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
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. These are the ONLY type of math problems that I will ask you to do on a test.
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
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
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
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
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 diamter and depth to the ones on Mars. Can you guess at the reason for the differences? Explain your answer.
W11. Go to the Satellite
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
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
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 prgram 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?
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