nd Law:
First, click on the “Kepler’s 2nd Law” tab at the lower left of the Planetary Orbit
simulator.
Then, check the “sweep continuously” option
2. Select Mercury from the Orbit Settings pull-down menu and then click “start sweeping”.
Watch the simulation and explain what it is doing.
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3. Now select “Neptune” from the pull-down menu and describe how and why the sweeps
appear different from Mercury’s.
TASK 4: KEPLER’S 3 RD LAW
Kepler’s 3rd law is often confused with Kepler’s 2nd law. The 2nd Law describes the orbit of just
one plant while the 3rd 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 3rd 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?
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2. Use Kepler’s 3rd Law to find out the orbital period of Vesta, an asteroid orbiting our sun
with a semimajor axis of 2.36 AU.
TASK 5: PULLING IT ALL TOGETHER
1. How did Kepler’s three laws of planetary motion change human understanding of the
solar system? (Be specific and thorough.)
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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?
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