Download Solar System-3

Solar System-3-planets
ACTIVITY NAME
Solar System: Trial 2 (Our Solar System)
DESCRIPTION
In this activity students use a computer model to study the planets in our Solar System.
DISCOVERY QUESTION
How do the planets' orbits change with their distance from the Sun?
http://atropos.as.arizona.edu/aiz/teaching/a204/images/solar_system.gif
MATERIALS
NetLogo model:[ SolarSystem.nlogo add trace, remove some of his buttons
having to do with comets. Count earth years in tenths?]
SAFETY
There are no special safety concerns in this activity.
PROCEDURE
For more information on NetLogo, go to <a href="http://ccl.northwestern.edu/netlogo/"
target="new">the NetLogo Home Page</a>.
PREDICTION
How do the planets' orbits change with their distance from the Sun?
This activity will look at the inner six planets (including Earth), which were the ones that
were known by astronomers before the invention of telescopes. Each one has a different
size, color, composition, and distance from the Sun. List these six planets in order,
starting with the one closest to the Sun.
Each planet takes a different amount of time to go once around the Sun, called its period.
To your list, add your guess of the period for each planet, in terms of Earth days and
years. Don't do any research on this question right now. Just make an "educated guess".
Do you think the closer planets go around faster, or more slowly? Explain your
reasoning.
COLLECT DATA
Open the NetLogo model. It is set up with the six planets at their proper relative distances
from the Sun.
Measure the time for each orbit compared to one Earth year. For the close-in planets, use
the ZOOM slider to get a better look at them. Slow down the model (using the slider
above graphics window) and let them do one revolution and then stop the model. Then
observe what portion of a year the Earth has moved. For the farther-out planets, run the
model full speed and make them do one revolution and stop the model. Then read the
number of earth years in the monitor.
table:
Planet
orbit radius (avg)
actual orbit time
your measured orbit time
(AU)
(Earth years)
(Earth years)
Mercury
.38
.24 (88 days)
Venus
.72
.61 (224 days)
Earth
1
1
Mars
1.5
1.9
Jupiter
5.2
11.9
Saturn
9.5
29.5
Compare your measurements to the actual orbit times. How good were your
measurements?
Note: An Astronomical Unit (AU) is defined as the distance from the Earth to the Sun.
It's a convenient unit for measuring planetary distances in the Solar System.
ANALYSIS
Compare your measured orbit time to the astronomically measured one. How good is the
model? Did it give the correct orbit time?
Johannes Kepler proposed the following law, based on his observations of the planets:
(period in years) squared = (radius in AU) cubed
This is true for the Earth, since its period is 1 year and its radius (distance to the Sun) is 1
AU.
See if it is true for the other planets. Fill out the following table:
Planet
Mercury
Venus
Earth
Mars
Jupiter
Saturn
radius cube of radius
.38
.72
1
1.52
5.20
9.54
period square of period
.24
.61
1
1.88
11.86
29.46
How well does Kepler's law fit the data?
CONCLUSION
Johannes Kepler (1571 – 1630), a German astronomer and mathematician, proposed three
laws based on his and others' observations of planetary motion.
1. The planets travel in ellipses, with the Sun at one focus (see Solar System
Trial 2, Ellipses).
2. The planets don't move at constant speeds along these ellipses (see Solar
System Trial 2, Ellipses.)
3. The cube of each planet's radius is proportional to the square of its period.
You have observed this relationship in this activity.
Isaac Newton was able to demonstrate that a gravitational force between the Sun and the
planets would lead to these three laws. This was very strong evidence that the Sun, rather
than the Earth was the center of the Solar System. Up to that time, most observers and
philosophers believed that the Sun and all the planets went around the Earth and moved
in perfect circles.
FURTHER INVESTIGATIONS
Here's a real challenge. If you watch the graph in the model, you will notice that the
Earth-Sun distance changes with two different rhythms – a short cycle and a longer more
gradual cycle. See if you can figure out what each of these rhythms corresponds to and
what causes it. Here are some hints:
Compare the rhythm to the period of the earth's year.
Remember that other planets pull on the Earth just as the Sun does. So another
planet could cause the Earth to be pulled closer to and farther from the Sun. Can you
figure out which planet might do this? Does it match with the rhythm you observe in the
model?