W2. Go to the Astronomical Sizes program. If the Earth were the size of a marble, approximately how large would the Moon, Jupiter and the Sun be?
W3. Go to the Universe Timeline program. Compress the history of the Universe into one year. When in the year do the Sun and Earth form? How much time does the entire history of the human race occupy?
W4. Go to the
Inner Solar System Viewer.
a)
Kepler's Third Law: Look at Mercury, Venus, and Earth. Earth (the
blue dot) goes around the Sun in one year. Venus and the Earth start
out together near the right - about how many years does it take Venus
to lap the Earth? About how many times does Mercury lap Earth in one
year? How does this illustrate Kepler's third law? Hit "Reload" to
restart the simulation.
b) Kepler's First Law: Toggle
the asteroid orbit to a=1AU,e=0.0, and w=0 degrees. Now increase the
eccentricity (e) of the asteroid to 0.3 in increments of 0.05. What do
elliptical orbits with low eccentricity look like?
c)
Kepler's Second Law: Now toggle the asteroid orbit to
a=1AU,e=0.9,and w=40 degrees. Watch the asteroid for a full orbit;
where is it fastest? Draw a picture showing how this relates to
Kepler's second law. Finally, make a prediction for the period of the
asteroid's orbit using Kepler's third law. Now check your prediction
by waiting until the asteroid goes through its closest approach to the
Sun (its pericenter) and note Earth's position - where is Earth when
the asteroid returns to pericenter?
W5. a) Go to the Scientific Notation
program. Run it until you are sure that you can do this type of
problem in your sleep (or on an exam!). What happens when you get a
problem right?
b) Do the same with the Working with
Equations program. Who wrote this program? If you have trouble
doing either of these problems, be sure to talk to me or the grader
about it.
W6. Go to the Solar System Viewer
program. Explore the various options that the program has.
a) Toggle to the Asteroid Belt. Watch the purple
asteroids for a while, focusing on some individuals in the main
belt. What evidence do you see for elliptical orbits? Are Trojan
asteroids on elliptical orbits too? If the gravitational effects of
Jupiter were in this simulation, then the Trojan clouds should remain
tightly clustered. Do they? On the other hand, without Jupiter's
gravity, Trojan objects would pass Jupiter, or be passed by
it. Does this happen, and if so, when?
b) Toggle to Comets and watch them several times from 2000
through 2012. You can use the Reload button to start from 2000 again.
From your observations, how close can comets get to the Sun? Which
comets, between now and 2012, appear to get within 0.1 AU of the
Earth. Since the comet orbits are projected into the XY-plane,
they might actually pass far above or below the Earth. Finally, what
do you notice about the comet tails? Are these dust tails or gas tails?
W7. Go to the Rogue Star
program.
a) Although stars are so far apart that they
effectively never come with even tens of AU of one another, it is
interesting to see what would happen if they did.
a) Start with the default values and describe what happens to
each of the planets: orbit only slightly affected, orbits moderately
affected so that planetary orbits now cross, retrograde orbits,
capture by the rogue star or ejection from the system.
b) Now vary the distance of close approach from 2.6 to 0.0 in
steps of 0.2 (Use 0.01 instead of 0). Make a table of results
describing what happens to each planet for each encounter.
c) Discuss any patterns that you see in your data. When are
planets most strongly affected?
d) Explore different masses and geometries on your own!
W8. Go to Gravity
Comparisons.
This program lets you compare your weight on
different planets and satellite in the Solar System.
a) Use it to
determine on which planet the gravity is most similar to Earth's.
b) On which two terrestrial planets would your weight be most
similar?
c) Do these answers surprise you? Use the equation for
weight: W= m*g = G*M*m/(R*R) to solve for the relative masses of the
two planets in a). Here m is your mass, G is the Gravitational
constant, M is the planet's mass, and R is the planet's radius. Hint:
form a ratio of your weight on the two planets, and use find values
for the planet's radius from the table at the beginning of your
book.
d) Repeat for the planets in part b). Check your answers with
Planetary
Calculator.
