- Using the Starry Night software, switch off the daylight and set your latitude to 90o (North Pole). Center and lock on Jupiter and zoom in until the four Galilean moons (from close to far they are Io, Europa, Ganymeade, and Callisto). are plainly visible. Note the positions of the moons. Step forward in increments of 1 hour and calculate the periods of all four moons. Then, using Kepler’s third law, calculate the distances from Jupiter of Europa, Ganymeade, and Callisto in terms of Io’s distance. (For example Ganymeade is ___ Io distances from Jupiter). You do not need to know Jupiter’s mass or Io’s distance in km (or AU) to do this. All you need to assume is that the mass of the moons are small compared to the mass of Jupiter. Do your results agree roughly with what you see on Starry Night?
- A satellite is said to be in a "geosynchronous" orbit if it appears always to remain over the exact same spot on Earth.
a). What is the period of this orbit?
b). At what distance from the center of the Earth must such a satellite be placed into orbit? Express this distance as a fraction of the earth-moon (center to center) distance.
c). Explain why the orbit must be in the plane of the Earth’s equator.
Note: There is only one orbit which is geosynchronous. Often one will read an article in the news about how crowded this orbit has become. Almost all communications satellites are in this orbit.
- Suppose you have discovered an alien solar system in which a planet circles a star once every three years at an average distance of 9 AU. How does the mass of this star compare with that of our Sun? (Assume the planet’s mass is very small compared to the Sun’s).