The rules: Collaborative work is encouraged. This homework can be done in consultation with your fellow classmates, the AI, or the professor. However, everyone must submit their own solutions to get credit, and all help should be acknowledged (a single sentence mentioning the others in your study group is sufficient). Show your work.
1. Just the facts [5 pts]
(a) [3 pts] The Space Shuttle and other spacecraft orbit Earth well within the Earth's Roche limit. Explain why these spacecraft are not torn apart by tidal forces.
(b) [2 pts] Many of the gases in the atmosphere of Titan, such as methane, ethane, and acetylene, are highly flammable. Why, then, doesn't Titan's atmosphere catch fire?
2. Goodnight Moon [10 pts]
(a) [5 pts] Assuming material is ejected from Io into Jupiter's magnetosphere at the rate of 1000 kg/s, how long will it be before Io loses 10% of its mass? How does your answer compare with the age of the solar system?
(b) [5 pts] At what distance would a satellite orbit Jupiter in the time taken for Jupiter to rotate once, so that the satellite would appear stationary above the planet?
3. Superior Observing Conditions [35 pts]
(a) [6 pts] While most solar system missions operate by uploading a series of commands to the spacecraft/vehicle, you can imaging trying to drive one of the Martian Rovers - Spirit or Opportunity - in "real time." Approximately how long will it take for you to see the effect of your uploaded command if Mars is located at opposition? What if Mars is at conjunction?
(b) [8 pts] The angular diameter of Jupiter at opposition varies little from one opposition to the next. By contrast, the angular diameter of Mars at opposition is quite variable. Provide a quantitative analysis to explain why there is a difference between these two planets.
(c) [3 pts] Uranus's epsilon ring has a radius of 5.115 x 104 km. How long does it take a particle in the epsilon ring to make one complete orbit of Uranus?
(d) [6 pts] Jupiter's Great Red Spot rotates in 6 days and has a circumference equivalent to a circle with radius of 10000 km. Neptune's Great Dark Spot is one-quarter as large and rotates in 17 days. For each, calculate the wind speeds at the outer edges of the spots. How do these compare with the winds in terrestrial hurricanes?
(e) [6 pts] What is the gravitational force exerted on Uranus by Neptune at closest approach? Compare your answer with the Sun's gravitational force on Uranus.
(f) [6 pts] Neptune's apparent motion relative to the stars is actually due mainly to Earth's orbital motion. Given this fact, estimate the angle through which Neptune moves over the course of a week around the time of opposition.