Name:
Date:
Exploring the physics of
planetary motion via
computer modeling
Scientists commonly use computer models
to observe systems that exist in scales too
big or small to observe directly. The scales
might be that of size or of time. In this
exercise you will use models to observe how
physics drives planetary motion. You will
manipulate variables and see how other
variables respond. Your tasks are to
explore the following:
1. Escape Velocity
2. Gravity Variations
3. Kepler’s 2nd Law
4. Orbital Velocity
5. Solar System Builder
Website: http://highered.mcgraw-hill.com/sites/0072482621/student_view0/interactives.html
Once you have your two assigned tasks, you will review the “Introduction” and “How To” tabs on the
website and answer the associated questions. You can add any additional observations below the
questions. As you develop any of your own questions while using the model, you are encouraged to
“play around” and try to answer your questions.
After completing your exploration of the interactive, you will state how Newton’s 3 Laws of Motion are
demonstrated by your planetary motion models.
Exercise Questions:
1. Escape Velocity
1) If you decrease the mass of the Earth, but leave the initial velocity alone, does the
maximum altitude of the ship increase or decrease? Can you explain why?
2) If you decrease the radius of the Earth, but leave the initial velocity alone, does the
maximum altitude of the ship increase or decrease? Explain why?
3) Use the “Earth button to reset the slider values. Watch the motion of the ship that is
fired horizontally. What happens to the shape of it orbit as you gradually increase its
initial speed from 7.9 km/sec? What happens to its orbit if you decrease it initial speed
from 7.9 km/sec?
4) Press the “Earth” button. fire the ships at a speed of 10.4 km/sec. What is the name for
the shape of the horizontally fired ship’s orbit?
5) Now increase the “Velocity” slider to a value of 13 km/sec and again fire the ships. How
is the shape of the horizontally fired ship’s orbit different? Is there a name for this
shape?
6) Which of the four planets has the smallest escape velocity? Which has the largest
escape velocity?
7) Is the escape velocity for a ship shot vertically upwards the same as the escape velocity
for a ship shot horizontally? Do the experiment to find out.
8) In order to double the escape velocity of a planet, by what factor must you change its
mass? Or, if you leave the mass alone, by what factor must you change its radius?
9) What is the escape velocity of the Earth’s moon?
10) Add extra observations you made will “playing around”:
11) Add questions that came to you while using this model:
12) How was Newton’s 1st Law of Motion demonstrated by this model?
13) How was Newton’s 2nd Law of Motion demonstrated by this model?
14) How was Newton’s 3rd Law of Motion demonstrated by this model?
2. Gravity Variations
1) Set the angle to 33 degrees, and leave it there for these exercises. On Earth, what
velocity yields a hit at this angle?
2) Switch to the Moon, but keep the velocity where it was in the previous question. What
happens when you fire the cannon now? Why?
3) What speed yields a hit on the Moon when the angle is 33 degrees?
4) The surface gravity on the Moon is about one-sixth that of the Earth. For a given angle,
is the ration of speeds required to hit the target also one-sixth?
5) What speed is required to hit the target on the Sun, at an angle of 33 degrees
6) Can you figure out the acceleration due to gravity at the photosphere of the Sun?
7) Which planet in the Solar System has the strongest surface gravity?
8) Which planet in the Solar System has the weakest surface gravity?
9) Add extra observations you made will “playing around”:
10) Add questions that came to you while using this model:
11) How was Newton’s 1st Law of Motion demonstrated by this model?
12) How was Newton’s 2nd Law of Motion demonstrated by this model?
13) How was Newton’s 3rd Law of Motion demonstrated by this model?
3. Kepler’s 2nd Law
1) Which planet has the most circular orbit? Which one has the least circular orbit?
2) Which of these planets could Kepler (and all the other ancient astronomers) actually
observe?
3) Set the eccentricity of the orbit to 0.4 and the time interval to 3, and let the planet run
for a complete cycle. What is the ratio of the largest distance between the Sun and
planet to the smallest distance between Sun and planet? (Perhaps it would help to use
a ruler to measure items on the screen)
4) You can estimate the speed of the planet in its orbit by measuring the width of the
rough triangle it sweeps out. Using the same settings *(eccentricity = 0.4, time step =
3), measure the ratio of the widest triangle to the narrowest t triangle. (Pause the action
and use a ruler to make these measurements)
5) Can you find a simple relationship between the distance between the planet and the
Sun, and the speed with which it moves?
6) How does your relationship compare to Kepler’s Second Law?
7) Add extra observations you made will “playing around”:
8) Add questions that came to you while using this model:
9) How was Newton’s 1st Law of Motion demonstrated by this model?
10) How was Newton’s 2nd Law of Motion demonstrated by this model?
11) How was Newton’s 3rd Law of Motion demonstrated by this model?
4. Orbital Velocity
1) According to this interactive, what is the Earth’s orbital velocity around the Sun?
2) Set the mass of the star to two solar masses. Does the Earth’s speed double?
3) How much more massive would the Sun have to be in order for the Earth’s orbital speed
to be double its actual value?
4) If you decrease the radius of the orbit, does the orbital speed increase or decrease? Can
you exp0leain why?
5) Set the orbital radius to 1 AU and star mass to 1 solar mass. Note the orbital speed.
Now, if you increase the orbital radius by 50 percent? If not, by what percent does it
change?
6) Reset the orbital radius to 1 AU and star mass to 1 solar mass, and again not the orbital
speed. Now if you increase the stellar mass by 50 percent (to 1.5 solar masses), does
the speed also change by 50 percent, if not, by what percent does it change?
7) Compare the effect on orbital velocity of changes in the stellar mass and changes in the
orbital size.
8) Vary the orbital radius over its entire range for one choice of stellar mass. Then change
the stellar mass, and vary radius again. Describe the shape of the points on the graph
corresponding to an single choice of mass.
9) Add extra observations you made will “playing around”:
10) Add questions that came to you while using this model:
11) How was Newton’s 1st Law of Motion demonstrated by this model?
12) How was Newton’s 2nd Law of Motion demonstrated by this model?
13) How was Newton’s 3rd Law of Motion demonstrated by this model?
5. Solar System Builder
1) Choose the preset for “Earth and Sun.” Place a Jupiter mass planet at position Y = 0 and
X = 5 AU (this is about the real position of Jupiter). On the line joining the Earth and this
Jupiter, place 5 more Jupiter sized masses and 5 Earth sized masses. Hit play and watch
the evolution. Use “Create planets by clicking once” so that yo planets will also start on
circular orbits. Describe the state of the planetary systems after 30 years. Repeat the
exercise three times. What do you find in common with each evolved planetary system?
2) Choose the preset for “Solar System.” Place two hot Jupiters inside Earth’s orbit of the
Sun. How might the presence of such enormous planet have affected Earth?
3) What would happen if the Earth’s orbit were changed from nearly circular to highly
elliptical? How would life on the planet be affected?
4) Scientists studying the evolution of planetary systems need to let their computer
simulation run for billions simulated years. Use your watch to determine how ling (in
seconds) it took your computer to simulate 10 years of evolution. How long would you
have to wait to get a billion years of evolution? Based on your results why do you think
they call the most advance machines “supercomputers”?
5) Add extra observations you made will “playing around”:
6) Add questions that came to you while using this model:
7) How was Newton’s 1st Law of Motion demonstrated by this model?
8) How was Newton’s 2nd Law of Motion demonstrated by this model?
9) How was Newton’s 3rd Law of Motion demonstrated by this model?