W9. Go to the Solar System
Collisons program.
a) Start with a 1 cm rocky particle moving
at 20 km/s. Start making a table recording i) what happens, ii) how
often it happens, and any other details (energy released, crater
diameter) if appropriate. Now increase the size by 10 times and run
again. Continue to increase the impactor size until you reach 9999
km.
b) The energy contained in the motion of an object of mass m
moving at speed v is m*v*v/2. How well does this formula fit the
energy released by your impactors? (Use ratios as in problem W7).
c) How much does the impact rate decrease for each factor of 10
increase in impactor diameter? Can you find a simple function of
impactor diameter that fits the impact rate?
d) Try to find a simple function of impactor diameter to fit the
crater diameter.
e) Finally, play around with different impactor
sizes and densities, and different planets. Bring interesting patterns
that you notice and questions to class!
W10. Go to the Solar System
Collisons program.
a) The Hellas impact basin on Mars is 1800
km in diameter and about 6 km deep. Use the Collision Calculator with
v=20 km/s to work out how large the impactor must have been if it was
an asteroid (made of rock) or a comet (made of ice).
b) Try the same
rocky and icy impactors on the Earth and compare the crater diameter
and depth to the ones on Mars. Can you guess at the reason for the
differences? Explain your answer.
W11. Go to the Satellite
Viewer program.
a) Toggle through all of the planets to
familiarize yourself with the moons in our Solar System. Where are the
retrograde moons found? (retrogrades are the ones that go around
clockwise)
b) Toggle to Jupiter (Galilean Moons). Watch Io, Europa
and Ganymede for while - the three satellites whose orbital periods
are in a 1:2:4 ratio. Notice that they regularly fall on a straight
line passing through Jupiter. How often do these straight line
configurations occur (in Callisto orbital periods?). When they occur,
two satellite are on one side of Jupiter and one is on the other -
which moon is always alone?
c) Now toggle to Saturn (middle moons) -
which satellites share the same orbit (1:1 resonance)?
W12. Go to the Extrasolar
Planets program.
Toggle through all of the different multiple
planet systems. Describe several ways in which the systems differ from
our Solar System.
W13. Go to the Build Your Own Solar
System program.
a) Toggle the central star to a Blue
Supergiant, and build a four-planet system, choosing cool names,
different distances, eccentricities, and semimajor axes for each
planet. Your goal is to map out combinations of parameters that lead
to planets that could lead to the existence of life. Toggle your
middle two planets to eccentricities of 0.2, and map out the maximum
and minimum semimajor axis that leads to life being possible.
What did the authors of this program assume is necessary for the
existence of life?
W14. Go to the Extrasolar Planetary
Satellites program. In this problem you will explore satellite
stability around a strange extrasolar planet.
a) Accept the
defaults and submit the form and do the same for the Graphics Driver
screen that comes up next. What you are seeing is a satellite orbit
(in yellow) around a green planet that orbits extremely close to its
parent star (see W12). The orbit can never cross the blue curves, so
although this orbit may someday collide with the planet, it can never
escape. Now toggle back to the form and look at the Star and Planet
Information - the defaults correspond to 51 Pegasus, the first of the
"Hot Jupiters" that orbit extremely close to their parent stars. Go
down to Satellite Initial Conditions and vary the "Distance from the
planet" parameter from 1.5 to 2.5 in steps of 0.1. Make a table of
your the outcome of your investigations: (stable satellite orbit,
crash into planet, escape into space). When do the blue curves open up
to allow escape?
W15. Go to the Earth's Seasons
website.
Run the defaults for College Park (latitude 39
degrees). a) How many hours of sunlight do we get in mid summer? Mid
winter? b) How do these numbers change in Anchorage Alaska at latitude
60 degrees? c) What happens if you are on the equator? d) What is
special about the Arctic Circle and the Tropic of Cancer? d) Under
what conditions would Earth's Arctic Circle be south of its Tropic of
Cancer?